What is chi-square distribution?

The chi-square distribution is a probability distribution used to test the independence of categorical data.

The chi-square distribution is a continuous probability distribution that is used to test the independence of categorical data. It is often used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. The distribution is characterized by a single parameter, the degrees of freedom (df), which determines the shape of the distribution.

The chi-square distribution is derived from the sum of squared standard normal deviates. The formula for the chi-square distribution is:

χ² = Σ(O-E)²/E

where χ² is the chi-square statistic, O is the observed frequency, E is the expected frequency, and Σ is the sum of all observations. The degrees of freedom for the chi-square distribution is equal to the number of categories minus one.

To use the chi-square distribution, we first calculate the chi-square statistic using the formula above. We then compare this value to a critical value from a chi-square table with the appropriate degrees of freedom and level of significance. If the calculated value is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference between the observed and expected frequencies.

In summary, the chi-square distribution is a useful tool for testing the independence of categorical data. It is characterized by a single parameter, the degrees of freedom, and is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies.