1. Hypothesis Testing with the Chi-squared test
On to our last hypothesis test statistic. The chi-squared test.
2. Applications of the chi-squared test
Chi-squared tests are used all the time. When you are doing research you often have a set of prior observations and after some treatment like applying a new drug you need to know if the treatment actually made a difference. This is determined with the chi-squared test.
3. Testing before and after
When you have prior observations and a new sample you are left with two choices...the difference in the new group stems from random sampling variations OR that there is in fact a meaningful difference. These two choices are used for the NULL and alternate hypotheses. Further as before the chi square tests will provide a probability that the two groups are independent, or truly different.
4. Chi-squared test conditions
For a chi-square test to be useful keep in mind the data has to be in groups such as old treatment, and new treatment or values based on gender or other dividing data characteristic. Lastly, chi square tests break down with really small expected values. The general consensus is that the expected numbers you are measuring should be greater than 5. Otherwise you will need to perform different tests, which aren't covered in this introductory course.
5. Testing the independence of two groups
When you see drug or supplement commercials with before and after pictures purporting to help with weight loss they often use statements like "clinically proven" or "lab tested". In order to make claims about how the drug improves outcomes ethically and legally, the owners need to create an experiment controlling for lifestyle factors and ultimately comparing weight within two groups one treated with the supplement and the other not. Its in this lab or clinic that a chi squared test is often performed to test the independence of the two groups.
6. Chi-squared test in Google Sheets
To perform a chi squared test in sheets, use the CHITEST function. Since you are reviewing the independence of two groups, you first pass in the observed group and then the expected group. As before the probability is returned. So you Fail to Reject the NULL hypothesis if the value is greater than 0 point 05. And the converse is still true REJECT the NULL hypothesis when p-values are less than 0 point 05.
7. Let's practice!
Last part of these dreaded hypothesis test methods. Its tough but worthwhile as you apply statistical inferences to your data. Enjoy!