# Hypothesis Testing

**Understanding Hypothesis Testing**

- Hypothesis testing involves making
**assumptions**about a population, based on sample data. - The initial assumption made is known as the
**Null Hypothesis (H**._{0}) - An alternative to this initial assumption is called the
**Alternative Hypothesis (H**._{1}) - These hypotheses are mutually exclusive meaning if one is true, the other must be false.

**Steps in Hypothesis Testing**

- Step 1: Define the
**Null Hypothesis (H**and_{0})**Alternative Hypothesis (H**._{1}) - Step 2: Choose a
**significance level**(commonly 0.05), which determines the probability of rejecting the null hypothesis if it is true. - Step 3: Collect and summarise the sample data through a
**test statistic**. - Step 4: Calculate the
**probability**of the observed test statistic under the null hypothesis (the p-value). - Step 5:
**Compare**the p-value to the significance level to decide whether to reject the null hypothesis.

**Types of Hypotheses**

- The
**Null Hypothesis (H**states that there is no effect or difference – this is the hypothesis that the test seeks evidence against._{0}) - The
**Alternative Hypothesis (H**is the statement of what a hypothesis test is seeking to prove._{1})

**Types of Errors in Hypothesis Testing**

- A
**Type I error**occurs when the null hypothesis is true, but is falsely rejected. It is equivalent to a false positive finding. - A
**Type II error**is the opposite, occurring when an incorrect null hypothesis is not rejected. It equates to a false negative finding.

**One-tailed and Two-tailed Tests**

- A
**one-tailed (or one-sided) test**is used when the direction of the effect being tested is known (greater than or less than). - A
**two-tailed (or two-sided) test**is used when the direction of the effect is not known or is not relevant to the hypothesis.

**Understanding p-values**

- The
**p-value**is the probability, under the null hypothesis, of obtaining a result equal to or more extreme than what was actually observed. - If the p-value is small (typically ≤ 0.05), it is possible to
**reject the null hypothesis**in favour of the alternative hypothesis. - The p-value alone does not determine the significance of a test result. Other factors, such as the science being tested and the consequences of a wrong conclusion, should be considered.

**Power and Sample Size**

**Statistical power**is the probability of correctly rejecting a false null hypothesis. It’s affected by the sample size, variance, significance level, and effect size.- An appropriately large sample size increases the power of a statistical test.