Statistical Tests
1 Dependent Variable/ 0 Independent Variables
| statistical test | description | example in R |
|---|---|---|
| one sample t-test | test whether a sample mean significantly differs from a hypothesized value (assumes your vairable is normally distributed) | t.test(data, mu = meanToTest) |
| one sample median test | test whether a sample median differs significantly from a hypothesized value (does not assume your variable is normally distributed) | wilcox.test(data, mu = medianToTest, alternative = "two.sided") |
| binomial test | test whether the proportion of successes on a two-level categorical dependent variable significantly differs from a hypothesized value - | binom.test(numberOfActualSuccesses, numberOfTrialsYouDo, probabilityOfSuccessToTest) |
| chi-square goodness of fit | test whether the observed proportions for a categorical variable differ from hypothesized proportions | chisq.test(vectorOfCounts, hypothesizedProportions) |
1 Dependent Variable/ 1 Independent Variables with 2 Levels
| statistical test | description | example in R |
|---|---|---|
| two independent samples t-test | compare the means of a normally distributed dependent variable for two independent groups | t.test(data1, data2) |
| wilcoxon-mann-whitney test | non-parametric analog to the independent samples t-test and can be used when the dependent variable is not normally distributed | wilcox.test(data1, data2, alternative = "two.sided") |
| chi-square test | tests for a relationship between two categorical variables (makes the assumption that each cell has at least 5 when you split by table!) | chisq.test(table(variable1,variable2)) |
| fisher’s exact test | tests for a relationship between two categorical variables, but can be used when cells have counts less than 5 | fisher.test(table(variable1,variable2)) |
1 Dependent Variable/ 1 Independent Variables with 2 or More Levels
| statistical test | description | example in R |
|---|---|---|
| one-way analysis of variance(ANOVA) | test for differences in the means of the dependent variable broken down by the levels of the independent variable - assumes dependent variable is normally distributed, variances for each of the groups are the same | aov(numericDependentVariable ~ categoricalIndependentVariable, data = dataFrameWithBothVariables) |
| analysis of co-variance(ANCOVA) | test for differences in the means of the dependent variable broken down by the levels of two independent variable - assumes dependent variable is normally distributed, variances for each of the groups are the same | aov(numericDependentVariable ~ categoricalIndependentVariable1+categoricalIndependentVariable2, data = dataFrameWithBothVariables) |
| shapiro-wilk test | tests for normality of a variable - small p-value = not normally distributed / big p-value = is normally distributed | shapiro.test(variableToTest) |
| levene test | tests for differences in variances among groups - small p-value = there are differences among groups / big p-value = no differences among groups | levene.test(numericDependentVariable ~ categoricalIndependentVariable, data = dataFrameWithBothVariables) |
| kruskal wallis test | test for differences between a dependent variable broken down by the levels of the independent variable - non-parametric alternative to one way anova, does not assume normality or equal variances | kruskal.test(numericDependentVariable ~ categoricalIndependentVariable, data = dataFrameWithBothVariables) |
1 Dependent Variable/ 1 Independent Variables with 2 Paired Levels
| statistical test | description | example in R |
|---|---|---|
| paired t-test | compare the means of a normally distributed dependent variable for two dependent/related groups | t.test(data1, data2, paired = TRUE, alternative = "two.sided") |
| wilcoxon signed rank sum test | non-parametric version of paired t-test - does not assume normality | wilcox.test(data1, data2, paired = TRUE, alternative = "two.sided") |
| mcnemar test | tests for differences in proportions between paired data - like before and after some event | mcnemar.test(table(pairedVariable1,pairedVariable2)) |
1 Dependent Variable/ 1 Independent Variables with 2 or More Paired Levels
| statistical test | description | example in R |
|---|---|---|
| one-way repeated measures analysis of variance(ANOVA) | tests for differences between the means of three or more groups where the same subjects show up in each group | aov(numericDependentVariable~factor(categoricalVariableThatChanges)+Error(factor(subject)), data = dataFrameWithAllVariables) |
| friedman test | non-parametric alternative to the one-way repeated measures ANOVA | friedman.test(y=numericDependentVariable, groups=categoricalVariableThatChanges, blocks=subjects) |
1 Dependent Variable/ 1 Numeric Independent Variables
| statistical test | description | example in R |
|---|---|---|
| correlation | tests for a relationship between normally distributed variables | cor.test(variable1, variable2, method="pearson") |
| non-parametric correlation | tests for a relationship between non-normally distributed variables | cor.test(variable1, variable2, method="spearman") |
2 or More Dependent Variables/ 2 Independent Variables with 2 or More Levels
| statistical test | description | example in R |
|---|---|---|
| one-way multivariate analysis of variance(MANOVA) | assess how two or more dependent variables are affected by a categorical variable | manova(cbind(numericDependentVariable1, numericDependentVariable2) ~ independentCategoricalVariable, data = dataframeWithAllTheVariables) |
References