02-RQs.Rmd

# (PART) Asking research questions {-}


# Research questions {#RQs}


<!-- Introductions; easier to separate by format -->
```{r, child = if (knitr::is_html_output()) {'./introductions/02-RQs-HTML.Rmd'} else {'./introductions/02-RQs-LaTeX.Rmd'}}
```


## Introduction {#Chap2-Intro}

Asking clear and answerable *research questions* (RQs) is important, as the RQ impacts all other components of the research.
Since quantitative research summarises and analyses the data using numerical methods (such as averages or percentages), the RQ must be appropriate for analysis using quantitative methods.


Studies often have an overall, broad research goal with many sub-questions (which may be quantitative or qualitative).


::: {.example #RQs name="Research questions"}
Consider this broad research goal:

> How well are permeable pavements (PPs) working in urban areas?

This goal has many component RQs (Fig.\ \@ref(fig:PermPavements)), and each can be answered separately.
:::

```{r PermPavements, fig.cap="A study of permeable pavements (PPs) may have many sub-questions", fig.align="center", fig.height=1.75, fig.width=7, out.width = '80%'}
par( mar = c(0.10, 0.15, 0.10, 0.15))
openplotmat()

pos <- array(NA, 
             dim = c(4, 2))
pos[1, ] <- c(0.50, 0.175) # RQ
pos[2, ] <- c(0.15, 0.40) # sub1
pos[3, ] <- c(0.85, 0.40) # sub2
pos[4, ] <- c(0.50, 0.825) # sub3


straightarrow(from = pos[1, ], 
              to = pos[2, ], 
              lty = 1, 
              lwd = 2)
straightarrow(from = pos[1, ], 
              to = pos[3, ], 
              lty = 1)
straightarrow(from = pos[1, ], 
              to = pos[4, ], 
              lty = 1)

textrect( pos[1, ], 
           lab = "Are PPs effective\nin urban areas?", 
           radx = 0.13, 
           rady = 0.20, 
           shadow.size = 0,
           box.col = ResponseColour,
           lcol = ResponseColour)
textrect( pos[2, ], 
           lab = "What is the\ncost of using PPs?", 
           radx = 0.16,
           rady = 0.18, 
           shadow.size = 0,
           box.col = GroupColour,
           lcol = GroupColour)
textrect( pos[3, ], 
           lab = "Do PPs improve\nrun-off quality?", 
           radx = 0.16, 
           rady = 0.18, 
           shadow.size = 0,
           box.col = GroupColour,
           lcol = GroupColour)
textrect( pos[4, ], 
           lab = "How do people perceive\nPP aesthetics?", 
           radx = 0.16, 
           rady = 0.18, 
           shadow.size = 0,
           box.col = GroupColour,
           lcol = GroupColour)
```





## Elements of RQs

A RQ must be *written* carefully so they can be *answered* effectively.
This section introduces the four potential components of a quantitative RQ:

* The **P**opulation (Sect.\ \@ref(Population));
* The **O**utcome (Sect.\ \@ref(Outcome)); 
* The **C**omparison or **C**onnection (Sect. \@ref(Comparison));
* The **I**ntervention (Sect.\ \@ref(Intervention)).

These form the **POCI** acronym (sometimes seen as the PICO acronym).



### The population {#Population}

All quantitative RQs study a *population*: a (usually large) group of interest in the study.
Populations comprise *individuals*, sometimes called *cases*.
If the individuals are people, they are sometimes called *subjects*. 


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Pics/iconmonstr-friend-5-240.png" width="50px"/>
</div>


::: {.definition #Population name="Population"}
The *population* is the group of *individuals* from which the total set of observations of interest *could* be made, and to which the results will (hopefully) generalise.
:::


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
To fully understand *individuals*, you should also read about **units of analysis and units of observation** (Sect.\ \@ref(UnitsObsAnalysis)).
The *individuals* are the *units of analysis*.
:::


The population is *any* group of individuals of interest; for example:

* all German males between 18 and 35 years of age.
* all bamboo flooring materials manufactured in China.
* all elderly females with glaucoma in Canada.
* all *Pinguicula grandiflora* growing in Europe.


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
The words *population*, *individuals* and *cases* do **not** just refer to people, though they may be commonly used that way in general conversation.
:::


The *population* is rarely the individuals from which the data are actually *obtained*: *all* elements of the population are rarely accessible in practice.
For example, testing a new drug cannot possibly study *all* people (especially people not yet born who might use the drug). 
The population is 'all people', *not* just those studied.


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
The **population** in a RQ is *not* just those studied; it is the whole group to which our results would generalise.
:::


In contrast, a *sample* is the *subset* of the population from which data are obtained (Chap.\ \@ref(Sampling)).


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-sitemap-20-240.png" width="50px"/>
</div>


::: {.definition #Sample name="Sample"}
A *sample* is a subset of the population from which data are collected.
:::



::: {.example #Samples name="Samples"}
Consider a study of American college women [@data:woolf:ironstatus], which aimed to (p. 52):

> ...assess iron status [...] in highly active (>12 hr purposeful physical activity per week) and sedentary (<2 hr purposeful physical activity per week) women...

The *sample* comprises 28 'active' and 28 'sedentary' American college women, from which data are collected.
The *population* is *all* 'active and sedentary' American college women, not just the 56 in the study.
The group of 56 subjects is the *sample*.
:::


Completely and precisely defining the population sometimes requires *refining* or *clarifying* the population, using *exclusion* and/or *inclusion criteria*.
Exclusion and inclusion criteria clarify which individuals may be explicitly included or excluded from the population.

Exclusion and inclusion criteria should be explained when their purpose is not obvious.
Both exclusion and inclusion criteria are not *necessary*; none, one or both may be used.


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-checkbox-4-240.png" width="50px"/>
</div>


::: {.definition #InclusionExclusionCriteria name="Inclusion and exclusion criteria"}
*Inclusion criteria* are characteristics that individuals must meet explicitly to be included in the study.

*Exclusion criteria* are characteristics that explicitly disqualify potential individuals from being included in the study.
:::


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-checkbox-14-240.png" width="50px"/>
</div>

::: {.example #ExclusionCriteriaEG name="Inclusion and exclusion criteria"}
A study of a certain bird species may only include sites where with a confirmed sighting within the last two years.

Concrete test cylinders with fissure cracks may be explicitly excluded from tests of concrete strength.

People with severe asthma may be explicitly excluded from exercise studies.
:::


:::{.exampleExtra  data-latex=""}
A study on the influenza vaccine [@kheok2008efficacy] listed the **P**opulation as 'health-care workers' [@kheok2008efficacy, p. 466], and the sample comprised healthcare workers at two specific hospitals.
The population was refined using exclusion criteria: those
  
> ...declining to give consent, a history of egg protein allergy, and neurological or immunological conditions that are contraindications to the influenza vaccine.
>
> --- @kheok2008efficacy, p. 466
:::


::: {.example #ExclusionAmoutees name="Inclusion and exclusion criteria"}
A study [@data:Guirao2017:amputees] of the walking abilities of amputees used inclusion *and* exclusion criteria. 
Inclusion criteria included (p. 27):

> ... length of the femur of the amputated limb of at least 15cm measured from the greater trochanter; use of the prosthesis for at least 12 months prior to enrollment and more than 6 h/day...

Exclusion criteria included (p. 27):

> ... the presence of cognitive impairment hindering the ability to follow instructions and/or perform the tests; body weight over 100kg...
:::


### Units of observation and analysis {#UnitsObsAnalysis}

*Units of observation* and *units of analysis* are important, but similar, concepts that need to be distinguished to properly identify a population.

Consider this RQ (based on @vaughn2009comparison):

> In Australian 20-something men, is the average thickness of head hair strands the same for
`r if (knitr::is_latex_output()) {
   'blond-haired men'
} else {
   '[blond-haired men](https://www.dictionary.com/browse/blonde)'
}`
and
`r if (knitr::is_latex_output()) {
   'brunet-haired men?'
} else {
   '[brunet-haired men](https://www.dictionary.com/browse/brunet?s=t)?'
}`


Comparing 100 hair strands from one blond-haired man, to 100 hair strands from one brunet-haired man, is problematic since *only one man of each hair colour is represented*.
While there are 200 observations, only two people are compared; little is learnt about 20-something men *in general*.
Instead, a lot is learnt about two specific men.
The population is represented by just two men.


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/pexels-moose-photos-1036627.jpg" width="200px"/>
</div>


In this study, each individual hair is a *unit of observation*: the hair strands are what must be measured to obtain 'thickness of head hair strands'.


::: {.definition #UnitOfObservation name="Unit of observation"}
*Unit of observation*: The 'who' or 'what' which are observed, from which measurements are taken and data collected.
:::


Since each blond hair comes from the same man, each of those hairs have essentially 'lived their life together': They are washed at the same time, with the same shampoo, exposed to the same amount of sunlight and exercise, share genetics, etc.
However, different men would potentially use different shampoo, exercise differently, have different genetics, and so on.
Each man tends to be different, and lives differently and independently of others.

The RQ aims to compare blond *men* with brunet *men*; *men* are being compared.
Each man is a collection of units of observations (hair strands).
This leads to a similar, but different, concept: the *unit of analysis*.
In the example above, each man is a *unit of analysis*, where each unit of analysis gives 200 observations.


::: {.definition #UnitOfAnalysis name="Unit of analysis"}
*Unit of analysis*: The smallest collection of units of observations (and perhaps the units of observations themselves) about which generalizations and conclusions are made; the smallest *independent* 'who' or 'what' for which information is analysed.
:::


In the hair-thickness study, each *person* is a *unit of analysis*.
The sample size is just two.
*Each unit of analysis (man) has 100 units of observation (hair strands).*
Importantly, the sample size for the study is the number units of analysis; so here, *only two examples of the population of men are in the study*.


