Chi-square goodness of fit tests
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? Chi-square goodness of fit
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
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.
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
Example problem #1
Chi-square probability table df
Chi-square probability table df Only 5% chance that the difference between your obs and exp values comes from chance alone Your hypothesis can be rejected
Chi-square probability table df % chance differences are from random chance
Example problem 2
Female Song Worksheet
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?
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