33 Selecting a test
Selecting the correct hypothesis test (or confidence interval) can be tricky... and in this book only a small number of hypothesis tests were described. (Literally hundreds of tests exist.)^{498}
For the tests studied in this book, determining if the response and explanatory variables are qualitative or quantitative is important (Table 33.1).
So far, only situations with a qualitative explanatory variable have been considered. In the next chapters, cases where both the response and explanatory variables are quantitative are studied.
You might also find Appendix C useful.
Graphical summary | Numerical summary | Hypothesis test | Confidence interval |
---|---|---|---|
Mean of one sample | |||
Histogram; stem-and-leaf plot; dot chart | Means, medians; Std. dev., IQR; etc. | One-sample \(t\) | CI for one mean |
Mean of differences (paired data) | |||
Histogram of differences; case-profile | Mean, std. dev. etc. of differences | \(t\)-test for mean differences | CI for mean difference |
Comparing means in two groups | |||
Error bar chart | Mean and std. error of the difference; mean, std. dev. etc. of each group | \(t\)-test for the difference between two means | CI of the difference between two means |
Comparing odds/percentages in two groups | |||
Side-by-side bar chart; stacked bar chart | Odds; OR; percentages | Chi-square test | CI for ORs |
Suppose researchers compare the average number of hours of exercise per week for office workers, both in summer and in winter, to see if the averages are different.
What would be a suitable test?Suppose we wish to compare the number of hours of sunlight exposure per day for female and male teachers.
What would be a suitable test?Suppose researchers wish to compare the proportion of trees with koalas in them, comparing trees more than 10 metres tall with trees 10 metres or shorter.
What would be a suitable test?Suppose researchers are wanting to compare the number of hours spend on social media for people aged over 30, to people aged 30 and under. What would be a suitable test?
To select the correct test, it is important to know how many
are measured, observed, or recorded on each unit of
, and what type they are.
If one quantitative variable is recorded, we can conduct a test about the
.
If two variables are recorded, there are a lot of possible options.
If both variables are qualitative, we could use a to compare the odds (or the proportions) in the two groups.
If one variable is qualitative and one is quantitative, we could use a to compare the in both groups.
If the change in the value of a quantitative variable is of interest, we have paired data so we could use a \(t\)-test, based on the .
The following short video may help explain some of these concepts. Note that the test for correlation and regression have not yet been covered in this book (but they will be in the next few chapters).