HYPOTHESES Terminology - The Null Hypothesis (H0) => the original hypothesis we are testing. - The Alternative Hypothesis (H1) => the new hypothesis it could potentially replace. The 1. 2. 3. 4. 5. 6. 7.
Process‌ State H0, H1 Select the test statistic Specify the level of significance State the decision rule regarding the hypothesis Collect sample and calculate the sample statistics Make a decision regarding the hypothesis Make a decision based on the results of the test
Test Statistic A test statistic is a standardized value which is calculated from a sample data set during a hypothesis. It aids us in comparing the sample to the population and thus allows us to make a decision regarding the null hypothesis.
Error Types - Type I Error => reject the H0 given that it is true. - Type II Error => fail to reject the H0 given that it is false. Significance, Confidence and Power
p-Value The p-value is the smallest significance level for which we reject the null hypothesis. Example 1: with a p-value of 7% and a significance level of 5% => fail to reject H0 Example 2: with a p-value of 7% and a significance level of 10% => reject H0 Test Statistics t-statistic if the variance is unknown…
z-statistic if the variance is known…
Two Samples - Normal and Independent… “difference in means” by t-statistic. a) If σ12 = σ22 (assumed) => denominator uses σ2 b) If σ12 ≠ σ22 (assumed) => denominator uses combination of σ1 and σ2. - Normal and Dependent… “mean of the differences” by t-statistic; testing if σ1 = σ2.
Chi-Squared Test, Χ2 Tests the population variance to the sample variance…
F-test
Tests two variances (both independent and normal) to see which variance best fits the population from which the samples have been taken.
[Tip: remember “larger/smaller” for the numerator-denominator relationship.]
Parametric Tests Like those we have seen above both… 1. Make assumptions of distribution, and 2. Use population parameters
Non-parametric tests For example ‘Spearman’s Rank’ are used when parametric tests aren’t suitable. These either… 1. Don’t consider population parameters, or 2. Make few assumptions