Use of an 𝝌𝟐 test

Use of an 𝝌𝟐 Test

A 𝝌² test is a statistical tool used to determine if observed data fits an expected distribution.
This test is a type of hypothesis testing and helps analysts understand if differences between observed and expected data are due to random chance or if they are statistically significant.
The 𝝌² test can be used for goodness-of-fit, which checks if the observed data fits a particular distribution, or for independence, which tests if two variables are related.

The basic steps to perform a 𝝌² test are to formulate null and alternative hypotheses, calculate the 𝝌² test statistic, compute the p-value and decide whether to reject or not reject the null hypothesis.
The null hypothesis generally postulates that there is no significant difference between the observed and expected data, while the alternative hypothesis assumes the opposite.
The 𝝌² test statistic is calculated by applying the formula [(Observed-Expected)²/Expected]
The higher the 𝝌² statistic, the bigger the difference between observed and expected data, implying a lower likelihood of the differences being due to chance.
The p-value is the probability of obtaining the observed data (or more extreme) given that the null hypothesis is true. A lower p-value (below the significance level, usually 0.05) leads us to reject the null hypothesis.

If the 𝝌² test statistic is below the critical value or the p-value is larger than the significance level, we fail to reject the null hypothesis, concluding the observed data fits the expected distribution.
If the 𝝌² test statistic is above the critical value or the p-value is less than or equal to significance level, we reject the null hypothesis, concluding the observed data does not fit the expected distribution.
It’s important to bear in mind that failing to reject the null hypothesis doesn’t prove it to be true, and it may still be incorrect.

A 𝝌² test assumes that the data is a random sample and that the variable is categorical or ordinal.
Observed frequencies for each category must be independently obtained and large enough (usually at least 5) for the 𝝌² test to be valid. Lower counts can lead to inaccurate results.
Like every statistical method, a 𝝌² test is a tool – it provides evidence but it is not proof. The results should always be interpreted in the context of other information and expertise.