A.5 Answers for TW 5 tutorial

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!
The RQ is about a discrepancy in proportions, or odds, but these are not present in the table.

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 \(70\,\text{mins}\)! Do a quick project! -->
Reasonably good! The label on the vertical axis is a bit misleading: it is the number of students; some wear grey-scale clothing and some do not.
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.

Correlation is inappropriate for Plot 4 (non-linear) and Plot 5 (non-linear).
Plot 1: \(0.94\) (correlation D); Plot 2: \(-0.95\) (correlation A); Plot 3: \(0.12\) (correlation B); Plot 6: \(0.75\) (correlation C).
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 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 quantitative 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.