Chi square

Comparison of the results we expect with what we actually observe purpose To determine if results are due to random chance or are statistically significant Comparison of the results we expect with what we actually observe

“Any difference between observed and expected data is due to chance” Null hypothesis A prediction that something is not present, treatment will have no effect, or no difference between treatment and control “Any difference between observed and expected data is due to chance”

Sample problem A magician friend give you a coin that you suspect might not be on the up and up. You devise a test. You flip the coin 400 times, recording each time whether it lands on heads or tails. You get heads 262 times and you get tails 138 times. Is this random chance, or statistically significant?

Analysis of the chi square value 1st, determine the degrees of freedom =number of possible outcomes minus 1 For our sample problem, we have 2 possible outcomes (heads or tails), so our degrees of freedom is 1

Chi square analysis table In order for results to be considered significant, you need to be a 95% sure that they are NOT simply due to random chance (in other words, only a 5% chance that they are actually due to random chance)

For our sample problem, our chi square needs to be larger than 3 For our sample problem, our chi square needs to be larger than 3.84 in order to be considered significant.

Is the coin rigged? Our chi square value was 38.44, so we can say with over 99.9% surety that the coin the magician gave you was NOT a normal coin!