Chi-square test

1. Chi-square test

We will now explain how to use the chi-square test of independence to analyze surveys.

2. Chi-square test

The chi-square test is a statistical method used to make inferences about the distribution of a categorical variable. It compares actual observations to expected observations of categorical variables.

3. Chi-square test in survey analysis

In survey analysis, it helps us to determine whether there is a relationship between two categorical variables of a population. The null hypothesis indicates that the two variables are independent and have no relationship. The alternate hypothesis indicates that there is a relationship between both variables. If the p-value is significant, with less than 0-point-05, we can reject the null hypothesis and claim that the findings support the alternative hypothesis.

4. Why use chi-square testing in survey analysis

The chi-square test is important in survey analysis because we need to know if the input variables are relevant to the output variable; this helps us better understand the impact of different variables on the population and checks if the differences we see are by chance, or statistically significant.

5. Assumptions of chi-square test on survey analysis

Assumptions associated with this test are that the two variables analyzed are categorical, that the sample data is randomly selected from the population and is greater than 100, and that the expected frequencies are greater than five. Let's see how we test for these with an example.

6. Survey data for chi-square analysis

Here is the sample of results of a survey given to pet owners. It asks the type of pet they own, the number of pets they currently have, and the amount of time they spend with their pets, and whether having a pet decreases stress.

7. Survey data for chi-square analysis

The random sample set we have has more than 100 entries, and the two categorical variables we are testing are the pet type owned and whether having a pet decreases stress. Our null hypothesis is that there is NO relationship between the type of pet owned and the owner's perceived reduced stress, while the alternate hypothesis is that there IS a relationship between the type of pet owned and owner's perceived reduced stress.

8. Steps of chi-square analysis on pet_survey in python

To analyze this in Python, we first import pandas and scipy-dot-stats. Second, we perform a cross tabulation of the two groups and assign it to a variable. Then, we pass that variable to a chi-square contingency method to conduct the chi-square test of independence.

9. Result and interpretation of pet_survey

Once the results are calculated, we check them. We ensure sure that the expected frequencies, or the fourth part of the output, are greater than or equal to five. The expected frequencies are the values we would expect to see if the null hypothesis is true for our population. Here, the expected frequencies are greater or equal to five, therefore the chi-squared test results can be trusted. The second part of the output is the p-value; if it is less than 0-point-05, we reject the hypothesis. The p-value is less than 0-point-05. Therefore, we reject the null hypothesis that a pet owner experiencing stress reduction and the type of pet they own, are unrelated. In conclusion, the type of pet owned has an effect on whether pet owners perceive stress reduction.

10. Let's practice!

Now it's your turn to practice!

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