Selecting Statistical Analyses

Variable(s)	Graphical Displays	Numerical Summaries	Inferential Statistics
one qualitative (categorical) variable	bar chart pie chart	raw and relative frequencies mode	one-sample z test about a proportion one-sample z confidence interval for a proportion chi-square goodness-of-fit test
one quantitative (numerical) variable	boxplot histogram frequency polygon stem-and-leaf display dotplot ogive	five-number summary mean median mode range interquartile range standard deviation	one-sample t test about a mean one-sample t confidence interval for a mean
repeated measures of one quantitative (numerical) variable on the same group	boxplot(s) histogram(s) frequency polygon(s) stem-and-leaf display(s) dotplot(s) ogive(s) line graph (if the repeated measures are made over time)	five-number summary of differences mean difference median difference range of differences interquartile range of differences standard deviation of differences	paired t test about a mean difference paired t confidence interval for a mean difference repeated measures ANOVA (with more than one repeated measurement)
repeated measures of one ordinal-qualitative (categorical with a natural ordering on the categories) variable on the same group	bar charts	raw or relative frequencies	Wilcoxon signed rank test Friedman nonparametric ANOVA (with more than one repeated measurement)
comparison of one nominal-qualitative (categorical with no natural ordering on the categories) variable for two or more groups or relationship between two nominal-qualitative (categorical with no natural ordering on the categories) variables	stacked bar chart multiple bar charts multiple pie charts	raw or relative frequencies in a contingency table	two-sample z test about a difference between proportions two-sample z confidence interval for a difference between proportions chi-square test about independence
comparison of one ordinal-qualitative (categorical with a natural ordering on the categories) variable for two or more groups or relationship between one nominal-qualitative (categorical with no natural ordering on the categories) variable and one ordinal-qualitative (categorical with a natural ordering on the categories) variable	stacked bar chart multiple bar charts multiple pie charts	raw or relative frequencies in a contingency table	Mann Whitney rank sum test (with two samples) Kruskal-Wallis test (with more than two samples)
relationship between two ordinal-qualitative (categorical with a natural ordering on the categories) variables	stacked bar chart multiple bar charts multiple pie charts	Spearman rank correlation	Spearman rank correlation test
relationship between one ordinal-qualitative (categorical with a natural ordering on the categories) variable and one quantitative (numerical) variable or comparison of one quantitative (numerical) variable for two or more ordered groups	multiple boxplots multiple histograms multiple frequency polygons multiple stem-and-leaf displays multiple dotplots multiple ogives	Spearman rank correlation five-number summaries means medians ranges interquartile ranges standard deviations	Spearman rank correlation test
comparison of one quantitative (numerical) variable for two or more groups or relationship between one qualitative (categorical) variable and one quantitative (numerical) variable	multiple boxplots multiple histograms multiple frequency polygons multiple stem-and-leaf displays multiple dotplots multiple ogives	five-number summaries means medians ranges interquartile ranges standard deviations	two-sample t test about a difference between means two-sample t confidence interval for a difference between means one-way analysis of variance (with more than two samples)
relationship between two quantitative (numerical) variables	scatterplot line graph (if one variable is time)	least squares line Pearson correlation	simple linear regression t test (or Pearson correlation t test)