The Chi Square Test “The Goodness Fit” Test

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?!

Formula Observed = what your experiment showed Expected = what the experiment SHOULD have shown ObsExp(Obs – Exp)(Obs – Exp)² Exp Tall Plants290 Short Plants 110 TOTALS400

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!! ObsExp(Obs – Exp)(Obs – Exp)² Exp Tall Plants Short Plants TOTALS400

The X² is the chi square value! ObsExp(Obs – Exp)(Obs – Exp)² Exp Tall Plants Short Plants TOTALS400 X² = 1.33 Add!

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!

Our example: Tall plants and Short plants df = 1 X² = 1.33 Find 0.5 and df 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

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

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

ObsExp(Obs – Exp)(Obs – Exp)² Exp Round, Yellow 315 Round, Green 101 Wrinkled, Yellow 108 Wrinkled, Green 32 TOTALSX² = df? Critical Value? Accept or Reject data??