Many people embarrass themselves by saying CHEE - Square. Well, how many people really use this in regular conversation? The following illustration will give you the correct pronunciation! It's like the beginning of KI TE . Chi-square is an incredibly useful statistic. What it does is test whether one set of proportions is different from another. It does this by comparing frequencies . 2
3 Up to this point, the inference to the population has been concerned with “scores” on one or more variables, such as SAT scores, mathematics achievement, and hours spent on the computer. We used these scores to make the inferences about population means. To be sure not all research questions involve score data. Today the data that we analyze consists of frequencies; that is, the number of individuals falling into categories . In other words, the variables are measured on a nominal scale. The test statistic for frequency data is Pearson Chi-Square. The magnitude of Pearson Chi- Square reflects the amount of discrepancy between observed frequencies and expected frequencies.
You are hired as a statistician by a disgruntled employee who says that the company discriminates on the basis of gender. The employee's evidence - there are 6 male mangers and 4 female managers . Let's look at the complaint : There are 10 managers. If there were perfect gender equality - then you would expect 5 males and 5 females . That would be a 50-50 split based on equal proportions of .5 and .5 or 50% vs. 50% Expected Males = 5 Expected Females = 5 However, she observed 6 males and 4 females . This is a 60-40 split and the observed is different from the expected. In other words: 4
But, you tell your client that's not good enough evidence. You make up the following chart: It's just chance. The office could be 5 males or 5 females and the change of one person would make it 6 to 4. It could have just as easily been 4 males or 6 females. Intuitively, you can see that it would be hard to convince someone that this 60 - 40 split is discrimination. It's too easy to be just luck. 5
What if the company only had 5 managers in the office? With an odd number of managers, there will always be one more male OR female. So, this ISN’T discrimination, mostly because our numbers are too small. 6
If you understand these pictures, you understand chi- square's purpose . You have a set of proportions that you think should be true (Expected) and you test them against a set that you have observed (Observed) . In this case, the differences between the proportions of male and female managers could easily be chance as the value of O - E is very small Your client won't give up. She says "I will get data from all the company's offices across the city. I will measure 100 people – not just ten!" Ok. If there were no discrimination, you should get the following picture with 50 men and 50 women .
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- Spring '18
- Donald Sweeney
- Chi-Square Test, Statistical tests, Chi-square distribution, Pearson's chi-square test, Non-parametric statistics