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
The *individuals* are the *units of analysis*.
:::


::: {.tipBox .tip data-latex="{iconmonstr-info-6-240.png}"}
The number of units of *analysis* in a study is the size of the sample.
:::


::: {.tipBox .tip data-latex="{iconmonstr-info-6-240.png}"}
Sometimes the *units of analysis* and *units of observation* are the same.
:::


::: {.example #UnitsAnalysis name="Units of analysis"}
In the hair-strand study, each hair strand is a *unit of observation*: measurements of hair strand thickness are taken from individual hair strands.
The *unit of analysis* is the *person*: the hair strands from each man share much in common.
'Men' operate independently, but the hairs on each man are not independent entities.
:::


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/winter-tires-4664205_640.jpg" width="200px"/>
</div>


::: {.example #UnitsAnalysis2 name="Units of analysis"}
A study compares the wear on two brands of car tyres.
Four tyres of Brand A are allocated to each of Cars 1--5, and four tyres of Brand B are allocated to each of Cars 6--10.

After 12 months, the amount of wear is recorded on each tyre.
The *unit of observation* is the *tyre*: the amount of wear is measured on each tyre.

The tyres on any one car do not operate independently; the four tyres on a single car 'live their life together'.
They all are exposed to the same day-to-day use, the same drivers, have driven almost identical distances, under the same conditions, etc.

The *unit of analysis* is the *car*: the brand of tyre is allocated to the car, and all wheels on the car get the same brand of tyre.
Each unit of analysis (car) produces four units of observations.
The *sample size* is 10 cars, with $10\times 4 = 40$ observations.
:::


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/pexels-nappy-936018.jpg" width="200px"/>
</div>


:::{.exampleExtra  data-latex=""}
A report on the *Spectrum* website reported:
<!-- (https://www.spectrumnews.org/news/statistical-errors-may-taint-many-half-mouse-studies/) -->
<!-- (https://www.spectrumnews.org/) -->
  
> Seven years ago, Peter Kind [...] was reading a study about fragile X syndrome, a developmental condition characterized by severe intellectual disability and, often, autism [...]
> Kind was surprised when he noticed a potentially serious statistical flaw.
>
> The research team had looked at 10 neurons from each of the 16 mice in the experiment [...] 
> the researchers had analyzed each neuron as if it were an independent [individual observation]. 
> That gave them 160 data points to work with, 10 times the number of mice in the experiment.
>
> `The question is, are two neurons in the brain of the same animal truly independent data points? The answer is no,' Kind says.
>
> --- [Spectrum report](https://www.spectrumnews.org/news/statistical-errors-may-taint-many-half-mouse-studies/), accessed 18 Nov 2022

<!-- (https://www.spectrumnews.org/news/statistical-errors-may-taint-many-half-mouse-studies/) -->

The study used 16 units of analysis (mice), but the authors treated the $16\times 10 = 160$ neurons as the units of analysis.
The 10 neurons from each mouse share the same genetic information

A total of 160 neurons from 16 mice is very different to a study of 160 neurons from 160 genetically-different mice.
:::


The units of observation and units of analysis *may* be the same, and often are.
However, they are sometimes different, and identifying these situations is *crucial*.
Importantly, studies compare units of analysis, not units of observation.


::: {.example #UnitsAnalysis3 name="Units of analysis"}
A study compared two school physical activity (PA) programs.
Each of 44 children (with parental agreement) was allocated to one of two PA programs.
The improvement in children's fitness was measured for every student in the study over six months.

The *units of observation* are the individual students, as the fitness measurements are taken from the students.
The *units of analysis* are also the individual students, as the PA program was allocated to each student individually, and each student has their own sport, family routines and activities, etc.
Each unit of analysis (student) has one unit of observation.

There are 44 units of analysis, and 44 units of observations.
:::


::: {.example #UnitsAnalysisGroups name="Units of analysis"}
Consider comparing the percentage of females and males wearing sunglasses at a specific beach.

People in a *group* at the beach will probably not be operating 'independently': people with similarities tend to group together.
For example, a couple will often *both* be wearing or both *not* wearing sunglasses; families will often all be wearing sunglasses or not wearing sunglasses.

The researchers have two options; either

* Use the people *groups* as the *unit of analysis* (some will be groups of one), and record data from just *one* person in any group.
  Ideally, the researchers would specify before-hand from which group member to take data (e.g., the person closest to the researchers when the group is noticed).
* Alternatively, the researchers may decide not to use data from groups at all, and only gather data from individuals.
:::




`r if (knitr::is_latex_output()) '<!--'`
::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
<iframe src='https://www.ferendum.com/en/embeded.php?pregunta_ID=1252809&sec_digit=992403757&embeded_digit=1479848444' style='width:100%; height:500px; overflow: auto; background: #badaff' frameBorder='0'></iframe><BR>
<A href='https://www.ferendum.com' target='_blank'>Free Online Poll Maker</A>


<iframe src='https://www.ferendum.com/en/embeded.php?pregunta_ID=1252811&sec_digit=285796637&embeded_digit=6372971' style='width:100%; height:500px; overflow: auto; background: #badaff' frameBorder='0'></iframe><BR>
<A href='https://www.ferendum.com' target='_blank'>Free Online Poll Maker</A>


`r webexercises::hide()`
**Units of observation**: the individual students, as the fitness measurements are taken from the students individually.

**Units of analysis**: the *schools*, as the PA program was allocated to each *school*. 
All students at School A are exposed Program 1, but all students at School A are also likely to be exposed to similar weather, fitness opportunities, physical conditions, teachers and school-based philosophies, and so on.

*The improvement in the children's fitness levels* and *the program* are both **variables**.
`r webexercises::unhide()`
:::
`r if (knitr::is_latex_output()) '-->'`



`r if (knitr::is_html_output()){
  'The following short video may help explain some of these concepts:'
}`
<!-- From: https://stackoverflow.com/questions/43840742/how-to-embed-local-video-in-r-markdown -->


<div style="text-align:center;">
```{r}
htmltools::tags$video(src = "./videos/UnitsOfObsAnalysis-B.mp4", 
                      width = "550", 
                      controls = "controls", 
                      loop = "loop", 
                      style = "padding:5px; border: 2px solid gray;")
```
</div>


<iframe src="https://learningapps.org/watch?v=pmy2wjmun22" style="border:0px;width:100%;height:650px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>



### The outcome {#Outcome}

All RQs study something *about* the population, called the *outcome*.
Because the RQ concerns a population, the outcome describes a group (not individuals).
Hence, the outcome is usually an *average*, *percentage*, or *general* numerically quantity summarising the population.


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-process-1-240.png" width="50px"/>
</div>


::: {.definition #Outcome name="Outcome"}
The *outcome* in a RQ is the result, output, consequence or effect of interest in a study, numerically summarising the population.   
:::


The outcome of interest in a population may be (for example):

* *average* increase in heart rates after 30 minutes of exercise.
* *average* amount of wear after 1000 hours of use.
* *proportion* of people whose pupils dilate.
* *average* weight loss after three weeks.
* *percentage* of seedlings that die.


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
The **outcome** in a RQ summarises a *population*; it does not describe the *individuals* in the population.
:::


### The comparison or connection {#Comparison}


Some RQs may seek to establish a relationship in the **P**opulation between the **O**utcome and another attribute of the individuals.
This is other attribute is called a **C**omparison or **C**onnection.
The implication is that a change in the value of the comparison or connection may be associated with a change in the value of the outcome (which *may* or *may not* be a cause-and-effect relationship).

A *comparison* refers to an attribute recorded in a small number of distinct groups for which the outcome is compared.
A *connection* refers to a attribute that can take many different values for which a connection with the outcome is explored.
The values of the comparison or connection may be *imposed* on the individuals by the researchers (e.g., fertilizer dose) and called *treatments*, or naturally occur (e.g., age) and called *conditions*.


::: {.definition #Comparison name="Comparisons"}
The *comparison* in the RQ identifies the small number of different, distinct subsets of the population between which the outcome is compared.
:::


::: {.definition #Connections name="Connections"}
The *connection* in the RQ identifies another attribute of the individuals that can take many different values, and may be related to the outcome. 
:::


::: {.example #ComparisonConnectionCaloric name="Comparisons and connections"}
A study [@CaloricIntake] examined the mean daily sodium excretion (the **O**utcome) in Israeli adults (the **P**opulation).

The daily sodium excretion was *compared* for two separate groups: those diagnosed with diabetes, and those not diagnosed with diabetes.

A possible *connection* was explored between the daily sodium excretion and the systolic blood pressure.
:::


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-tree-16-240.png" width="50px"/>
</div>


The distinction between *between*-individuals comparisons (being discussed here) and *within*-individuals comparisons is important.


::: {.definition #Betweenindividuals name="Between-individuals comparisons"}
*Between-individuals comparisons* mean that the comparison is between different groups of individuals.
In contrast, *within-individual comparisons* make comparison *within* the same individuals.
:::


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/football-5441486_1920.jpg" width="200px"/>
</div>


:::{.example #WithinBetweenComparison name="Between- and within-individual comparisons"}
Consider studying the strength of left and right legs of football players.

A *between*-individuals comparison would compare the left and right leg strengths *between* different groups: one group would have their left-leg strength measured, and the other their right-leg strength measured.
The **C** refers to *between*-individual comparisons or connections.

In contrast, a *within*-individuals comparison would measure both the right and left strength of the same individuals: the comparison is *within* each individual.
In this example, *no within-individuals comparison* exists, so this study does not have a *comparison* for the purpose of writing a RQ.
Instead, the **O**utcome may be given as "the average difference between individuals' right- and left-leg strength".
:::


The outcome may be *compared* between two or more separate, distinct subsets of the population; for example:

* Comparing the average amount of wear in floor boards (O) between two groups: standard wooden flooring materials, and bamboo flooring.
* Comparing the average heart rates (O) across three subsets: those who received no dose of a drug, those who received a daily dose of the drug, and those who received a twice-daily dose of the drug.

Explicitly, the comparison here is *between different individuals in separate groups*, not *within the same individuals*.

Studies may use *both* within- and between-individuals comparisons.
For instance, a study may examine the *change* in each individuals blood pressure (the within-individuals comparison), for two drugs given to different groups (the between-groups comparison).


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
Be careful!

The definition of a *comparison* refers to a *between-individuals comparison*, that may be *imposed* (e.g., one group is given one dose of fertilizer per day, and another given two doses of fertilizer per day) or *existing* (e.g., one group of people aged under 30, and another aged 30 or over).

If all individuals are treated in the same way, or do not have existing difference that allow them to be divided into groups to be compared, no *comparison* exists according to this definition.
:::


::: {.example #Comparisons name="Comparison"}
Consider comparing the average blood pressure (the Outcome) in the right and left arms of Australians (the Population).
The blood pressure is measured on both arms of every studied individual.

