Chi-square goodness of fit tests - KBS GK12 Project

Chi-square goodness of fit tests - KBS GK12 Project

Chi-square goodness of fit tests Chi-square goodness of fit Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend? When to use a chi-square test Your response variable is count data Your response falls into different categories You have a hypothesis for the responses you expect You want to know if the difference between the responses you observe and the responses you expect is significant or not

How to interpret a chi-square test If the test tells you your data is not significantly different from what you expect, you support the hypothesis If the test tells you your data is significantly different from what you expect, you reject the hypothesis No statistical test ever proves a hypothesis. What is chi-square? x2 = Chi-square value = Sum of x2 = (Observed Value Expected Value)Observed Value Expected Value)2 Expected Value Observed Expected Obs-Exp (Obs-Exp) 2 Category 1 Category 2 .. X2 total Degrees of Freedom (Obs-Exp)2 Exp Example problem #1 Chi-square probability table 0.99 0.95

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 1 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71 3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 1.02

1.39 1.83 2.41 3.22 4.61 5.99 9.21 3 0.115 0.352 0.584 1.00 1.42 1.87 2.37 2.95 3.67 4.64 6.25 7.81 11.3

4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88 5.99 7.78 9.49 13.3 5 0.554 1.15 1.61 2.34 3.00 3.66

4.35 5.13 6.06 7.29 9.24 11.1 15.1 6 0.872 1.64 2.20 3.07 3.83 4.57 5.35 6.21 7.23 8.56

10.6 12.6 16.8 7 1.24 2.17 2.83 3.82 4.67 5.49 6.35 7.28 8.38 9.80 12.0 14.1 18.5 8 1.65

2.73 3.49 4.59 5.53 6.42 7.34 8.35 9.52 11.0 13.4 15.5 20.1 df Chi-square probability table 0.95 0.9 0.8 0.7 that 0.6 the 0.5 difference 0.4 0.3 0.2 0.1

Only 5% chance between your obs and exp values comes 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71 from chance alone 0.05 0.01 3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 1.02 3 0.115 0.352 0.584 1.00 4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88

5 0.554 1.15 1.61 2.34 3.00 3.66 4.35 5.13 6 0.872 1.64 2.20 3.07 3.83 4.57 5.35 7

1.24 2.17 2.83 3.82 4.67 5.49 8 1.65 2.73 3.49 4.59 5.53 6.42 0.99 df 1 1.39 1.83 2.41

3.22 4.61 5.99 9.21 Your hypothesis can be rejected 1.42 1.87 2.37 2.95 3.67 4.64 6.25 7.81 11.3 5.99 7.78 9.49 13.3 6.06 7.29 9.24 11.1 15.1 6.21

7.23 8.56 10.6 12.6 16.8 6.35 7.28 8.38 9.80 12.0 14.1 18.5 7.34 8.35 9.52 11.0 13.4 15.5

20.1 Chi-square probability table 50-60% chance differences are from random chance 0.99 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 1 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71

3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 1.02 1.39 1.83 2.41 3.22 4.61 5.99 9.21 3 0.115 0.352 0.584 1.00 1.42 1.87 2.37 2.95 3.67

4.64 6.25 7.81 11.3 4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88 5.99 7.78 9.49 13.3 5 0.554 1.15

1.61 2.34 3.00 3.66 4.35 5.13 6.06 7.29 9.24 11.1 15.1 6 0.872 1.64 2.20 3.07 3.83 4.57

5.35 6.21 7.23 8.56 10.6 12.6 16.8 7 1.24 2.17 2.83 3.82 4.67 5.49 6.35 7.28 8.38 9.80 12.0

14.1 18.5 8 1.65 2.73 3.49 4.59 5.53 6.42 7.34 8.35 9.52 11.0 13.4 15.5 20.1 df Example problem 2

Female Song Worksheet Bird song: Its not just for males anymore Male house wrens sing to attract mates and defend territories Females sing a lot too! Why? Why do females sing? H1: To help coordinate their behavior with their male Prediction Why do females sing? H2: To solicit copulations from the male Prediction Why do females sing? H3: To defend their nests against other house wrens Prediction Why do females sing? Null hypothesis: Female song occurs randomly Prediction

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