Introduction to Chi-Square Statistics – Learn It 3

  • Calculate and describe the value of a chi-square statistics in context of a real-world problem
  • Write a null and alternative hypothesis for a chi-square test

So, what does our chi-square test statistic value mean? To assess what our chi-square value tells us about the distance between the expected and observed counts, we’ll turn to the chi-square distribution.

Let’s explore the Chi-Square Distribution using the statistical tool below.

Note that the number of degrees of freedom is one fewer than the number of possible categories for our categorical variable, that is, [latex]df = (\text{number of categories} – 1)[/latex].


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Suppose that the claim made is: “The distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population”. You would like to decide if there’s convincing evidence against this claim.

  • Formally, the null hypothesis, [latex]H_0[/latex], is that the distribution of birthdates among all professional Italian football players is the same as the distribution of birthdates in the general Italian population.
  • The alternative hypothesis, [latex]H_A[/latex], is that the distribution of birthdates among all professional Italian football players is different from the distribution of birthdates in the general Italian population.