Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Χ2 (Chi-square) Test What is a χ2 (Chi-square) test used for? Statistical test used to compare observed data with expected data according to a hypothesis. Let’s look at the next slide to find out… Χ2 (Chi-square) Test Ex. Say you have a coin and you want to determine if it is fair (50/50 chance of gets heads/tails). You decide to flip the coin 100 times. If the coin is fair what do you expect/predict to observe? 50 heads and 50 tails Now come up with a hypothesis (two possibilities) Χ2 (Chi-square) Test Hypotheses 1. The coin is fair and there will be no real difference between what we will observe and what we expect. 2. The coin is not fair and the observed results will be significantly different from the expected results. The first hypothesis that states no difference between the observed and expected has a special name… NULL HYPOTHESIS Χ2 (Chi-square) Test NULL HYPOTHESIS This is the hypothesis that states there will be no difference between the observed and the expected data or that there is no difference between the two groups you are observing. Ex. You wonder if world class musicians have quicker reaction times than world class athletes. What would the null hypothesis be? That there is no difference between these two groups. Let’s get back to flipping coins… Χ2 (Chi-square) Test You flip the coin 100 times and you getting the following results: Observed Expected Heads 41 50 Tails 59 50 Is the coin fair or not? It’s not easy to say. It looks like it might, but maybe not… This is where statistics, in particular the χ2 test, comes in. Χ2 (Chi-square) Test The formula for calculating χ2 is: Where O is the observed value and E is the expected. What happens to the value of χ2 as your observed data gets closer to the expected? 2 Χ approaches 0 Let’s determine χ2 for the coin flipping study… Χ2 (Chi-square) Test Observed Expected Heads 41 50 Tails 59 50 Χ2 = (41-50)2/50 + (59-50)2/50 Χ2 = (-9)2/50 + (9)2/50 Χ2 = 81/50 + 81/50 Χ2 = 3.24 So what does this number mean…? Χ2 (Chi-square) Test Converting Χ2 to a P(probability)-value Statisticians have devised a table to do this: Great, but how do you use this? Χ2 (Chi-square) Test Converting Χ2 to a P(probability)-value First we need to determine Degrees of Freedom (DoF): DoF = # of groups minus 1 We have two groups, heads group and tails group. Therefore our DoF = 1. Χ2 (Chi-square) Test Converting Χ2 to a P(probability)-value Then scan across and find your X2 value (3.24) Lastly go up and estimate the p-value… P-value = ~0.07 What does this value tell us? Χ2 (Chi-square) Test The P-value P-value = ~0.07 The p-value tells us the probability that the NULL hypothesis (observed and expected not different) is correct. Χ2 (Chi-square) Test Observed Expected Heads 41 50 Tails 59 50 P-value = ~0.07 Therefore, there is a 93% chance that the null hypothesis (there is no real difference between observed and expected) is correct. Χ2 (Chi-square) Test 50 50 P-value = ~0.07 However, statisticians have a p-value = 0.05 cutoff. In order for the hypothesis to be supported, p must be less than 0.05 (95% chance that null is correct). Therefore the null hypothesis cannot be rejected.