What are the null and alternative hypotheses for the chi square test of independence? Calculate the row and column totals Calculate the expected frequencies for each "cell"
Problem 2:
The research scenario: Do you think there might be a relationships between people's personality and the profession they pursue? Here's a fictional set of data that explores that question.
There are two personality types in the data, 'thinkers' and 'feelers.' There are 3 professions.
A chi square analysis says, OK, there is a certain proportion of people who are thinkers overall (you will be calculating that, but is comes directly from the data). Is that same proportion (or close to it) found among each of the three professions? For example, if the population at large is divided into 50% thinkers and 50% feelers, then 50% of each profession would be thinkers and 50% would be feelers. But maybe some professions have 'lopsided' percentages of feelers, or lopsided percentages of thinkers.
The following crosstab table shows the "crossed" frequencies for 2 variables:
"Myers-Brigg" personality type "T" = "thinking" personality
"F" = "feeling" personality
"profession" clergy
physician
laywer
Blank tables are provided for your calculations.
- What are the null and alternative hypotheses for the chi square test of independence?
- Calculate the row and column totals
- Calculate the expected frequencies for each "cell"
- Using the steps shown in the lecture and in the text, calculate the chi square to investigate whether "personality type" and "profession" are independent of each other or not.
- Compare your calculated chi square to the critical value of chi square per the chi square table in Appendix B, using the correct degrees of freedom.
- Calculate the effect size Cramér's V for the chi square statistic and interpret it.
Given data:
| Clergy | Physicians | Lawyers | |
| "thinking" personality | 114 | 785 | 176 |
| "feeling" personality | 420 | 818 | 95 |
The objective is to test whether there is a relationship between people's personality and the profession they pursue.
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