*There is no (between-individuals) comparison*: the individuals are not divided into separate groups to compare average blood pressure; every person is treated the same way, and a left and right arm belongs to each person.
This is a *"within-individuals" comparison*.
The outcome might be best described as 'the average *difference* between right- and left-arm blood pressure'.

A study comparing the average blood pressure between (a) people aged under 40, and (b) people aged 40 or over *does* have a (between-individuals) comparison: two different subsets (under 40; 40 and over) of the population are compared.
:::


Often, one of the comparison groups is the *control group*.
The *control group* comprises units of analysis *as similar as possible* to the other units of analysis (called *controls*), but without the receiving the treatment, or having the condition, being studied.
The control groups acts like a benchmark for detecting changes in the outcome.
Sometimes the control group receives a *placebo*: a non-effective treatment that appears to be the real treatment.


::: {.definition #Control name="Control"}
A *control* is a unit of analysis without the treatment or condition of interest, but as similar as possible in *every other way* to other units of analysis.
:::


::: {.definition #Placebo name="Placebo"}
A *placebo* is a treatment with no intended effect or active ingredient, but appears to be the real treatment.
:::


::: {.example #ControlGroup name="Control group"}
To test the effectiveness of a new drug, patients report to a doctor to receive injections of a new drug.
Some patients are assigned to the *control group*, but the controls are *not* just people who don't get the injections.

Ideally, controls would be people who, like the treatment group, report to a doctor and receive an injection... however, they just receive a injection that does nothing.
:::


The above ideas also apply to RQs with *connections*.
As the value of the *connection* changes between many possible values, the value of the outcome (potentially) changes; for example:

* Connecting the average heart rate (O) with exposure to amount of caffeine consumption in the previous day (C).
  Heart rate and caffeine consumption are both recorded for many different people (the individuals).
* Connecting the percentage seed germination (O) with hours of sunlight per day (C).
  The percentage germination and sunlight hours per day are measured on many pots (the individuals) of 10 seeds each.

Again, as with comparisons, the connections here refer to those *between individuals*, but not *within-individuals*.


:::{.example #WithinBetweenConnections name="Between- and within-individual connections"}
Consider studying the relationship between daily water intake and amount of sun exposure per day for athletes.

A *between*-individuals comparison would record the daily water intake and the daily sun exposure once each for many individuals.

In contrast, a *within*-individuals comparison would record the daily water intake and the daily sun exposure for one individual over many days: the comparison is *within* each individual.

Explicitly, the connection here is *between different individuals*, not *within the same individuals*.
:::


### The intervention {#Intervention}

RQs with a connection or comparison (C) sometimes also have an *intervention*.


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-14-240.png" width="50px"/>
</div>


::: {.definition #Intervention name="Intervention"}
An *intervention* is a comparison or connection whose value can be *manipulated* by the researchers.
That is, the researchers *impose* the connection or comparison upon the individuals in the study.
:::


The intervention may be: 

* explicitly giving doses of a new drug to patients.
* explicitly applying wear testing loads to two different flooring materials.
* explicitly exposing people to different stimuli.
* explicitly applying a different dose of fertiliser.


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-6-240.png" width="50px"/>
</div>




:::{.example #InterventionHimalaya name="Intervention"}
A study by @data:Bird2008:wholegrain *gave* one group of participants a diet using refined flour, and gave another group of participants a diet using a new flour variety (*Himalaya 292*).
The type of diet is the comparison.
Since the researchers can manipulate which subject ate which flour, this study has an intervention.
:::


::: {.example #Interventions name="Interventions"}
A study comparing the average blood pressure in female and male Australians measured blood pressure using a blood pressure machine (a sphygmomanometer).

The research team needs to interact with the participants and use the machine to measure blood pressure, but there is *no* intervention.
Using the sphygmomanometer is just a way to measure blood pressure, to *obtain* the data.

*There is no intervention*: the *comparison* is between females and males, which cannot be manipulated or imposed on the individuals by the researchers.
:::


::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
A study of American college women [@data:woolf:ironstatus] measured 'iron status' in highly active women (>12 hr purposeful physical activity per week) and sedentary women (<2 hr purposeful physical activity per week).

What is the Outcome; Comparison or Connection (if any), and Intervention (if any)?\label{thinkBox:POCIWomen}


`r if (knitr::is_latex_output()) '<!--'`
`r webexercises::hide()`
*Outcome*: 'average iron status' (which would need an *operational definition*.) 

*Comparison*: between two groups of individuals: highly active and sedentary women (i.e., between individuals). 
These terms would also need operational definitions!

*Intervention*: Probably none; an intervention would mean the *researchers* tell each individual woman to be highly active or sedentary, which seems unlikely.
`r webexercises::unhide()`

`r if (knitr::is_latex_output()) '-->'`
:::


::: {.exampleExtra  data-latex=""}
Researchers examined numerous studies of chest compressions by paramedics.
They examined research papers in which the **P**opulation was patients who had experienced a cardiac arrest, and where manual chest compressions were compared with another method.

The table below shows the interventions and outcomes of interest:

**Interventions**              | **Outcomes** 
-------------------------------|--------------------------------------------------------------------
* Mechanical chest compression | * Mean survival time to hospital discharge
* Mechanical CPR               | * Percentage with a return of spontaneous circulation (ROSC)
* Powered chest compressions   | 
* Powered CPR                  | 

The research concluded that:

> Overall, the evidence analysed suggests that mechanical chest compression devices are statistically superior to manual chest compressions of a high quality, when up-to-date protocols and guidelines are followed.
>
> --- @williams2021mechanical, Table 1
:::


<iframe src="https://learningapps.org/watch?v=pip2dnpq222" style="border:0px;width:100%;height:500px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>



## Definitions {#OperationDefinitions}

Research studies usually include terms that must be carefully and precisely defined, so that others know *exactly* what has been done, without ambiguity.
Two types of definitions can be given when necessary: 

* A *conceptual definition* explains *what* is being studied (i.e., what a word or a term *means* in the study).
* An *operational definition* defines *how* something will be studied or measured.


::: {.definition #ConceptualDefinition name="Conceptual definition"}
A *conceptual definition* articulates precisely *what* words or phrases mean; that is, what is being identified, measured, observed or assessed in a study.
:::


::: {.definition #OperationalDefinition name="Operational definition"}
An *operational definition* articulates exactly *how* something will be identified, measured, observed or assessed.
:::


In many cases, a clear *operational definition* is needed to describe how data will be collected to ensure repeatability and consistent data collection, by removing any ambiguity about how data are obtained.


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/pexels-oladimeji-ajegbile-2696299.jpg" width="200px"/>
</div>


::: {.example #DefinitionsStress name="Operational and conceptual definitions"}
Consider a study examining stress in students.
A *conceptual definition* would describe *what is meant* by 'stress' (in contrast to, say, 'anxiety').
An *operational definition* would describe *how* 'stress' is *measured*, since stress cannot be measured directly (like height, for example).

'Stress' could be *measured* using a questionnaire or measuring physical characteristics, for instance.
Other ways of measuring stress are also possible, and all have advantages and disadvantages.
:::


<iframe src="https://learningapps.org/watch?v=pt0rqa5t522" style="border:0px;width:100%;height:500px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>


Sometimes the definitions themselves are not important; a clear definition is simply needed.
However, to avoid confusion, commonly-accepted definitions should be used unless good reasons exist for using a different definition.
When a commonly-accepted definition does not exist, the definition being used should be very clearly articulated.



::: {.example #DefinitionsFlexibility name="Operational and conceptual definitions"}
A research article [@gillet2018shoulder] entitled "Shoulder range of motion and strength in young competitive tennis players with and without history of shoulder problems" provided these necessary conceptual definitions (among others):

* Young: 8--15 years;
* Competitive tennis players: Some of the best players in their age category in France, and members of a French tennis centre of excellence.

An operational definition was provided for 'Shoulder strength': as measured using a hand-held dynamometer.
:::


<!-- ::: {.example #DefinitionsFlexibility name="Operational and conceptual definitions"} -->
<!-- A student project at my university used this RQ: -->

<!-- > Amongst students [...], on average do students who participate in competitive swimming have greater shoulder flexibility than the remainder of the able-bodied student population? -->

<!-- *Shoulder flexibility* needs a *conceptual definition* to describe exactly what it *means*. -->
<!-- Additionally, how *shoulder flexibility* is being *measured* is not clear, so an *operational definition* is needed (which was not provided...). -->
<!-- ::: -->
<!-- Zac R., SEM1 2020 -->


::: {.exampleExtra data-latex=""}
Players, administrators and fans are wary of concussions and head injuries in sport.
A conference on concussion in sport developed this *conceptual definition* [@McCrory250]:

> ... a complex pathophysiological process affecting the brain, induced by biomechanical forces...


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/women-6905793_1920.jpeg" width="200px"/>
</div>


However, an *operational definition* is needed to explain *how* to identify a player with concussion during a game.
Rugby decided on this *operational definition* [@Raftery642]:

> ... a concussion applies with any of the following:
>
> 1. The presence, pitch side, of any Criteria Set 1 signs or symptoms (table 1)... [Table 1 includes symptoms such as 'convulsion', 'clearly dazed', etc.];
>
> 2. An abnormal post game, same day assessment...;
>
> 3. An abnormal 36--48&nbsp;h assessment...;
>
> 4. The presence of clinical suspicion by the treating doctor at any time...
:::
    



::: {.example #DefinitionsWater name="Operational and conceptual definitions"}
Consider a study requiring water temperature to be measured.

An *operational definition* would explain *how* the temperature is measured: the thermometer type, how the thermometer was positioned, how long was it left in the water, and so on.

In contrast, a *conceptual* definition might describe the scientific definition of temperature (and would not be needed, as 'temperature' is a well-understood term).
:::



::: {.exampleExtra data-latex=""}
A study of snacking in Australia [@data:Fayet2017:Snacks] used this conceptual definition of an 'eating occasion':

> ...one or more food or beverage items consumed at the same time of day...

and a 'snacking occasion' as

>  ...one or more food or beverage items consumed at the same time of day within a snacking time period...

