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|