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

the chi-square statistic

A chi-square ([latex]\chi^2[/latex], pronounced “kai-square”) statistic is a test that measures how a model compares to actual observed data.

Let’s look into how to test hypotheses about the frequency distribution of a categorical variable and consider hypotheses that compare the proportion of a population that falls into two or more possible categories.

Italian Football (or in America, soccer)

In Italy, youth football leagues create cohorts of children based on year of birth.

For example, children born in 2015 only played with other children born in that same year. If a child was born on December 31, 2014, they played with the 2014 cohort (rather than the younger 2015 cohort). So, children born earlier in the year (e.g., January or February) tend to be the eldest players in their leagues. Children born later in the year (e.g., November or December) tend to be the youngest players in their leagues.

Research question: Could this seemingly unimportant practice—grouping by year of birth—have an effect on players’ later football careers?

Let’s explore this question using data^[1] compiled by researchers on professional Italian football players.

Fun fact: Why Do Americans Call It Soccer Instead of Football? Blame England

---