Finally then, 'snacking' was defined as:
  
> Eating occasions that occurred during breakfast, midday and evening meals were meals and all eating occasions that occurred between these meals were classified as snacking. 

These are all *conceptual* definitions, explaining what the terms *mean*.

An *operational* definition would explain *how* the data were obtained from the participants (e.g., using a food diary).
:::



::: {.exampleExtra data-latex=""}
@data:Meline2006:InclusionExclusion discusses five studies about stuttering, each using a different *operational* definition:
  
* Study 1: As diagnosed by speech-language pathologist.
* Study 2: Within-word disfluences greater than 5 per 150 words.
* Study 3: Unnatural hesitation, interjections, restarted or incomplete phrases, etc.
* Study 4: More than 3 stuttered words per minute.
* Study 5: State guidelines for fluency disorders.

People may be classified as stutterers by some definitions but not others, so it is important to know which definition is used.
:::



:::{.exampleExtra data-latex=""}
A study examined the possible relationship between the 'pace of life' and the incidence of heart disease
[@data:levine1990:paceoflife] in 36 US cities.

The researchers used four different *operational* definitions for 'pace of life' (remember the article was published in 1990!):

1. The walking speed of randomly chosen pedestrians.
1. The speed with which bank clerks gave 'change for two $20 bills or [gave] two $20 bills for change'.
1. The talking speed of postal clerks.
1. The proportion of men and women wearing a wristwatch.

None of these *perfectly* measure 'pace of life', of course.
Nonetheless, the researchers found that, compared to people on the West Coast,

> ... people in the Northeast walk faster, make change faster, talk faster and are more likely to wear a watch...
>
> --- @data:levine1990:paceoflife (p. 455)
:::




::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
Define a 'smoker'.\label{thinkBox:Smoker}

`r if (!knitr::is_html_output()) '<!--'`
`r webexercises::hide()`
This is very difficult!

Some studies use the categories *Never smoked*, *Past smoker*, and *Current smoker*... or ask people to *self*-identify as a smoker or not.
`r webexercises::unhide()`
`r if (!knitr::is_html_output()) '-->'`
:::




## Types of RQs {#TypesOfRQs}

All RQs have a population (P) and an outcome (O).
Different *types* of RQ emerge depending on whether the RQ has a comparison/connection (C) and whether this comparison or connection can be manipulated by the researchers (an intervention, I).
This section explores different types of research questions:

* Descriptive RQs (Sect.\ \@ref(RQsDescriptive));
* Relational RQs (Sect.\ \@ref(RQsRelational));
* Interventional RQs (Sect.\ \@ref(RQsInterventional)).

These are compared in Sect.\ \@ref(RQsCompare).

RQs can also be written with one of two purposes in mind (Sect.\ \@ref(TwoPurposesOfRQs)):

* *Estimation*:
  These RQs ask how precisely a *value* in the *population* is estimated by using the *sample* data.
* *Making decisions*:
  These RQs are concerned with making a decision about a population, based on the sample data.

Examples for both forms are given for the different types of RQs below.


### Descriptive RQs (PO) {#RQsDescriptive}

*Descriptive RQs* are the most basic RQs, giving the **P**opulation to be studied, and the **O**utcome of interest about this population.
Typically, descriptive RQs have one of these forms:

* *Estimation*: Among {*the population*}, what is {*the outcome*}?
* *Decision-making*: Among {*the population*}, is {*the outcome*} equal to {*a given value*}?


::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
These are **not** 'recipes', but guidelines.
:::


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-6-240.png" width="50px"/>
</div>


::: {.example}
A study examined the 'body temperature of 148 healthy men and women' [@data:mackowiak:bodytemp] aged between 18 to 40 (the P).
One descriptive RQ was:

> What is the mean body temperature?

This RQ is an *estimation* RQ. 
A *decision-making* RQ they also studied was whether the average body temperature was the value that had been commonly accepted by medical professionals:

> Is the mean body temperature really 98.6^o^F?
:::


::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
Consider this RQ:\label{thinkBox:POCICoeliacs}
'Among Indonesian adults, what proportion are coeliacs?'
For this RQ, identify the **P**opulation and the **O**utcome.

`r if (knitr::is_latex_output()) '<!--'`
`r webexercises::hide()`
**P**: Indonesian adults; **O**: The proportion that are coeliacs.
This is a estimation-type descriptive RQ.
`r webexercises::unhide()`
`r if (knitr::is_latex_output()) '-->'`
:::


### Relational RQs (POC) {#RQsRelational}

Usually, studying *relationships* is more interesting than simply describing a population.
*Relational RQs* explore existing relationships, and state the **P**opulation, the **O**utcome, and the **C**omparison or **C**onnection.
Relational RQs have no intervention; the connection or comparison is *not* manipulated by, nor imposed by, the researchers.

Typically, relational RQs with a *comparison* have one of these forms:

* *Estimation*: Among {*the population*}, what is the difference in {*the outcome*} for {*the groups being compared*}? 
* *Decision-making*: Among {*the population*}, is {*the outcome*} the same for {*the groups being compared*}?

Typically, relational RQs based on a *connection* have the form:

* *Estimation*: Among {*the population*}, how strong is the relationship between {*the outcome*} and {*something else*}?
* *Decision making*: Among {*the population*}, is {*the outcome*} related to {*something else*}?


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-6-240.png" width="50px"/>
</div>


::: {.example #RelationalRQ name="Relational RQ"}
Consider this RQ (based on @estevez2019influence):

> Among Cubans between 13 and 20 years of age, is the average heart rate the same for females and males?

The *population* is 'Cubans 13 and 20 years of age', the *outcome* is 'average heart rate', and the (between-individuals) *comparison* is between two separate groups: 'between females and males'.

This is a *relational RQ* since the sex of the individual (the C) is *not* manipulated by, or imposed by, the researchers.
This RQ is a *decision-making RQ*, since it asks if the average heart rate is the same for females and males.
An *estimation*-type relational RQ would ask about the *size* of difference in the average heart rate between females and males.

The same study could also have asked:

> Among Cubans between 13 and 20 years of age, is the average heart rate related to age?

The *connection* is with 'age', which cannot be manipulated by the researchers, so this is a *relational RQ*.
This RQ is a *decision-making RQ*, since it asks if the average heart rate is related to age.
An *estimation*-type relational RQ might be:

> Among Cubans between 13 and 20 years of age, how strong is the relationship between average heart rate and age?
:::


::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
Consider this RQ (based on @data:Brown2000:WarningLights):\label{thinkBox:POCIAmbo}
\vspace{-2ex}

> In the London Ambulance Service last year, what was the difference between the average response time to emergency calls between weekdays and weekends?

\vspace{-2ex}
Identify the population, outcome, and comparison.
:::


::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
Consider this RQ:
\vspace{-2ex}

> In Queensland state forests, is there a *relationship between* the average number of sulphur-crested cockatoos and the number of eucalypt trees, in general?

\vspace{-2ex}
Identify the population, outcome, and comparison.
:::


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-6-240.png" width="50px"/>
</div>


### Interventional RQs (POCI) {#RQsInterventional}

*Interventional RQs* explore relationships where the comparison/connection can be manipulated by, or imposed by, the researchers (i.e., an intervention is present).
Interventional RQs state the **P**opulation, the **O**utcome, the **C**omparison or **C**onnection, and use an **I**ntervention.

Interventional RQs are like relational RQs, except that the comparison or connection can be manipulated by the researchers (i.e., has an intervention).
Sometimes, the use of an intervention is unclear from the RQ.
When writing an interventional RQ, clarify if an intervention is used if possible.


<div style="float:right; width: 75px; padding:10px">
<img src="Pics/iconmonstr-medical-6-240.png" width="50px"/>
</div>


::: {.example #InterventionalRQ  name="Interventional RQ"}
A study [@data:Khair2015:Earthworms] compared the time needed for organic waste to turn into compost, when earthworms were either added or not added to the waste.
Since the researchers manipulated which waste samples had earthworms added, the study uses an *intervention*, and research question is *interventional*.

An *estimation-type RQ* could be used to estimate the difference in composting time when worms were added to waste, and when worms were *not* added.
A *decision making-type RQ* could be used to determine if the composting times for waste with and without earthworms was the same or not. 
:::


:::{.exampleExtra  data-latex=""}
Consider this RQ [@data:McLinn:otitis]:

> In children with acute otitis media, what is the difference in the average duration of symptoms when treated with cefuroxime compared to amoxicillin?

The population is 'children with acute atitis media', the outcome is 'average duration of symptoms', and the comparison is between two groups (taking 'cefuroxime' or 'amoxicillin').

If the drugs are *given* to the children by the researchers, the RQ has an intervention.
If the researchers find children who are already taking the two drugs and measure the outcome ('average duration of symptoms'), the RQ has no intervention. 
:::


<iframe src="https://learningapps.org/watch?v=p8a16ig8a22" style="border:0px;width:100%;height:500px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>


### Two purposes of RQs {#TwoPurposesOfRQs}

As noted earlier, RQs can also be written with one of two purposes in mind:

* *Estimation*:
  These RQs ask how precisely a *value* in the *population* is estimated by using the *sample*, and are answered using *confidence intervals*.
  Answering estimation RQs are discussed for:
  
  - descriptive RQs (Chaps.\ \@ref(CIOneProportion) to\ \@ref(PairedCI));
  - relational or interventional RQs with a comparison (Chaps.\ \@ref(CITwoMeans) and\ \@ref(OddsRatiosCI)), where the value being estimated measures the size of the difference between groups; and
  - relational or interventional RQs with a connection (Sect.\ \@ref(RegressionCI)) where the value being estimated measures the strength of a relationship.
* *Making decisions*:
  These RQs are concerned with making a decision about a population, and are answered using *hypothesis testing*.
  Answering decision-making RQs are discussed for:
  
  -  descriptive RQs (Chaps.\ \@ref(TestOneProportion) to\ \@ref(TestPairedMeans));
  - relational or interventional RQs with a comparison (Chaps.\ \@ref(TestTwoMeans) and\ \@ref(TestsOddsRatio)), where the decision is about the difference between groups; and
  - relational or interventional RQs with a connection (Sects.\ \@ref(RegressionHT) and\ \@ref(CorrelationTesting)) where the decision is about the strength of a relationship.


