I. CHI SQUARE ANALYSIS Statistical tool used to evaluate variation in categorical data Used to determine if variation is significant or instead, due to random error, chance Specifically, used to support or reject null hypothesis Null Hypothesis Chi Square Analysis The sum of the variation in the data is calculated using the Chi Square formula.

I. CHI SQUARE, cont The sum, or Chi2, is then compared to the critical value in the Probability Table using the correct degrees of freedom. The P Value represents the probability that the null hypothesis is correct; that is, the probability that the differences seen are random and due to chance alone. Degrees of freedom = n – 1 where n represents # categories, possible outcomes By convention, the accepted probability value in science is > 0.05. In other words, the P Value must be > 0.05 to accept the null hypothesis.,

I. CHI SQUARE, cont To determine the P Value, Calculate Chi Square Find the 0.05 Critical Value for the correct degrees of freedom, If your calculated Chi Square value is less than the critical value, P Value is > 0.05 This means there is more than a 95% probability the differences seen are random; therefore, less than a 5% chance the differences are significant. Null hypothesis is accepted If your calculated Chi Square value is greater than or equal to the critical value, P Value is ≤ 0.05 The probability the differences are due to random chance does not exceed 95%; therefore they must be considered significant. Null hypothesis is rejected

I. CHI SQUARE, cont A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck. In a test, you counted 1600 cards and observed the following: Spades = 404 Hearts = 420 Diamonds = 400 Clubs = 376 Is the machine dealing randomly? Null Hypothesis: Chi Square Formula: Expected =

I. CHI SQUARE, cont Chi Square = (404-400)2 + (420-400)2 + (400-400)2 + (376-400)2 = 2.48 400 400 400 400 Degrees of Freedom = P Value Interpretation: