# 36 Selecting an analysis

Selecting the correct confidence interval or hypothesis test can be challenging This book only describes a small number of possible scenarios. For the situations studied in this book, determining if the variables are qualitative or quantitative is important (Table 36.1). To compare more than two means, analysis of variance (ANOVA) is used but is only briefly covered in this book (Sect. 34.4).

So far, only descriptive and relational RQs have been studied. The next two chapters consider correlational RQs (Sect. 2.6). Appendix C may also prove useful.

TABLE 36.1: Five different scenarios studied so far, plus one to follow
Summaries
Analysis
Graphical display Numerical summary Hypothesis test Confidence interval
Descriptive RQ: Proportion in one sample (i.e., one qualitative variable)
Bar charts; pie chart Counts; percentages; odds One-sample $$z$$ CI for one mean
Descriptive RQ: Mean of one sample (i.e., one quantitative variable)
Histogram; stemplot; dot chart Means, medians; Std. dev., IQR; outliers One-sample $$t$$ CI for one mean
Repeated-measures RQ: paired quantitative data
Histogram of differences; case-profile Mean, std. dev. etc. of differences $$t$$-test for mean differences CI for mean difference
Relational RQs: comparing quantitative variables
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
Relational RQs: comparing qualitative variables
Side-by-side bar chart; stacked bar chart Odds; OR; percentages $$\chi^2$$-test for OR CI for odds ratios
Correlational RQs
Scatterplot Correlation Correlation; regression CI for regression parameters

## 36.1 Exercises

Answers to odd-numbered exercises are available in App. E.

Exercise 36.1 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 methods would be a suitable for creating a summary and performing analyses?

Exercise 36.2 Suppose we wish to estimate the difference between the mean number of hours of sunlight exposure per day for female and male teachers.

What methods would be a suitable for creating a summary and performing analyses?

Exercise 36.3 Suppose researchers wish to compare the proportion of trees with koalas in them, comparing trees more than $$10$$ m tall with trees $$10$$ m or shorter.

What methods would be a suitable for creating a summary and performing analyses?

Exercise 36.4 Suppose researchers are wanting to estimate the difference between the mean number of hours spent on social media for people aged over $$30$$, to people aged $$30$$ and under.

What methods would be a suitable for creating a summary and performing analyses?

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).