::: { .example name="Various types of RQs"}
Studies can incorporate many types of RQs.
For example, a study [@data:Thane2004:ZincVitA] of 'British young people aged 4--18' (the P) asked and answered numerous RQs.
Two *descriptive* RQs were:

1. What is the average zinc intake of the children? 
  This is an *estimation* RQ.
2. Does the average zinc intake meet recommended dietary guidelines? 
  This is a *decision-making* RQ.

A relational RQ with a connection is:

3. What is the strength of the association between plasma zinc and retinol concentrations?
  This is an *estimation* RQ, estimating the *strength* of the relationship between plasma zinc and retinol concentrations.

A relational RQ with a comparison is:

4. Is the average zinc intake the same for boys and girls? 
  This is an *decision-making* RQ.
  
Decision-making RQ have two possible answers.
For the example above: the average zinc intake either *is* the same for females and males, or *is not* the same for females and males (Fig.\ \@ref(fig:ZincRQ)).
However, answers are rarely clear in practice, since only one of the countless possible samples from the population are studied.
Instead, researchers decide *how much* sample evidence support a particular hypothesis about the *population*.

Evidence may *support* or *contradict* a hypothesis; evidence rarely *proves* a hypothesis (at least, without any other support, such as theoretical support).
Ultimately, after collecting data from a *sample*, a decision must be made about which explanation about the *population* is more consistent with the data collected.
:::


```{r ZincRQ, fig.align="center", fig.cap="Two possible answers to the RQ about zinc intake", out.width='95%', fig.width=8.25, fig.height=4}

par( mar = c(0.5, 0.5, 0.75, 0.5))
openplotmat()

pos <- array(NA, dim = c(3, 2))
pos[1, ] <- c(0.18, 0.5) # RQ 
pos[2, ] <- c(0.75, 0.70) # Yes
pos[3, ] <- c(0.75, 0.30)   # No

straightarrow(from = pos[1,], to = pos[2,], 
            lty = 2,
            lcol = "grey")
straightarrow(from = pos[1,], to = pos[3,], 
            lty = 2,
            lcol = "grey")

textrect( pos[1,], 
           lab = "In British young people aged 4--18,\nis the average zinc intake the same\nfor boys and girls?", 
           radx = 0.18, 
           rady = 0.15, 
           shadow.size = 0,
           box.col = ResponseColour,
           lcol = ResponseColour)

textrect( pos[2,], 
           lab = expression( atop(bold(YES)*":"~the~average~zinc~intake,
                                  italic(is)~the~same~"for"~boys~and~girls)),
           radx = 0.20, 
           rady = 0.1, 
           shadow.size = 0,
           box.col = ExtraneousColour,
           lcol = ExtraneousColour)
textrect( pos[3,], 
           lab = expression( atop(bold(NO)*":"~the~average~zinc~intake,
                                  italic(is~not)~the~same~"for"~boys~and~girls)),
           radx = 0.20, 
           rady = 0.1, 
           shadow.size = 0,
           box.col = GroupColour,
           lcol = GroupColour)

text(x = 0.18,
     y = 0.90,
     font = 2, # Bold
     labels = "Research question")
text(x = 0.75,
     y = 0.90,
     font = 2, # Bold
     labels = "Hypotheses")
```




### Contrasting the types of RQs {#RQsCompare}

*Descriptive RQs* are usually used when initially exploring a new research topic.
*Relational RQs* then examine relationships between the outcome and some other attribute, which may set the platform for asking interventional questions.
*Interventional RQs* (when possible) can be used to test theories or models, or to establish cause-and-effect relationships (i.e., causality).
Research often develops through these stages of RQs as knowledge grows and develops; see Table\ \@ref(tab:ThreeTypesOfRQs).


```{r ThreeTypesOfRQs}
RQtypes <- array( dim = c(3, 5) )

colnames(RQtypes) <- c("RQ type", 
                       "P", 
                       "O",
                       "C",
                       "I")

RQtypes[1, ] <- c("Descriptive (D)",   
                  "Yes", 
                  "Yes", 
                  "",    
                  "")
RQtypes[2, ] <- c("Relational (R)",     
                  "Yes", 
                  "Yes", 
                  "Yes", 
                  "")
RQtypes[3, ] <- c("Interventional (I)", 
                  "Yes", 
                  "Yes", 
                  "Yes", 
                  "Yes")


if( knitr::is_latex_output() ) {
  kable(RQtypes,
        format = "latex",
        longtable = FALSE,
        booktabs = TRUE,
        escape = FALSE, # For latex to work in \rightarrow
        caption = "The three types of RQs",
        align = c("r", "c", "c", "c")
  ) %>%
    kable_styling(full_width = FALSE) %>%
    kable_styling(font_size = 10) %>%
    row_spec(0, bold = TRUE) # Columns headings in bold
}

if( knitr::is_html_output() ) {
  out <- kable(RQtypes,
               format = "html",
               align = c("r", "c","c", "c"),
               longtable = FALSE,
               caption = "The three types of RQs",
               booktabs = TRUE)
  
    kable_styling(out, 
                  full_width = FALSE) %>%
      row_spec(row = 0, 
               bold = TRUE)  
}
```


:::{.example #CoeliacStudies name="Different study types"}
Coeliac disease in an inherited auto-immune condition where individuals have an intolerance to the gluten found in wheat, rye, barley and some other grains.
Initially, the proportion of individuals suffering from coeliac disease was unknown (e.g., @kenwright1972coeliac).
*Descriptive* RQs were answered to make estimates (e.g., @data:Cook2000:Coeliac).

Then, *relational* RQs compared the proportion of females and males who were coeliacs (e.g., @data:Cook2000:Coeliac).
Then, *interventional* RQs were posed to understand the disease further; for example, if the percentage with adverse symptoms is the same for those given a diet *without* oats and those given a diet *with* oats (e.g., @data:Janatuinen2002:Coeliac; @data:Lundin2003:Coeliac).
:::


`r if (knitr::is_latex_output()) '<!--'`
::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
`r if (knitr::is_latex_output()) '<!--'`
<iframe src='https://www.ferendum.com/en/embeded.php?pregunta_ID=1246683&sec_digit=18335469&embeded_digit=240558911' style='width:100%; height:425px; overflow: auto; background: #badaff33' frameBorder='0'></iframe><BR>
<A href='https://www.ferendum.com' target='_blank'>Free Online Poll Maker</A>

<iframe src='https://www.ferendum.com/en/embeded.php?pregunta_ID=1246699&sec_digit=110957782&embeded_digit=1207607588' style='width:100%; height:425px; overflow: auto;background: #badaff33;' frameBorder='0'></iframe><BR>
<A href='https://www.ferendum.com' target='_blank'>Free Online Poll Maker</A>


`r webexercises::hide()`
1. **Relational**: A between-individuals comparison exists (comparing amputees with transradial and transhumeral amputations), but would not be **manipulated** or **imposed** by the researchers.
1. **Interventional**:
   The RQ has a between-individuals comparison ('comparing trees planted in a concrete sidewalk and a grassed sidewalk'), and the wording sounds like these trees were planted here intentionally.
   The researchers could pick a trees, and decide where to plant it (concrete or grassed sidewalk).
`r webexercises::unhide()`
:::
`r if (knitr::is_latex_output()) '-->'`



## Writing RQs: an example {#Writing-RQs}


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/pexels-andrea-piacquadio-3807629.jpg" width="200px"/>
</div>

RQs emerge from observations, which lead to questions, and the need for evidence to answer those questions.
Suppose you notice some people taking echinacea when they get a cold.
You may wonder: does taking echinacea help with a cold?
This may lead to an initial RQ:

> Is it better to take echinacea when you have a cold?

*This RQ is clearly poor, but is a starting point.*
This RQ can be refined by clarifying the POCI elements.
For example, what *population* could we study?
Many options exist: All Australians, or Australian adults in a specific location.
Some of these may not be practical (i.e., when a sample cannot easily be obtained from the population).

What *outcome* could be used to to determine echinacea's effectiveness?
Many options exist, such as the *average* cold duration, or the *percentage* of people who take days off work.

The initial RQ is also vague: better than *what*?
The outcome could be *compared* between groups (such as those taking echinacea and those who do not), or *connected* to something else (such as the daily intake of fresh fruit).

We could also decide to *intervene* or not, which has implications for *how* the study is conducted and how the results are interpreted.
If we *decided not to intervene*, the subjects decide for themselves how to treat their cold.
If we *did decide to intervene*, various interventions could be used; the dose *frequency* or the doses *amounts* could be imposed.

After making some decisions about P, O, C and I, a revised RQ (based on @data:barrett:echinacea) could be posed:

> Among Australian teenagers with a common cold, is the average duration of cold symptoms shorter for teens taking a daily dose of echinacea compared to teens taking no echinacea?

The P, O, C and I do not have to be comprehensively described in the RQ; some information could be provided later as operational definitions (e.g., dose) and using exclusion and inclusion criteria (e.g., exclude teens with chronic health conditions).

Many terms need defining: What is meant by 'echinacea' (fresh? tablet form? as a tea); 'cold' (self-diagniosed? diagnosed by a doctor?), and so on.

<iframe src="https://learningapps.org/watch?v=p2x991pot22" style="border:0px;width:100%;height:600px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>


`r if (knitr::is_html_output()){
  'The following short video may help explain some of these concepts:'
}`


<div style="text-align:center;">
<iframe width="560" height="315" src="https://www.youtube.com/embed/rgR073gyYXk" frameborder="0" allow="accelerometer; encrypted-media; gyroscope; picture-in-picture"></iframe>
</div>


## Variables: from populations to individuals {#PopToIndividuals}
  
Consider this RQ seen above:

> Among Australian teenagers with a common cold, is the average duration of cold symptoms shorter for teens given a daily dose of echinacea compared to teenagers taking no echincaea?

This is an interventional RQ about a *population* (Australian teenagers).
However, the data to answer this RQ come from a sample of *individuals* in that population.
Each piece of information obtained from or about each individual is called a *variable*, because the values can *vary* from individual to individual.


::: {.definition #Variable name="Variable"}
A *variable* is a single aspect or characteristic associated with the individuals, whose values can vary from individual to individual.
:::


Examples of variables include: the duration of cold symptoms, gender, place of birth, or hair colour.
The RQ identifies the variables *needed* to answer the RQ, though other variables may be (and typically are) measured also (Sect.\ \@ref(ExtraneousVariables)).
	 

::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
A variable is a single aspect that can vary from *individual to individual*.
While *your* city of birth may not change, 'city of birth' is a variable because it can vary from *individual* to *individual*.
:::


<div style="float:right; width: 222x; border: 1px; padding:10px">
<img src="Illustrations/pexels-andrea-piacquadio-3807629.jpg" width="200px"/>
</div>


::: {.example #Variables  name="Variables"}
'Duration of cold symptoms' is a *variable*: it is obtained from individuals, and its value can vary from individual to individual.

The '*average* duration of cold symptoms' is the *outcome*, a numerical summary of many individuals' cold durations.
:::


While many variables can be recorded from individuals in the population, two essential variables are (Table\ \@ref(tab:RQsPopulationIndividuals)):

* The **response variable**, which records information to determine the outcome. 
* The **explanatory variable**, which records information to determine the comparison or connection.

The value of the *response* variable may change in *response* to the value of the explanatory variable.
The value of the *explanatory* variable may *explain* the value of the response variable.


::: {.definition #ResponseVariable name="Response variable"}
A *response variable* is a variable that records the result, output, consequence or effect of interest from the individuals in the population.
:::

::: {.definition #ExplanatoryVariable name="Explanatory variable"}
An *explanatory variable* is a variable that records the comparison or connection on individuals in the population.
:::



::: {.importantBox .important data-latex="{iconmonstr-warning-8-240.png}"}
The *response variable* is sometimes called the *dependent variable*, and the *explanatory variable* is sometimes called the *independent variable*.

We avoid these terms, since the words "dependent" and "independent" have many different meanings in research.
:::


	
```{r RQsPopulationIndividuals}
if( knitr::is_latex_output() ) {
  
  PopInd <- array( dim = c(2, 3) )
  colnames(PopInd) <- c("Population", 
                        "",
                        "Individuals")
  PopInd[1, ] <- c("Outcome", 
                   "$\\rightarrow$", 
                   "Response variable")
  PopInd[2, ] <- c("Comparison/Connection", 
                   "$\\rightarrow$", 
                   "Explanatory variable")
  
  kable(PopInd,
        format = "latex",
        longtable = FALSE,
        booktabs = TRUE,
        escape = FALSE, # For latex to work in \rightarrow
        linesep  =  c("", "", "", "\\addlinespace", "", "", ""), # Otherwise addes a space after five lines... 
        caption = "The relationship between the population and the individuals",
        align = c("r", "c", "l"))   %>%
    kable_styling(full_width = FALSE) %>%
    kable_styling(font_size = 10) %>%
    row_spec(0, bold = TRUE) # Columns headings in bold
}

if( knitr::is_html_output() ) {
  
  PopInd <- array( dim = c(4, 3) )
  
  PopInd[1, ] <- c("![](./Pics/iconmonstr-friend-5-240.png){#id .class height=100px}",
                   "",
                   "![](./Pics/iconmonstr-generation-16-240.png){#id .class height=100px}")
  PopInd[2, ] <- c("Population", 
                   "", 
                   "Individuals")
  
  PopInd[3, ] <- c("Outcome:", 
                   "$\\rightarrow$", 
                   "Response variable")
  PopInd[4, ] <- c("Comparison/Connection:", 
                   "$\\rightarrow$", 
                   "Explanatory variable")
  
  out <- kable(PopInd,
               format = "html",
               align = c("r", "c", "l"),
               longtable = FALSE,
               caption = "The relationship between the population and the individuals",
               booktabs = TRUE)
  
    row_spec(out, 
             2, 
             bold = TRUE) # Columns headings in bold
}
```


The RQ cannot be answered without information about these two variables.
The *outcome* is a summary of the values of the response variable (Table\  \@ref(tab:RQsPopulationIndividualsExamplesOutcome)) recorded from many individuals.
Similarly, the values of the explanatory variable measured on the individuals distinguish between the values of the *comparison* (Table\ \@ref(tab:RQsPopulationIndividualsExamplesComparison))) or the *connection* (Table\ \@ref(tab:RQsPopulationIndividualsExamplesConnection)) being made.



```{r POCIVariables, fig.cap="The POCI elements", fig.align="center", fig.height=2, fig.width=6, out.width='55%'}
showPOCI(addOCXYArrows = TRUE,
         addC = TRUE, 
         addI = TRUE, 
         addX = TRUE, 
         addY = TRUE)
```

```{r RQsPopulationIndividualsExamplesOutcome}
PopInd2 <- array( dim = c(7, 3) )

if( knitr::is_latex_output() ) {
  PopInd2[1, ] <- c("![](./Pics/iconmonstr-friend-5-240.png){#id .class height=100px}",
                    "",
                    "![](./Pics/iconmonstr-generation-16-240.png){#id .class height=100px}")
  PopInd2[2, ] <- c("Outcome describing the population", 
                      "", 
                      "Response variable in individuals")
  
  PopInd2[3, ] <- c("\\emph{Average} increase in diastolic blood pressure, from before to after exercise", 
                    "", 
                    "Increase in diastolic blood pressure of \\emph{individuals}, from before to after exercise")
  PopInd2[4, ] <- c("\\emph{Percentage} of seedings that sprout", 
                    "", 
                    "Whether or not an \\emph{individual} seedling sprouts")
  PopInd2[5, ] <- c("\\emph{Proportion} owning iPad", 
                    "", 
                    "Whether or not an \\emph{individual} owns an iPad")
  PopInd2[6, ] <- c("\\emph{Average} cold duration", 
                    "", 
                    "Cold duration for \\emph{individuals}")
  PopInd2[7, ] <- c("\\emph{Percentage} of concrete cylinders having fissures", 
                    "", 
                    "Whether or not an \\emph{individual} cylinder has fissures")
  
  PopInd2[, 2] <- "$\\rightarrow$"
  
  kable(PopInd2[3:6, ],
        format = "latex",
        longtable = FALSE,
        booktabs = TRUE,
        col.names = c("Outcome describing the population", 
                      "", 
                      "Response variable in individuals"),
        escape = FALSE, # For latex to work in \rightarrow
        linesep = c( "\\addlinespace"), # Add a bit of space between all rows
        caption = "Examples of the outcome and the corresponding response variable",
        align = c("r", "c", "l")
  )   %>%
    kable_styling(full_width = FALSE, 
                  font_size = 10) %>%
    row_spec(0, bold = TRUE) %>% # Columns headings in bold
    column_spec(column = 1, width = "7cm") %>% 
    column_spec(column = 3, width = "7cm")
}

if( knitr::is_html_output() ) {
  PopInd2[1, ] <- c("![](./Pics/iconmonstr-friend-5-240.png){#id .class height=100px}",
                    "",
                    "![](./Pics/iconmonstr-generation-16-240.png){#id .class height=100px}")
  PopInd2[2, ] <- c("Outcome describing the population", 
                    "", 
                    "Response variable in individuals")

  PopInd2[3, ] <- c("*Average* increase in diastolic blood pressure, from before to after exercise", 
                    "", 
                    "Increase in diastolic blood pressure of *individuals*, from before to after exercise")
  PopInd2[4, ] <- c("*Percentage* of seedings that sprout",
                    "", 
                    "Whether or not an *individual* seedling sprouts")
  PopInd2[5, ] <- c("*Proportion* owning iPad", 
                    "", 
                    "Whether or not an *individual* owns an iPad")
  PopInd2[6, ] <- c("*Average* cold duration", 
                    "", 
                    "Cold duration for *individuals*")
  PopInd2[7, ] <- c("*Percentage* of concrete cylinders having fissures", 
                    "", 
                    "Whether or not an *individual* cylinder has fissures")
  
  PopInd2[, 2] <- "$\\rightarrow$"
  
  out <- kable(PopInd2,
               format = "html",
               align = c("r", "c", "l"),
               longtable = FALSE,  
               caption = "Examples of the outcome and the corresponding response variable",
               booktabs = TRUE)
  
    row_spec(out, 2, bold = TRUE) # Columns headings in bold
}
```



```{r RQsPopulationIndividualsExamplesComparison}
PopInd3 <- array( dim = c(4, 3) )
colnames(PopInd3) <- c("Comparison being made", 
                       "", 
                       "Explanatory variable in individuals")
PopInd3[1, ] <- c("Between males and females", 
                  "", 
                  "The sex of each \\emph{individual} person")
PopInd3[2, ] <- c("Between jarrah, beech and bamboo floor boards", 
                  "", 
                  "Type of floorboard in \\emph{individual} homes")
PopInd3[3, ] <- c("Between 30kg/ha and 40kg/ha fertilizer rates", 
                  "", 
                  "Application rate in \\emph{individual} paddocks")
PopInd3[4, ] <- c("Between people in their 20s, 30s and 40s", 
                  "", 
                  "Age group for each \\emph{individual} person")

PopInd3[, 2] <- "$\\rightarrow$"

if( knitr::is_latex_output() ) {
  kable(PopInd3,
        format = "latex",
        longtable = FALSE,
        booktabs = TRUE,
        escape = FALSE, # For latex to work in \rightarrow
        linesep  =  c( "\\addlinespace"), # Add a bit of space between all rows
        caption = "Examples of the comparison and the corresponding explanatory variable",
        align = c("r", "c", "l"))   %>%
    kable_styling(full_width = FALSE, 
                  font_size = 10) %>%
    row_spec(0, bold = TRUE) %>% # Columns headings in bold
    column_spec(column = 1, width = "72mm") %>% 
    column_spec(column = 3, width = "55mm")
}

if( knitr::is_html_output() ) {
  kable(PopInd3,
        format = "html",
        align = c("r", "c", "l"),
        longtable = FALSE,
        caption = "Examples of the comparison and the corresponding explanatory variable",
        booktabs = TRUE)    
}
```



```{r RQsPopulationIndividualsExamplesConnection}
PopInd3 <- array( dim = c(4, 3) )
colnames(PopInd3) <- c("Connection being made", 
                       "", 
                       "Explanatory variable in individuals")
PopInd3[1, ] <- c("With number hours of sunlight", 
                  "", 
                  "The hours of sunlight received by each \\emph{individual} plant")
PopInd3[2, ] <- c("With age", 
                  "", 
                  "The age of \\emph{individual} wombats")
PopInd3[3, ] <- c("With diastolic blood pressure", 
                  "", 
                  "Diastolic blood pressure \\emph{individual} person")
PopInd3[4, ] <- c("With the percentage aggregate", 
                  "", 
                  "The percentage aggregrate in \\emph{individual} batch of concrete")

PopInd3[, 2] <- "$\\rightarrow$"

if( knitr::is_latex_output() ) {
  kable(PopInd3,
        format = "latex",
        longtable = FALSE,
        booktabs = TRUE,
        escape = FALSE, # For latex to work in \rightarrow
        linesep  =  c( "\\addlinespace"), # Add a bit of space between all rows
        caption = "Examples of the connection and the corresponding explanatory variable",
        align = c("r", "c", "l"))   %>%
    kable_styling(full_width = FALSE, 
                  font_size = 10) %>%
    row_spec(0, bold = TRUE) %>% # Columns headings in bold
    column_spec(column = 1, width = "46mm") %>% 
    column_spec(column = 3, width = "82mm")
}

if( knitr::is_html_output() ) {
  kable(PopInd3,
        format = "html",
        align = c("r", "c", "l"),
        longtable = FALSE,
        caption = "Examples of the connection and the corresponding explanatory variable",
        booktabs = TRUE)    
}
```





