Inferential Statistics Tests List

The following is the list of different parametric and non-parametric lists of the Inferential Statistics Tests List. A short description of each Inferential Statistics Test is also provided.

Inferential Statistics Tests: Parametric Statistics

Sr. No.Statistical TestShort Description of Inferential Test
1)Z testLarge sample test for one mean/average when sigma ($\sigma$) is known (or $n$ is large), population distribution is normal.
2)t testSmall sample test for one mean/average when sigma ($\sigma$) is unknown (and $n$ is small), population distribution is normal.
3)Z testLarge sample test for one proportion.
4)Z testSmall sample test for two means/averages when sigmas ($\sigma_1$ and $\sigma_2$) are unknown, samples are independent, and are from normal populations. The variances are NOT pooled.
5)t testSmall sample test for two means/averages when sigmas ($\sigma_1$ and $\sigma_2$) are unknown, samples are independent, and are from normal populations. The variances are pooled.
6)t testSmall sample test for two means/averages when sigmas ($\sigma_1$ and $\sigma_2$) are unknown, samples are independent and are from normal populations. The variances are NOT pooled.
7)t testA test for two means/averages for dependent (paired or related) samples where $d$ (The difference between samples) is normally distributed.
8)Z testLarge sample test for two proportions.
9)$\chi^2$Chi-square goodness of fit, or multinomial distribution., where each expected value is at least 5.
10)$\chi^2_{ii}$Chi-square for contingency tables (rows & columns) where each expected value is at least 5.
Either a test of independence, a test of homogeneity, or a test of association.
11)$\chi^2$Test for one variance or standard deviation.
12)F testTest for two variances or standard deviations for independent samples from the normal populations.
13)F (Anova)Test for three or more means for independent random samples from normal populations. The variances are assumed to be equal.
14)Tukey QA multiple comparison test for all pairs of means (usually for equal sample sizes).
15)Dunnett qA multiple comparison test for a control mean to other means.
16)Hartley H,
Bartlett,
Levene,
Brown-Forsythe,
O’Brien
Test for homoscedasticity, and homogeneity of variances.
17)Pearson $r$Pearson product-moment correlation coefficient.
18)SlopeTest on the slope of the linear regression line.
19)InterceptIntercept Test on the y-intercept of the linear regression line.

Inferential Statistics Tests: Non-Parametric Tests

The following is the list of non-parametric Tests with a short description of the tests.

Sr. No.Statistical TestsShort Description of Inferential Statistics Tests
1)Runs TestUsed to determine whether the sequence of data is random.
2)Mann-Whitney U TestAnalogous to Test # 5 from Parametric test list.
3)Sign TestAnalogous to Test # 2 from Parametric Test (Single sample Median Test). or Test # 7 from Parametric Test.
4)Wilcoxon Signed-Ranked TestSimilar to the sign test, but more efficient, analogous to Parametric Test # 7.
5)Kruskal-Wallis TestAnalogous to Parametric Test # 13.
6)Multiple Comparison TestAnalogous to Parametric Test # 14.
7)Spearmna $r_s$ Rank CorrelationAnalogous to Parametric Test # 15.

Advanced Inferential Statistics Tests

Following is the list of some advanced inferential Statistics tests with a short description of the test.

Sr. No. Statistical TestShort Description of Inferential Statistics Tests
1)Two-factor ANOVA With ReplicationInteraction is possible between two factors.
2)Two-factor ANOVA Without ReplicationOnly one observation per cell; no interaction effect is observed between the two factors.
3)One Datum StatUsed to compare one piece of data (datum) to a mean.
4)McNemar StAtUsed to test a 2 x 2 table of matched discordant pairs.
5)Two Poisson CountsUsed to compare two Poisson counts.
6)Two Regression SlopesUsed to compare two regression equation slopes.
7)Several Regression SlopesUsed to compare several regression equation slopes.
8)Multiple RegressionUsed to test a linear relationship with more than two variables.
9)Holgate StatisticUsed to determine spatial distribution.
Inferential Statistics Tests

Learn about Estimate and Estimation

Learn R Programming Language