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) |