::: {.example #Variables2 name="Variables"}
For the final RQ for the echinacea study (Sect.\ \@ref(Writing-RQs)), 'the duration of cold symptoms' is the *response variable*, and 'whether echinacea is taken or not' is the *explanatory variable*.
The type of medication is taken *before* the cold symptoms disappear, and may even explain the duration of the cold symptoms.
:::


`r if (knitr::is_latex_output()) '<!--'`
::: {.thinkBox .think data-latex="{iconmonstr-light-bulb-2-240.png}"}
<iframe src='https://www.ferendum.com/en/embeded.php?pregunta_ID=1249763&sec_digit=365747699&embeded_digit=874385320' style='width:100%; height:550px; overflow: auto; background: #badaff33;' frameBorder='0'></iframe><BR>
<A href='https://www.ferendum.com' target='_blank'>Free Online Poll Maker</A>


`r webexercises::hide()`
The *Population* is 'carrots grown in Buderim' 8 weeks after planting.
From these carrots, we *need* to collect *Whether or not Thrive was applied* and the *weight of the carrots 8 weeks after planting*.

The *response* variable is 'the weight of each individual carrot 8 weeks after planting', and the *explanatory* variable is 'whether or not Thrive was used on each carrot'.

('The *number* of carrots planted' is not even a variable: it is not information recorded about the individuals, but a summary of information.)
`r webexercises::unhide()`
:::
`r if (knitr::is_latex_output()) '-->'`


::: {.exampleExtra data-latex=""}
Consider this RQ:

> For overweight men over 60, is the average weight loss after three weeks the same for a diet high in fresh fruit and a diet high in dried fruit?

The *outcome* is the average weight *loss*; the *response variable* is the weight loss for each individual man.
(This would be found by measuring their weight *before* and *after* three weeks on the diets; it is measured within-individuals.)

The between-individuals *comparison* is between the two diets; the *explanatory variable* is the diet each man is on.
:::


<iframe src="https://learningapps.org/watch?v=pe5br2opt22" style="border:0px;width:100%;height:550px" allowfullscreen="true" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe>


::: {.example #POCIaccelerometer name="POCI"}
Consider this RQ (based on @tudor2015comparison):

> For Australian adults, is the average number of steps per day the same for those using a waist accelerometer, and those using a wrist accelerometer?

The *population* is the group of interest: *all* Australian adults.
The *outcome* is the *average* number of steps per day, and the *response variable* is the number of steps per day for the individuals.

The *comparison* is "Between those wearing a waist accelerometer and those wearing a wrist accelerometer".
The *explanatory variable* is what varies from person to person: "The location of the accelerometer".

This RQ may or may not have an **intervention**.
If the researchers manipulate (i.e., tell people) where to wear the accelerometer, an intervention is present.
If the individuals have chosen themselves where to wear the accelerometer, an intervention is not present.
:::
 

## Preparing software {#DataEntry}

Most statistical software packages (including jamovi and SPSS) use the same approach for organising the data (though exceptions exist for some types of analyses):

* Each *row* represents one unit of analysis: the *number* of rows equals the *number* of units of analysis.
* Each *column* represents one variable: the *number* of columns equals the *number* of variables.
  (An additional  column of identifying information may also appear, such as the person's name, or concrete batch number.)


::: {.softwareBox .software data-latex="{iconmonstr-laptop-4-240.png}"}
In statistical software, the variable *names* are not placed in a row (say, in Row 1, above the data itself), which might happen when using a spreadsheet.
The *names* of the variables are the names of the columns.
:::


::: {.example #SoftwarePrep name="Preparing statistical software"}
In Sect.\ \@ref(PopToIndividuals), a RQ was asked about whether using echinacea or not reduced the duration of the common cold.

For this RQ, the *variables* are 'Duration of cold symptoms' (response), and 'Type of treatment' (explanatory); see Examples\ \@ref(exm:Variables) and\ \@ref(exm:Variables2).

The number of *rows* in the data worksheet will equal the number of people in the study.
The data worksheet will have two columns (Fig.\ \@ref(fig:DataPrepjamovi)):

* one to record the duration of each individual's cold symptoms (say, `Duration`);
* one to record whether the individual received a dose of echinacea or received no medication (say, `Treatment`).

There may be an additional column recording the name or ID of each individual.  
:::


```{r DataPrepjamovi, fig.show="hold", out.width='42%', fig.align="center", fig.cap="jamovi (left) and SPSS (right) prepared for the data, with some data entered, and the variable names as the column headers", fig.align="center", fig.width=3, fig.height=4}
knitr::include_graphics( c( "DataPrep-jamovi.png",  
                            "DataPrep-SPSS.png") )
```


## Summary {#Chap2-Summary}

In this chapter, you have learnt to write **research questions** for quantitative analysis.
Research questions (RQs) are always about an **outcome** (O) in some **population** (P).
Some RQs have a **comparison** or **connection** (C); some also have an **intervention** (I): When the values of C can be manipulated by the researchers.

By *comparison*, we mean "between-individuals" comparisons.
RQs may be **descriptive** (with only a P and O), **relational** (with a P, O and C), or **interventional** (with a P, O, C and I).

RQs may take one of two forms: *Estimation*-type RQs; or  *Decision-making*-type RQs.

For *quantitative* RQs, the outcome *numerically* summarises the population (or subsets of the population), so is usually worded in terms of percentages, averages, etc.
	
Data comes from **individuals** in the population by measuring, observing or assessing the **response** (or dependent) variable.
The *Outcome* is a numerical summary of the values of the response variable from many individuals.
Similarly, the data concerning the comparison or connection comes from measuring or observing the values of the **explanatory** (or independent) variables from individuals.

The *who* or *what* that observations are made from are called the **units of observation**.
The smallest independent collections of units of observations (that is, units with very little in common) are called the **units of analysis**.


```{r Chap2Summary, animation.hook="gifski",  interval=1.5, fig.cap="Chapter 2 summary", fig.height = 3, fig.align="center", dev=if (is_latex_output()){"pdf"}else{"png"}}
if (knitr::is_html_output()) {

for (i in (1:9)){
  
  par( mar = c(0.1, 0.1, 0.1, 0.1) ) # Number of margin lines on each side

  diagram::openplotmat()
  pos <- array(NA, 
               dim = c(4, 2))
  pos[1, ] <- c(0.35, 0.6) # P 
  pos[2, ] <- c(0.45, 0.6) # O
  pos[3, ] <- c(0.55, 0.6)   # C
  pos[4, ] <- c(0.65, 0.6)   # I

  
  if (i <=  2){
    textrect( colMeans( pos[1:2, ] )  + c(0, 0.15),
              lab = "Descriptive RQ",
              radx = 0.15,
              rady = 0.04,
              shadow.size = 0,
              lcol = "azure",
              box.col = "azure",
              cex = 1.0)
  }
  
  if ( (i == 3) | ( i == 4) ){
    textrect( colMeans( pos[1:3, ] ) + c(0, 0.15),
               lab = "Relational RQ",
              radx = 0.15,
              rady = 0.04,
              shadow.size = 0,
              lcol = "azure",
              box.col = "azure",
              cex = 1.0)
  }
  
  if ( (i >= 5) & ( i <= 7) ){
    textrect( colMeans( pos[1:4, ] ) + c(0, 0.15),
               lab = "Interventional RQ",
              radx = 0.15,
              rady = 0.04,
              shadow.size = 0,
              lcol = "azure",
              box.col = "azure",
              cex = 1.0)
    if (i == 7) {
      textplain( colMeans( pos[1:4, ] ) - c(0, 0.1),
                 lab = "(Intervention: when C can be manipulated by the researchers)",
                 cex = 0.85)
      
    }
  }
 
  # Show some arrow, and then over-write

  if ( i == 8 ) {
    straightarrow( from = colMeans( pos[1:4, ] ) + c(-0.1, -0.3),
                   to = pos[2, ],
                   lwd = 2)
  }
  if ( i == 9 ) {
    straightarrow( from = colMeans( pos[1:4, ] ) + c(0.1, -0.3),
                   to = pos[3, ],
                   lwd = 2)
  }
  
  if ( i == 8 ) {
    textrect( colMeans( pos[1:4, ] ) + c(-0.1, -0.3),
              lab = "Response variable",
              box.col = "white",
              lcol = "white",
              shadow.size = 0,
              radx = 0.05,
              rady = 0.02,
              cex = 0.85)
  }
  if ( i == 9 ) {
    textrect( colMeans( pos[1:4, ] ) + c(0.1, -0.3),
              lab = "Explanatory variable",
              box.col = "white",
              lcol = "white",
              shadow.size = 0,
              radx = 0.05,
              rady = 0.02,
              cex = 0.85)
  } 
  
  # Always need P and O
  textrect( pos[1,], 
            lab = "P",
            radx = 0.05,
            rady = 0.025,
            shadow.size = 0,
            lcol = "white",
            box.col = "white",
            cex = 2)
  textrect( pos[2,], 
            lab = "O", 
            radx = 0.05,
            rady = 0.05,
            shadow.size = 0,
            lcol = "white",
            box.col = "white",
            cex = 2)
  if (i >= 3) { # C
    textrect( pos[3,], 
              box.col = "white",
              lcol = "white",
              shadow.size = 0,
              radx = 0.05,
              rady = 0.05,
              lab = "C",
              cex = 2)
  }
  if (i >= 5) { # I
    textrect( pos[4,], 
              box.col = "white",
              lcol = "white",
              shadow.size = 0,
              radx = 0.05,
              rady = 0.05,
              lab = "I", 
              cex = 2)
  }

} 
  
}
```
  
`r if (knitr::is_html_output()){
  'The following short video may help explain some of these concepts:'
}`

<div style="text-align:center;">
<iframe width="560" height="315" src="https://www.youtube.com/embed/rgR073gyYXk" frameborder="10" allow="accelerometer; encrypted-media; gyroscope; picture-in-picture"></iframe> 
</div>



## Quick review questions  {#Chap2-QuickReview}

::: {.webex-check .webex-box}
Consider this RQ:

> In elite female netball players, do players in defence positions have a greater average number of knee injuries (per player, per season) than players in attacking positions?

