POLI 443 Applied Political Research
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1 POLI 443 Applied Political Research Session 6: Tests of Hypotheses Contingency Analysis Lecturer: Prof. A. Essuman-Johnson, Dept. of Political Science Contact Information: College of Education School of Continuing and Distance Education 2014/ /2017
2 CONTINGENCY ANALYSIS CHI-SQUARE TEST This refers to the idea of applying correlation to qualitative or non quantitative data. Contingency analysis deals with computing the relationship between two qualitative variables. As a test of the significance between two qualitative variables the computations assume that there is no relation between the two variables. On the basis of this assumption, a critical or expected frequencies are computed. Slide 2
3 The difference between the values given (observed values) and the expected values are compared and the greater the difference between the expected and observed frequencies, the stronger the relationship between the two variables. The usual measure of the discrepancy between the observed and expected frequencies is the chi-square test. It is defined as follows: χ 2 = (O F E F ) 2 /E F Slide 3
4 Steps to follow in the χ 2 Test Step 1: Set the Null (H O ) & Alternative (H A ) hypothesis Step 2: Select the test statistic i.e. T = χ 2 = (O F E F ) 2 /E F Step 3: Compute the Expected frequencies (E F ) for the data where E F = (R T )(C T )/N Step 4: Develop working sheet to compute χ 2 from the O F and E F values Step 5: Calculate DF and use it with the given probability level to read χ 2 from table Slide 4
5 Step 6: Set the DR (Decision Rule) as basis for accepting or rejection the Null hypothesis Step 7: Draw conclusion: Compare the Calculated χ 2 (from the working sheet) and χ 2 read from the table and decide whether to accept or reject the H O and H A Illustration A study was conducted about the relationship between region and party vote of 412 voters during one general election in Ghana with the following data: Slide 5
6 Party Vote Ashanti Region Volta NDC NPP Using a 5% level of significance determine if a relationship exist between Region and Party Vote. Slide 6
7 Solution Step 1: Set the Null (H O ) & Alternative (H A ) hypothesis H O: There is no relationship between region and party vote H A : There is a significant relationship between region and party vote Step 2: Select the test statistic i.e. T = χ 2 = (O F E F ) 2 /E F Slide 7
8 Step 3: Compute the Expected frequencies (E F ) for the data where E F = (R T )(C T )/N Computations: 111 = (195)(206)/412 = = (217)(206)/412 = = (217)(206)/412 = = (195)(206)/412 = 97.5 Slide 8
9 Step 4: Developthe working sheet to compute χ 2 from the O F and E F values O F E F O F - E F (O F - E F ) 2 (O F - E F ) 2 /E F Slide 9
10 Step 5: Calculate DF (Degree of freedom) and use it with the given probability level to read χ 2 from table. DF = (#Rows 1)(#Columns 1) for a 2 by 2 table (2-1)(2-1) = 1 x 1 From χ 2 tables at 5% with 1 df, χ 2 = Slide 10
11 Step 6: Set the DR (Decision Rule) as basis for accepting or rejection the Null hypothesis: Accept H o if χ 2 calculated > χ 2 expected (from tables for 5%) Accept H o if χ 2 calculated (7.10) is < χ 2 expected (from tables for 5%) Reject H o otherwise Slide 11
12 Step 7: Draw conclusion: Compare the Calculated χ 2 (from the working sheet) and χ 2 expected (read from the table) and decide whether to accept or reject the H O and H A Conclusion: The calculated χ 2 (7.10) is > χ 2 from tables which means that our calculated χ 2 of 7.1 is significant at 5% level and we reject H o and conclude (with 95% confidence) that there is a relationship between Region and Party vote i.e. region influences how people vote. Slide 12
13 THANK YOU Slide 13
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