## A.5 Answer: TW 5 tutorial

### Answers for Sect. 5.2

- A few issues:
Five decimal places is to the nearest \(0.01\) of a mm!
The standard deviation of the difference is
*not*the difference between the individual standard deviations. A standard deviation cannot be negative. (Same applies to standard errors, but we aren't there yet.) Note that there is a sample size of \(0\) for the difference! - A few issues:
Five decimal places: That's accuracy to \(0.00001\) of a millimetre per second (I don't think so...).
There is no numerical measures of the most important thing and the thing the RQ (presumably) concerns:
The
*differences*between the two brands.

### Answers for Sect. 5.3

A few issues: vertical axis is not labelled (presumably burn time in seconds); horizontal axis is not labelled (we have no way of knowing what is happening there.)

A few issues: this is not a

*summary*: this shows the burn-time of every individual candle, and makes it hard to compare*means*(which is the RQ); why is every bar labelled, which just adds unnecessary clutter; fonts are hard too read (small); a boxplot (or dotchart) would be the appropriate graph. In addition: the largest value is over \(70\) mins! Do a*quick*project!A few issues: Compares just two numbers (means) using lots of ink; no indication of

*variation*in the data; a boxplot (or dotchart) would be appropriate.

### Answers for Sect. 5.4

**Plot 1**: \(0.94\) (correlation**D**);**Plot 2**: \(-0.95\) (correlation**A**);**Plot 3**: \(0.12\) (correlation**B**);**Plot 6**: \(0.75\) (correlation**C**).

Correlation is inappropriate for Plot 4 (non-linear) and Plot 5 (non-linear).- Examples of the direction in
**Plot 1**: any two variables moderately positively correlated, such as height and weight, distance lived from university and travel time, etc. - Examples of direction in
**Plot 2**: any two variables moderately negatively correlated, such as hours of weekly exercise and body weight, number of SCI110 tutorial missed and final mark, etc. **Plot 1**: \(88.4\)%;**Plot 2**: \(90.3\)%;**Plot 3**: \(1.4\)%;**Plot 6**: \(56.3\)%.

### Answers for Sect. 5.6

Answers implied by H5P.

- Five variables. ('Participants' would not be summarised, it is technically an
*identifier*and*not*a*variable*, as each person has a unique value). - Age; Height; Weight and quantitaive
**continuous**. - Gender (
**nominal**; two levels); GMFCS (**ordinal**; three levels) - As follows:
- 'Gender': Percentages (or number) F and M
- 'Age': Mean/median; standard deviation/IQR
- 'Height': Mean/median; standard deviation/IQR
- 'Weight': Mean/median; standard deviation/IQR
- 'GMFCS': Percentages (or numbers) in each group

- As follows:
- 'Gender': Barchart (not really needed)
- 'Age': Histogram/stemplot
- 'Height': Histogram/stemplot
- 'Weight': Histogram/stemplot
- 'GMFCS': Barchart/piechart

- As follows:
- Between Gender and Height: Boxplot
- Between Gender and GMFCS: Side-by-side or stacked bar chart.

### Answers for Sect. 5.7.1

- Relational.
- Observational: no intervention
- O: average accuracy. Response variable: the 'accuracy' for each individual.
- C: Between blind and sighted individuals. Explanatory variable: Whether the individual is blind, or not.
- No intervention: the C (whether someone is blind or not) cannot be manipulated by the researchers.
- Quantitative continuous.
- Qualitative nominal.
- A boxplot.
- The unit of analysis is the person.
- \(34 + 36 = 70\).
- One: each person gets one 'accuracy' value.

### Answers for Sect. 5.7.2

- Not shown.
- The median temperatures similar; a slight increase from Office A to C. IQR similar for each office, and range similar for Offices A and C (slightly larger for Office B). In summary: Office A a bit different (cooler) on average.
- Perhaps Office A.

### Answers for Sect. 5.7.3

- Stacked or side-by-side barcharts; whether bird injured or not, and whether upper or lower are both qualitative variables.
- Boxplots would be OK; one quantitative (length-of-stay) and one qualitative (therapy type) variable.
- Scatterplots; two quantitative variables (frequency; amount wheat consumed).

- Two-way table or stacked/side-by-side barchart, or table; two qualitative variables vars (\(30\) mins of physical activity or not; vigorous physical

### Answers for Sect. 5.7.4

Answers implied by H5P.

**Explanatory**variable is the number of hours of light each plant received;**response**variable is the number of flowers each plant received. The units of**observation**are the individual plants.**Explanatory**variable is the number of smokers at the restaurant;**response**variable is the concentration of fine particulate matter.**Response**variable is the waiting time;**explanatory**variable is the time of admission.**Explanatory**variable is the "Level of Playfulness";**response**variable is the "Level of Coping".

### Answer for Sect. 5.7.5

- To display the relationship between the age of athletes, and the times taken for each athlete to complete the `beep test':
*Scatterplot* - To display the percentage of elderly people in nursing homes that can independently complete a given task, for each of the seven tasks on a given list:
*Bar chart*or*Dot chart* - To display the relationship between the type of fertiliser applied to a vegetable crop (either A, B or C) and the yield per hectare, measured over numerous plots:
*Boxplot* - To display the distribution of the hardness measurements taken of 250 samples of bamboo:
*Histogram* - To display the relationship between the age of concrete test cylinders (under \(5\) years; \(5\) years and older) and their strength (fit for purpose; or not fit for purpose):
*Side-by-side or stacked bar chart*

### Answers for Sect. 5.7.6

- Observational; the ant nest would be pre-existing.
- Both are 'ant nests'.
- Looks good!
- Uphill looks different to the other two. Also: the lower dots comprise mostly blue dots (Sourdough Trail), so perhaps a difference between locations too.

### Answers for Sect. 5.7.7

- True experiment: treatments given (experiment), and the researchers selected the groups, groups did not previously existed (so
*true*experiment). - Observation: each patient. Analysis: The patient.
- Pretty good. A label on the horizontal axis would be better, but the caption does contain that information.
- Pain is
*reduced*. - Yes, probably. We cannot be sure due to randomness...

### Answer for Sect. 5.7.8

Boxplot; scatterplot.