Hypothesis Testing Concepts and Theory Notes

Hypothesis Testing Procedure -> 8 steps 1. Formulate NULL (Ho) or Alternative Hypothesis ↓ 2. Choose the relevant test and appropriate probability distribution ↓ 3. Choose the critical value * Input from left: Determine the significance level * Input from right: Determine the Degree of Freedom ↓ 4. Collect data & Calculate test statistic ↓ 5. Compare the test statistic with the critical value ↓ 6. Does the test statistic fall in the critical region or region of rejection? * Yes -> Reject the null hypothesis (Ho) * No -> Accept the null Hypothesis (Ho) ① Formulate the Hypothesis (Null or Alternative) Research understanding the researcher starts with defining the problem clearly. After that he/she is in a position to formulate the hypothesis Null or alternative. Null Hypothesis (H₀) assumes no significant difference exists between the population median and hypothesis sample mean (μH₀). Alternative Hypothesis (Hₐ) assumes that a significant difference exists between μ and some μH₀. ② Select Relevant test & Probability Distribution Choice of probability distribution depends upon the the purpose of hypothesis test. The researcher should carefully see how the test statistic is computed and which sampling distribution is it following i.e. normal, t-normal or poisson. ③ Choose Critical value is the criteria of accepting or rejecting null hypothesis. This involves the decision regarding: → Level of significance → should be specified in %. → Degree of Freedom → denoted by n → One Tailed or Two-tailed test. * rejection region on one side * rejection region on both sides ④ Collect data & Test statistics → The next stage involves drawing a sample and collecting data using a data collection strategy that suits the purpose of study. From this, test statistic is computed. It is this test statistic that determines, how close the sample is to null hypothesis. (5) Comparing the test-statistic with the critical value It is a crucial stage where the critical from last phase value of test statistic is computed. Example :- If 'Z' distribution is being used then to test a two-tailed test @ 5% level of significance with degree of freedom (n-1), involves calculating of 'Z' value from the sample data. Above value, is then compared to Z critical value @ 5% (1.96) (6) Taking the Final Decision :- Now the researcher has to take a decision of accepting or rejecting the null hypothesis (Ho). e.g. In case of Z-test, if computed value of Z @ 5% level of significance is more than 1.96 then the Ho will be rejected and alternative (Hₐ) will be accepted. Types of Hypothesis tests A. Parametric One Sample t-test Chi-square (χ² test) Z-test Two Samples Independent Samples Two group t-test F-test Z-test Paired samples Paired t-test B. Non-Parametric One Sample χ² test Runs test Two Samples Independent Samples Chi-Square Mann Whitney Kruskall-Wallis Dependent Samples Sign Test Wilcoxon Test Chi-Square Mc Nemar test