1. What is the *comparison* in this RQ, if any?\tightlist
`r if( knitr::is_html_output()) {
longmcq( c(
   answer = "Between players in defence and attacking positions", 
   "There is no comparison",
   "Between female and male players",
   "Between knee injuries and other types of injuries",
   "Between elite and non-elite players",
   "Between netball players and players of other sports") )}`
2. What is the *outcome*?
`r if( knitr::is_html_output()) {
longmcq( c(
   "The type of player (that is, defence or attacking)", 
   "Knee injuries",
   answer = "The average number of knee injuries per season") )}`
3. What is the *response variable*?
`r if( knitr::is_html_output()) {
longmcq( c(
   "The average number of injuries per player per season", 
   answer = "The number of injuries for each player, per season",
   "The type of player (defence or attacking)") )}`
4. What is the *unit of analysis*?
`r if( knitr::is_html_output()) {
longmcq( c(
   "The number of knee injuries", 
   "The type of player (defensive or attacking)",
   answer = "The elite netball players") )}`
5. What *type* of research question is this?
`r if( knitr::is_latex_output()) {'Descriptive, Relational or Interventional?'} else {
longmcq( c(
   "Descriptive", 
   answer = "Relational",
   "Interventional") )}`
6. In what *form* is this RQ?
`r if( knitr::is_latex_output()) {'Decision-making or estimation?'} else {
longmcq( c(
   answer = "Decision-making",
   "Estimation") )}`
:::


## Exercises {#RQsExercises}

Selected answers are available in Sect.\ \@ref(RQsAnswer).


::: {.exercise #RQsBloodPressure}
Consider this RQ:

> Among Danish university students, is the average resting diastolic blood pressure the same for students who regularly drive to university and those who regularly ride their bicycles to university?

1. For this RQ, identify the population.
1. For this RQ, identify the outcome.
1. For this RQ, identify the comparison, if any.
1. For this RQ, identify the intervention, if any.
1. What *type* of RQ is this?
1. What *operational* and *conceptual definitions* would be needed?
1. What information *must* be collected from each individual to answer the RQ?
1. What are the units of analysis?
1. What are the units of observation?
:::


::: {.exercise #RQsNutrition}
Consider this article extract (@data:checkley:diarrhea, p. 210):

> We conducted a 4-year (1995--1998) field study in a Peruvian peri-urban community... to examine the relation between diarrhoea and nutritional status in 230 children $<3$ years of age

For this study:

1. Identify POCI.
2. Infer the primary research question.
3. What *type* of question is used?
4. What *operational definitions* would be needed?
5. What are the *response* and *explanatory* variables?
:::


::: {.exercise #RQsOutcomeResponse}
For the following *response* variables, what would be the corresponding *outcomes*?

1. Whether a vehicle crashes or not.
1. The height at which people can jump.
1. The number of tomatoes per plant.
1. Whether or not a person owns a car.
:::

	
::: {.exercise #RQsWalkingSpeed}
Consider this RQ: 'Is the average walking speed the same when texting and talking on a mobile phone?'

1. What is the *explanatory* variable?
2. What is the *response* variable?
3. What is the *outcome*?
:::


::: {.exercise #RQsComparisonExplanatory}
For the following *comparisons*, what would be the corresponding *explanatory* variables?

1. Between 91 octane, 95 octane, and ethanol-blended car fuel.
1. Between caffeinated and decaffeinated coffee.
1. Between taking zero, one or two iron tablet per day.
1. Between vegans and vegetarians.
:::


::: {.exercise #RQsComparisonVsPaired}
For the following studies, determine which have a comparison and which do not.
In each case, identify the outcome.

1. A study to determine if a higher percentage of people at a particular city park wear hats in winter compared to summer.
1. A study to determine if average cholesterol levels are the same when measured on the same people before and after a diet change.
1. A study to determine if a person's average balance-time on their right leg is the same as on their left leg.
1. A study to determine if the average yield of tomato plants is the same when three different fertilisers are applied.
:::


::: {.exercise #RQsAnimals}
Animals in an experiment are divided into pens (three per pen), and feed is allocated to each pen [@sterndale2017increasing].
Animals in different pens receive different feed; animals in the same pen receive the same feed.
The weight gain of each animal is recorded.

1. What is the *unit of observation*? Why?
2. What is the *unit of analysis*? Why?
:::


<!-- SEM 2 2018: Christopher W.; WILLIAM L.; LOK R. B.--> 
::: {.exercise #ProjectRQ2}
Consider this actual student RQ from the university where I work.

> Among 10 Australian adults, does the time taken to read a passage of text change when different fonts are used? 

Critique the RQ, and write a better RQ (if necessary).
:::


<!-- SEM 2 2018: Alex B.; Levi C.; Stuart S.--> 
::: {.exercise #ProjectRQ3}
Consider this actual student RQ from the university where I work.

> Of students that study at (a University), do males have a larger lung capacity than females? 

Critique the RQ, and write a better RQ (if necessary).
:::



::: {.exercise #RQsCommonCold}
Consider this RQ:

> For Australian adults with a common cold, do people who take Vitamin C tablets daily have, on average, a shorter cold duration than people who do not take any Vitamin C tablets?

In this RQ, the *population* is
`r if( knitr::is_html_output() ) {mcq( c("Australians", answer = "Australian adults", "Australians who take Vitamin C tablets daily") )} else {"[Australians/Australian adults/Australians who take Vitamin C tablets]"}`, and the *outcome* is
`r if( knitr::is_html_output() ) {mcq( c("The cold duration", answer = "The average cold duration", "The cold") )}  else {"[The cold duration/The average cold duration/The cold]"}`.

The `r if( knitr::is_html_output() ) {mcq( c("intervention", answer = "comparison", "unit of analysis") )} else {"[intervention/comparison/unit of analysis]"}` is between those who take Vitamin C tablets and those who do not.

The `r if( knitr::is_html_output() ) {mcq( c("explanatory", answer = "response") )} else {"[explanatory/response]"}` variable is the duration of the cold symptoms for each individual person.
The `r if( knitr::is_html_output() ) {mcq( c(answer = "explanatory", "response") )} else {"[explanatory/response]"}` variable is whether or not each person take Vitamin C tablets or not.

It is not clear whether there is an intervention.
If there *is* an intervention, this would be `r if( knitr::is_html_output() ) {mcq( c(answer = "an interventional", "a relational") )} else {"[an interventional/a relational]"}` RQ, otherwise it would be
`r if( knitr::is_html_output() ) {mcq( c("an interventional", answer = "a relational") )} else {"[an interventional/a relational"}` RQ.
:::


::: {.exercise #RQsBlueGum}
A research study was comparing the average size of Blue Gum eucalypt leaves in two areas of Queensland.
A student takes 40 leaves from each of ten trees in Area A, and 40 leaves from each of ten trees in Area B.
Are the following statements true or false?

  
1. The unit of analysis is the individual leaf.\tightlist
`r if( knitr::is_html_output() ) { torf( FALSE )}`
2. The unit of observation is the individual leaf.
`r if( knitr::is_html_output() ) { torf( TRUE )}`
3. The unit of analysis is the tree.
`r if( knitr::is_html_output() ) { torf( TRUE )}`
4. The size of the sample in the study is
`r if( knitr::is_html_output() ) {longmcq( c(
   "80", 
   answer = "20",
   "800") )}`
:::



<!-- QUICK REVIEW ANSWERS -->
`r if (knitr::is_html_output()) '<!--'`
::: {.EOCanswerBox .EOCanswer data-latex="{iconmonstr-check-mark-14-240.png}"}
**Answers to in-chapter questions:**

- Sect. \ref{thinkBox:Smoker}: This is very difficult!
Some studies use the categories *Never smoked*, *Past smoker*, and *Current smoker*... or ask people to *self*-identify as a smoker or not.
- Sect. \ref{thinkBox:POCIWomen}: 
*Outcome*: 'average iron status' (which would need an *operational definition*.) 
*Comparison*: between two groups of individuals: highly active and sedentary women (i.e., between individuals). 
These terms would also need operational definitions!
*Intervention*: Probably none; an intervention would mean the *researchers* tell each individual woman to be highly active or sedentary, which seems unlikely.
- Sect. \ref{thinkBox:POCICoeliacs}: *P*: Indonesian adults. 
  *O*: The proportion that are coeliacs.
  This is a estimation-type descriptive RQ.
- \textbf{\textit{Quick Revision:}}
**1.** Between players in defence and attacking positions.
**2.** The average number of knee injuries per season.
**3.** The number of injuries for each player, per season.
**4.** The elite netball players.
**5.** Relational.
**6.** Decision-making.
- Sect.\ \@ref(thinkBox:POCIAmbo): 
  P is 'London Ambulance Service calls last year';
  O is 'average response time to emergency calls';
  Comparison is 'between weekdays and weekends'.
- Sect.\ \@ref(thinkBox:POCIMiners): 
  P is 'Queensland state forests';
  O is 'average number of noisy miners';
  Connection is 'with the number of eucalypts'.
:::
`r if (knitr::is_html_output()) '-->'`