Hypothesis tests can be one sided or two sided tests as explained below.
One tailed tests are directional in nature:
H0: µ1 - μ2 ≤ 0
H1: μ1 - μ2 > 0
This is a one-tailed test in which the critical region lies in the right-tail of the test statistic.
Two tailed tests are not directional:
H0: μ1 - μ2 = 0
H1: μ1 - μ2 ≠ 0
P-value ≤ α ⇒ Reject H0 at level α
P-value > α ⇒ Do not reject H0 at level α
Denoting our subject probability as follows:
Level of significance, α:It is defined before doing hypothesis test and is used to decide rejection region
Rejection region: Region outside the confidence interval as shown below.
| Comparison of means | Parametric Tests | Non-parametric Tests |
| Differences between the means of two independent groups | Independent t-test | Mann-Whitney test |
| Differences between paired (matched) samples e.g. weight before and after a diet for each subject | Paired t-test | Wilcoxon signed rank test |
| Differences in the means of 3+ independent groups for one variable | One-way ANOVA | One-way ANOVA |
| Differences between 3+ measurements on the same subject | Repeated Measures ANOVA | Friedman test |
| Strength of a relationship between 2 continuous variables | Pearson's Correlation Co-efficient | Spearman's Correlation co-efficient |
| Predicting the value of one variable given the value of a predictor variable | Simple Linear Regression | |
| Assessing the relationship between two categorical variables. | Chi-squared test |
