MATH: Chi-square Statistics

In the upcoming lab activity, you will perform a chi-square test to reveal the statistical significance between two groups of data. It differs from descriptive statistics like standard error and confidence intervals in that it compares observed values to expected values. Chi-square testing checks that experimental results match known or theoretical outcomes. The chi-square test is used to count data, as opposed to data that is measured. In biology, it is often used to analyze the results of genetic crosses, which is something you’ll do in Module 6.

Chi-square hypothesis testing either rejects the null hypothesis or fails to reject it, which means it’s analyzing experimental results to make sure they wouldn’t be that extreme just by chance. Not happening by chance would support an alternative hypothesis. For example, if we were testing out different color lights on the growth of plants, a null hypothesis would state that the color of the light does not affect plant growth and that all plants would be the same height. The alternative hypothesis would state that the plant would be tallest under a certain color of light.

Step 1: Calculate the chi-square value of a given set of data.

The formula for chi-square statistic is: step1 where o is the value of the observed data and e is the value of the expected data. Sigma ( $LaTeX: \sum_{}^{}$ ) means each repeated calculation should be added to the previous one. So, step2 …

Step 2: Determine the critical value for a given set of data.

Here is the table given by the College Board on the AP Biology equation sheet. It is a table of values for 1-8 degrees of freedom at the p=.05 and p=.01 significance level

Find the degree of freedom of your data. It is always your number of categories of data minus 1.
Use a p-value of 0.05, which is the standard p-value used in science.
Find where the p-value and the degrees of freedom intersect. This will be your critical value.

Step 3: Draw conclusions about the experiment based on the comparison of the chi-square value to the critical value.

Answer:

A p-value of 0.05 (5%) or less is considered significant.
If the chi-square value is lower than the critical value, we will fail to reject the null hypothesis because the data pretty well matches with the data we expected.
If the chi-square value is higher than the critical value, we can reject the null hypothesis because our observed data does not fit well with our expected data. There is less than a 5% chance that we would obtain this data if the null were true.

Here is a Chi-square for Hypothesis Testing video about the use of the chi-square statistical test.

Now, let’s practice some Chi-square Questions.

You’ll use this statistical test in your lab in the next assignment. You will NOT be assessed on the chi-square test on the module exam, but it will come back in the second semester.

[CC BY 4.0] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION