How do you know when your data aren’t “close enough”? …and hand grenades!

 Null hypothesis –  statement that illustrates that there is no relationship between two measured variables  i.e. “nothing’s going to happen/change”  Ex. “this coin is fair” (will create equal heads and tails)  Ex. “ the genes are not linked” (will show independent assortment)

 There is a relationship between these to variables…  Examples:  This coin is NOT fair… (produces more heads than tails)  These genes ARE linked… (are not assorting independently)

 Are differences between observed (collected) data and the predicted outcomes significant? Our threshold? 5%  If >5% chance that random chance caused there to be a difference between the observed and expected = accept the null hypothesis = accept that differences between prediction and observed results aren’t significant  (It’s a pretty generous tolerance!)

(Sum of)

CategoryOEO – E(O – E) 2 E Dom, dom12 Dom, rec9 Rec, dom8 Rec, rec.0 Total:∑

 How many possible outcomes are there in your experiment?  In genetics, this might be phenotypes…  Degrees of freedom (df) = # outcomes – 1…

 Say our df = 3 and our Chi-squared is 2.96

 Probability (p-value) would be 0.5<p<0.3

 The difference between observed and expected is Non-significant = accept null hypothesis (~40% chance that variation due to chance events)

CategoryOEO – E(O – E) 2 E Purple stem, jagged leaf Purple stem, smooth leaf Green stem, jagged leaf Green stem, smooth leaf Total: 29∑ = 6.4 x2x2

 df = 3  X 2 = 6.4  P = 0.5<P<0.1  Accept the null hypothesis!

CategoryOEO – E(O – E) 2 E Purple stem, jagged leaf Purple stem, smooth leaf Green stem, jagged leaf Green stem, smooth leaf Total: 800∑ = 2.027

 df = 3  X 2 =  P = 0.7<P<0.5  Accept the null hypothesis!