Statistical Hypothesis Testing

Basics of Hypothesis Testing

Understand Hypothesis Testing as a statistical method that is used in making statistical decisions using experimental data.
Familiarise with the term Null Hypothesis (H0), which is the statement being tested, usually a statement of no effect or no difference.
Know the concept of Alternative Hypothesis (H1 or Ha), it is a statement that there is an effect or difference.
Comprehend the Test Statistic, it is calculated from sample data and used in the test of hypothesis.

Identify a Type I Error, when the null hypothesis is true, but is rejected. It is equal to the level of significance (α).
Differentiate it from a Type II Error, when the null hypothesis is false, but erroneously not rejected. It is not usually possible to identify a Type II error, but it can be controlled.

Understand the concept of Level of Significance, typically a small predetermined value such as 0.05.
Grasp the idea of the Critical Region, if the test statistic falls within this region, the null hypothesis is rejected.
Know the P-Value, the smallest level of significance at which the null hypothesis would be rejected.
The Power of the Test is the probability of correctly rejecting a false null hypothesis.

Understand the general sequence in conducting a statistical hypothesis test: State the null and alternative hypotheses, choose the level of significance, estimate the probability of the sample outcome under the null hypothesis, reject or do not reject the null hypothesis.
Recognise the different methods of hypothesis testing: Chi-Squared Test, Student’s T-Test, F-Test, each is suitable for the data and hypothesis being tested.

Comprehend that hypothesis testing is used extensively in various fields like market research, drug testing, manufacturing quality control, etc.
Understand the importance of considering both probabilities of Type I and Type II errors in interpreting results of tests.

Regularly practise constructing hypotheses, and applying appropriate tests.
Familiarise yourself with interpreting test results, including understanding statistical significance and making decisions based on p-values.
Try a broad range of problems, recognising which types of test are suitable for which situations.
Persist with challenging problems; understanding statistical hypothesis testing thoroughly is achievable with determination and effort.