Chi-square Test

also called chi-squared or χ2  distribution

• In statistics, a result is significant if it is unlikely to have occurred by chance.

• Because maybe you’re not being a great scientist and the independent variable (the test condition being examined) has no effect. Maybe you got results by chance.

Null hypothesis

• In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. When used, the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise.

• So when you do a Chi-Square test you say “I have a null hypothesis that I got this result in my experiment because of chance” Now you don’t really think that. You are setting out to reject the null hypothesis so you can accept your alternative hypothesis. Your alternative hypothesis would be something like, “This experimental result is NOT because of chance it is because of the variables I set up. I am a genius.”

• The significance of a result is also called its p-value

• the smaller the p-value, the more significant the result is said to be.

• We say that if the p-value is low enough that we reject the null hypothesis and accept the alternative hypothesis.

• “it wasn’t chance, it was the thing in my experiment

• Popular levels of significance are 10%, 5%, and 1% , all represented by the Greek symbol, α (alpha). Remember you could write those as 0.10 0.05 and 0.01

• We use 5% a lot

• If the p-value is lower than 0.05 you can say there is less than a 5% possibility that this was chance. It was probably this other thing

• Maybe its chance that so people who smoke cigarettes get lung cancer.

• If you do a chi-square test and get a p-value of 0.01 it means that its only 1% likely that it’s chance. It’s the alternative hypothesis that cigarettes are causing lung cancer.

• Note that when there are only 2 categories there are some mathematical problems with this test, but variations exist to fix that.

• Chi-square tests accepts weak or less accurate data and there are stricter statistical tests

• However sometimes you can only get weak or slightly fuzzy data like when looking at tens of thousands of cases of lung cancer, those people lead pretty different lives.