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 Test | Short Description of Inferential Test |
|---|---|---|
| 1) | Z test | Large sample test for one mean/average when sigma ($\sigma$) is known (or $n$ is large), population distribution is normal. |
| 2) | t test | Small sample test for one mean/average when sigma ($\sigma$) is unknown (and $n$ is small), population distribution is normal. |
| 3) | Z test | Large sample test for one proportion. |
| 4) | Z test | Small 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 test | Small 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. |
| 6) | t test | Small 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 test | A test for two means/averages for dependent (paired or related) samples where $d$ (The difference between samples) is normally distributed. |
| 8) | Z test | Large 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 test | Test 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 Q | A multiple comparison test for all pairs of means (usually for equal sample sizes). |
| 15) | Dunnett q | A 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) | Slope | Test on the slope of the linear regression line. |
| 19) | Intercept | Intercept 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 Tests | Short Description of Inferential Statistics Tests |
|---|---|---|
| 1) | Runs Test | Used to determine whether the sequence of data is random. |
| 2) | Mann-Whitney U Test | Analogous to Test # 5 from Parametric test list. |
| 3) | Sign Test | Analogous to Test # 2 from Parametric Test (Single sample Median Test). or Test # 7 from Parametric Test. |
| 4) | Wilcoxon Signed-Ranked Test | Similar to the sign test, but more efficient, analogous to Parametric Test # 7. |
| 5) | Kruskal-Wallis Test | Analogous to Parametric Test # 13. |
| 6) | Multiple Comparison Test | Analogous to Parametric Test # 14. |
| 7) | Spearmna $r_s$ Rank Correlation | Analogous 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 Test | Short Description of Inferential Statistics Tests |
|---|---|---|
| 1) | Two-factor ANOVA With Replication | Interaction is possible between two factors. |
| 2) | Two-factor ANOVA Without Replication | Only one observation per cell; no interaction effect is observed between the two factors. |
| 3) | One Datum Stat | Used to compare one piece of data (datum) to a mean. |
| 4) | McNemar StAt | Used to test a 2 x 2 table of matched discordant pairs. |
| 5) | Two Poisson Counts | Used to compare two Poisson counts. |
| 6) | Two Regression Slopes | Used to compare two regression equation slopes. |
| 7) | Several Regression Slopes | Used to compare several regression equation slopes. |
| 8) | Multiple Regression | Used to test a linear relationship with more than two variables. |
| 9) | Holgate Statistic | Used to determine spatial distribution. |
