The Chi-Squared Test for Goodness of Fit compares a set of observed frequencies to values that are expected either by theoretical probability or prior research. The frequencies are separated into mutually exclusive possibilities for one categorical variable. The Greek letter chi, (pronounced "kye") looks similar to a script "X." When written with an exponent of two, this symbol represents the chi-squared statistic. This statistic represents the degree to which the observed frequencies in a data set differ from expected frequencies. Here is a contrived example of an experiment appropriate for a Chi-Squared Goodness of Fit Test. A botanist was working with plants that were either red, pink, or white. Her hypothesis was that if a plant expressed a red color, it had two alleles that were the same (RR). She also hypothesized that if a plant was white, it had two alleles that were the same (rr). However, if a plant was pink, she hypothesized that it had two alleles that were different (Rr). She decided to cross two pink plants to see if the observed results would be similar to her expected results of 25% red (RR), 50% pink (Rr), and 25% white (rr). She set her alpha at 0.05. The expected and observed results from her cross, which resulted in exactly 100 plants, are given below.
The null hypothesis was that there would be no difference between the observed data and the expected values. The alternative hypothesis is that there would be a difference.
H: At least one of the observed values will be different than expected/predicted._{A}To complete the test, the chi-squared statistic value and the degrees of freedom must be calculated. The chi-squared value is a single value that is the sum of the ratios of the squares of the differences between what is observed and what was expected, divided by what was expected, for each category in the contingency table. The degrees of freedom is the number of categories minus one. In order to ease this fairly formidable process, DIG Stats provides the use of a Chi-Squared Goodness of Fit Calculator which can be run in most recent web browsers. Click the button below to see if your browser can run the applet.
With our chi-squared value and degrees of freedom ( Another, related way to test the null hypothesis is to use the CHISQ.DIST.RT function in Excel. Entering the chi-squared value of 5.5 and The Cellular Phone and Dice activities in the inferential activities menu use Chi-Squared Goodness of Fit tests. Original work on this document was done by Central Virginia Governor's School students Richard Barnes, Kim Tibbs, and Ryan Nash (Class of '00). This document was updated by Central Virginia Governor's School students Matthew James and Kyle Nenninger (Class of '03). Copyright © 1999 Central Virginia Governor's School, Lynchburg, VA |