Chi Square Analysis

The new Advanced Placement Biology curriculum includes a few topics on statistical analysis under the section on Science Practices: “Students can use mathematics appropriately.”  Most introductory level biology classes (freshman) do not include these lessons because it can be difficult with students who haven’t advanced very far in algebra.   Seniors in  AP Biology should have no trouble tackling these concepts.   Chi Square Analysis fits in well with  a unit on genetics.  After students review the basics of Mendelian genetics, I start with a presentation on tigers that explores a scenario where two orange tigers have a cub that is white.  Most students correctly predict that the parents must be carrying a recessive gene.  The presentation walks through the steps of data analysis to show how you can then support your prediction with statistics.

Google Slides – Genetics and Statistics

After the presentation (about 20 minutes), students are tasked with running a chi square analysis on candy to determine if there are any equal number of each color.    You can have students either bring in their own candy or buy in bulk to share with the class.  Students practice taking data on the colors and numbers of candies and then use the chi square equation to determine if the numbers are equal.  This is often the first exposure students have to the idea of a NULL hypothesis.

Data Using Real Inheritance Patterns

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Finally, students use real data from plants that they grow to show that the parents of a cross were dihybrids, which resulted in the 9:3:3:1 ratio seen in the offspring.     If you don’t have time to grow plants, you can order genetic corn where students simply need to count the number of yellow, purple, and wrinkled seeds; see Investigation:  Corn Genetics

If you have the time, students can do an investigation on the Genetics of Wisconsin Fast Plants where they grow seeds that will also display the 9:3:3:1 ratio.  Students can then apply a chi square analysis to show that their hypothesis is correct.   I enjoy this experiment because it features many concepts of biology, botany, and horticulture and many of my urban students have never had any experience with growing plants.   Seeds can be ordered from Amazon or from most biological supply companies.

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Chi square analysis will also come up again when students do the Virtual Fruit Fly Lab, but the program has a built in calculator, students just need to input the observed and expected numbers.   By the time students get to this activity, they should have a pretty good grasp of how the equation works and why it is important in data analysis.

Summary of  Lessons on Chi Square Analysis:

Powerpoint Presentation  – examines how a white tiger can be born from two orange tigers

Candy and Chi Square – count skittles to see if colors are evenly distributed
Corn Genetics  – count kernels on corn (ordered from biological supply)
Genetics of Wisconsin Fast Plants –  grow plants, count phenotypic ratios

Chi Square Practice Set – Google Doc with practice data sets

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