Chi2 (A.K.A X2)

Simple Statistics X2 = ∑(o-e)2 / e O – observed result E – expected result

Calculate the following O – E = (O-E)2 = (O-E)2 /E = For each possible outcome ∑(O-E)2 /E = Once you calculate these items you can start using the chi2 table to determine significance

X2 table Degrees of freedom = (number of categories -1) Find your critical value for significance using the table and degrees of freedom. If the Chi-square value is greater than or equal to the critical value There is a significant difference between the groups we are studying. That is, the difference between actual data and the expected data (that assumes the groups aren’t different) is probably too great to be attributed to chance. So we conclude that our sample supports the hypothesis of a difference. If the Chi-square value is less than the critical value There is no significant difference. The amount of difference between expected and actual data is likely just due to chance. Thus, we conclude that our sample does not support the hypothesis of a difference.

Lets do a sample Flipping a coin 300 times Observed results Heads – 197 Tails – 103 Was the result significantly different than what would have been expected?

Simple Statistics X2 = ∑(o-e)2 / e O – observed result E – expected result

Calculate the following O = H= 197 T=103 E = H=150 T=150 O – E = H = 47 T = -47 (O-E)2 = H = 2209 T= 2209 (O-E)2 /E = H = 14.726 T=14.726 ∑ (O-E)2 /E for each value = Total 29.452 Critical Value = 3.84