Introduction to Chi-square Testing Lesson

In this unit we study yet another shape distribution called chi-square. We have limited our study thus far to basically symmetric probability curves like the normal curve and an adaptation of it in the student t-distribution. Now we meet a distribution that has a peak which slides along a horizontal axis as the degrees of freedom increase. Picture a "wave" in the ocean, with the wave moving horizontally according to the number of degrees of freedom.

This picture actually represents df = 4.

degrees of freedom

The presentation in the lesson below involves ONE instance of the use of chi-square: hypothesis testing of a variance or standard deviation. That is a new concept for us since we have only experienced inference for measures of center, either the numerical mean or the proportion (%) from categorical data.

The theory of performing a hypothesis test is exactly the same as before, however we have a new test statistic ( equation image indicator $X squared$ ) instead of "z" or "t". The chi-square formula for testing spread is:

chi square test spread

Where n is the sample size, equation image indicator is the sample variance and is the population variance.

This formula applies ONLY when testing a spread. Other formulas exist for other types of chi-square tests that you will learn about in the next unit. More detail and examples are contained in the lesson below. Click on the lesson to download.

Chi-Square Distribution

IMAGES CREATED BY GAVS