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# The Chi Square Test

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1. The Chi Square Test “The Goodness Fit” Test

2. Purpose • Used in genetics to determine how close to the expected ratio your data is • Determines if the experiment was “significant” and not just due to chance • Ex: Mendel crossed Tt x Tt (tall) plants • Expected ratio- 3:1 • Data: 290 Tall and 110 short • Pretty close... but how close?!

3. Formula Observed = what your experiment showed Expected = what the experiment SHOULD have shown

4. Find the expected by multiplying the TOTAL observed by the EXPECTED proportion • Expected should be 3:1 Tall: Short • (400)(.75) = 300 • (400)(.25) = 100 • You do the math!!

5. df = Degrees of freedom • # of categories/phenotypes minus 1 • p = Significance level • Percentage in decimal form • We will use p = 0.05 which means there is a 5% chance that the data is false • Or.. 95% that its true!

6. Our example: Tall plants and Short plants df = 1 X² = 1.33 Find 0.5 and df 1. - 3.841 is the critical value If your X² is LOWER than this value, then you can ACCEPT your hypothesis (yaay!) If your X² is HIGHER than this value, then you have to REJECT your hypothesis

7. Point?? • Since the critical value in the table was 3.841 and our value was 1.33… • Its lower… • We can accept our hypothesis! • It was “good enough!”

8. Practice • Mendel: RrYy x RrYy (Round, Yellow) • Expected Outcome: • 9/16 Round, Yellow • 3/16 Round, Green • 3/16 Wrinkled, Yellow • 1/16 Wrinkled, Green

9. df? Critical Value? Accept or Reject data??