# Hypothesis testing

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

## Significance of P-value:

P-value ≤ α ⇒ Reject H0 at level α

P-value > α ⇒ Do not reject H0 at level α

## When to Reject H0

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.

## When to use what?

**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 |

SUBMIT ASSIGNMENT NOW!