1. SADC Course in Statistics Revision on tests for proportions using CAST (Session 18)

2. To put your footer here go to View > Header and Footer 2 Learning Objectives By the end of this session, you will be able to discuss how two proportions may be compared using an z-test or several proportions compared using a chi-squared test set up hypotheses to test for independence between two categorical variables have a greater understanding of testing procedures and underlying assumptions when dealing with categorical variables

3. To put your footer here go to View > Header and Footer 3 Using CAST for SADC: Higher Level Further insight into the concepts introduced in sessions 14 and 15 can be obtained by working through some of the pages of CAST in Sections 8 and 9 Practical work using CAST will therefore form the main activity in this session Here we will just highlight a few of the features that the above pages in CAST aim to demonstrate

4. To put your footer here go to View > Header and Footer 4 CAST – Section 8.2 Consider CAST Section 8.2: Hypothesis test for difference This section has 2 sub-sections as follows: Testing for differences between probabilities Exercises about testing hypotheses Both these pages give a good illustration of the testing procedure for comparing two proportions. Evaluation and interpretation of p-values is re-enforced.

5. To put your footer here go to View > Header and Footer 5 CAST – Section 9.3 Consider CAST Section 9.3: Testing for independence This section has 6 sub-sections as follows: Independence from samples Testing for independence Chi-squared test statistic P-value for ch-squared test Examples Comparing groups

6. To put your footer here go to View > Header and Footer 6 CAST – Section 9.3 – Page 1 This section is aimed at showing clearly the meaning of independence using numerical examples the calculations of expected values under the hypothesis of independence are clarified The illustrations are clear and easy to follow.

7. To put your footer here go to View > Header and Footer 7 CAST – Section 9.3 – Page 2 This section is aimed at showing the need to compare observed and expected frequencies in order to judge whether two categorical variables are independent difficulties caused if the comparison is made by only looking at the deviation sums of squares between observed and expected values, e.g. due to its dependence on the sample size

8. To put your footer here go to View > Header and Footer 8 CAST – Section 9.3 – Page 3 This section illustrates quite a few points: The justification for the formula used in computing thechi-squared test statistic A simulation exercise to demonstrate that the 2 is little affected by changes in sample size Graphical demonstration to show –how the shape of the 2 changes to a more symmetric shape as its d.f. increases –That the mean of the 2 equals its d.f.

9. To put your footer here go to View > Header and Footer 9 CAST – Section 9.3 – Page 4 This section is aimed at: showing how the chi-squared test for independence is carried out graphically illustrating exactly what the p- value is and how it may be interpreted recognising that the chi-squared test is an approximate test and highlighting conditions under which it yields a reliable p- value

10. To put your footer here go to View > Header and Footer 10 CAST – Section 9.3 – Pages 5 & 6 These sections show: further illustrative examples how the test of independence can be extended to situations where interest lies in comparing several groups –e.g. comparing two proportions is equivalent to performing a chi-square test on a 2x2 table of frequency counts.

11. To put your footer here go to View > Header and Footer 11 Practical work on CAST follows…