2. Chi-square goodness of fit tests

3. Chi-square goodness of fit

4. Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit

5. Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit

6. Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit

7. Core issue in statistics: When are you viewing just random noise and when is there a real trend? Chi-square goodness of fit

8. Your response variable is count data When to use a chi-square test 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

9. If the test tells you your data is not significantly different from what you expect, you support the hypothesis How to interpret a chi-square test 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.

10. What is chi-square? x 2 = Chi-square valueΣ = Sum of x 2 = Σ (Observed Value – Expected Value) 2 Expected Value ObservedExpectedObs-Exp (Obs-Exp) 2 Exp Category 1 Category 2 ….. X 2 total Degrees of Freedom

11. Example problem #1

12. Chi-square probability table 0.990.950.90.80.70.60.50.40.30.20.10.050.01 df 10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.63 20.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.21 30.1150.3520.5841.001.421.872.372.953.674.646.257.8111.3 40.2970.7111.061.652.192.753.364.044.885.997.789.4913.3 50.5541.151.612.343.003.664.355.136.067.299.2411.115.1 60.8721.642.203.073.834.575.356.217.238.5610.612.616.8 71.242.172.833.824.675.496.357.288.389.8012.014.118.5 81.652.733.494.595.536.427.348.359.5211.013.415.520.1

13. Chi-square probability table 0.990.950.90.80.70.60.50.40.30.20.10.050.01 df 10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.63 20.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.21 30.1150.3520.5841.001.421.872.372.953.674.646.257.8111.3 40.2970.7111.061.652.192.753.364.044.885.997.789.4913.3 50.5541.151.612.343.003.664.355.136.067.299.2411.115.1 60.8721.642.203.073.834.575.356.217.238.5610.612.616.8 71.242.172.833.824.675.496.357.288.389.8012.014.118.5 81.652.733.494.595.536.427.348.359.5211.013.415.520.1 Only 5% chance that the difference between your obs and exp values comes from chance alone Your hypothesis can be rejected

14. Chi-square probability table 0.990.950.90.80.70.60.50.40.30.20.10.050.01 df 10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.63 20.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.21 30.1150.3520.5841.001.421.872.372.953.674.646.257.8111.3 40.2970.7111.061.652.192.753.364.044.885.997.789.4913.3 50.5541.151.612.343.003.664.355.136.067.299.2411.115.1 60.8721.642.203.073.834.575.356.217.238.5610.612.616.8 71.242.172.833.824.675.496.357.288.389.8012.014.118.5 81.652.733.494.595.536.427.348.359.5211.013.415.520.1 50-60% chance differences are from random chance

15. Example problem 2

16. Female Song Worksheet

17. Bird song: It’s not just for males anymore Male house wrens sing to attract mates and defend territories Females sing a lot too! Why?

18. Why do females sing? H1: To help coordinate their behavior with their male Prediction

19. Why do females sing? H2: To solicit copulations from the male Prediction

20. Why do females sing? H3: To defend their nests against other house wrens Prediction

21. Why do females sing? Null hypothesis: Female song occurs randomly Prediction