Hypothesis Testing Overview

Study Notes

Hypothesis testing is a statistical method used to determine if there is enough evidence to support a hypothesis about a population, based on sample data.
It plays a crucial role in scientific research, helping to make data-driven decisions and validate research findings.

State the hypotheses:
- Null hypothesis (H0): States no effect or difference. It serves as the starting assumption.
- Alternative hypothesis (Ha): States an effect or difference. It is what you want to prove.
Choose the significance level (α): The probability of rejecting the null hypothesis when it is true, often set at 0.05 (5%) or 0.01 (1%).
Collect and summarize the data: Obtain a sample and calculate relevant statistics, such as mean, standard deviation, or proportion.
Calculate the test statistic: Determine a value based on the data to help decide whether to reject or not reject the null hypothesis.
Determine the p-value: The probability of obtaining the observed results if the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis.
Make a decision:
- If the p-value ≤ α, reject the null hypothesis.
- If the p-value > α, do not reject the null hypothesis.

p-value: The probability, assuming no effect, of obtaining results as extreme as those observed. A smaller p-value indicates stronger evidence against the null hypothesis.
Significance level (α): The threshold for rejecting the null hypothesis, often set at 0.05 (5%).
Decision rule: If the p-value is less than or equal to the significance level, reject the null hypothesis. Otherwise, do not reject the null hypothesis.

Type I error (α): Rejecting the null hypothesis when it is true (false positive). For example, concluding a drug is effective when it is not.
Type II error (β): Failing to reject the null hypothesis when it is false (false negative). For example, concluding a drug is not effective when it actually is.