Contigency Table the Proportion of Teachers Agreeing that Sex Education should be Taught in Primary School
Introduction
A group of 120 teachers were asked: "Do you 'agree' or 'disagree' that sex education should be taught to primary school children? Their responses were recorded as follows:
The two-variable classification of data presented in the table above is called a contingency table because the objective of the study is to investigate whether the proportion of teachers who agree or disagree whether sex education should be taugh in the primary school depend (or are contingent) on gender of respondents. Thus, the purpose of of a contengency table analysis is to determine whether a dependence exists between two qualitative variables (gender and opinion).
Gender Agree Disagree TOTAL
(%) (%) (%)
Males 37.5 62.5 100
(n=45) (n=75) (n=120)
Females 58.3 41.6 100
(n=70) (n=50) (n=120)
The data in the contingency table can also be expressed as percentages of the total number of teachers interviewed. Note that generally more females agreed than males who agreed that that sex education should be taught in the primary school.
Can we draw the conclusion that opinion on teaching sex education in primary varies between male and female teachers?
OR
Can the differences in percentages between males and females be attributed to sampling variation?
Percentage of Teachers' Agreeing that Sex
Education should be Taught in Primary School
To answer this question, you will need to conduct a contigency analysis. What is a contengency analysis? You need to test the null hypothesis that the distributions of percentages are identical for both males and females. If you are able to reject the this hypothesis, you will be able to conclude that the differences seen in the table above are not due to chance but are likely differences in the population of male and female teachers.
Let us suppose the distributions of respondents observed for those who agreed and disagreed are identical for males and females. i.e. the distribution of respondents is independent of gender. One method of detecting a difference in the distributions of the responses is to compare the observed number of responses in each of the FOUR CELLS to the number of responses we would expect to see if in fact the reponses were identical. The larger the deviations or differences between the OBSERVED numbers and their respective EXPECTED numbers, the more evidence that there the responses are different.
Gender Agree Disagree TOTAL
(n) (n)
Males 45 75 120
Females 70 50 120
Contigency Table the Proportion of Teachers Agreeing that Sex Education should be Taught in Primary School
