A researcher asked 921 people what their favorite type of TV program was: news, documentary, soap or sports. They could only choose one answer. As such, the researcher had the number of people who chose each category of programme. How should she analyse these data?
Question
A researcher asked 921 people what their favorite type of TV program was: news, documentary, soap or sports. They could only choose one answer. As such, the researcher had the number of people who chose each category of programme. How should she analyse these data?
Solution
The researcher should analyze these data using a chi-square test for goodness of fit. This test will allow the researcher to determine if there is a significant difference in the number of people who prefer each type of TV program. The chi-square test for goodness of fit is appropriate for this analysis because the data are categorical and the researcher is interested in whether the observed distribution of preferences fits an expected distribution. The steps for this analysis would be:
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Calculate the expected frequencies for each category (news, documentary, soap, sports). If there is no information about what to expect, the researcher might assume that each category is equally likely, so each expected frequency would be the total number of people divided by the number of categories.
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Calculate the chi-square statistic, which is the sum of the squared differences between observed and expected frequencies, divided by the expected frequency, for each category.
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Determine the degrees of freedom, which is the number of categories minus one.
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Use the chi-square distribution with the appropriate degrees of freedom to find the p-value associated with the calculated chi-square statistic.
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If the p-value is less than the chosen significance level (often 0.05), reject the null hypothesis that the observed distribution fits the expected distribution. This would mean that there is a significant difference in the number of people who prefer each type of TV program.
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