The shape of the chi-square distribution depends on the number of degrees of freedom. Using the CHIDIST function in a spreadsheet, you enter =CHIDIST(2.13, 1) and calculate that the probability of getting a chi-square value of \(2.13\) with one degree of freedom is \(P=0.144\). The number of degrees of freedom is the number of categories minus one, so for our example there is one degree of freedom. This means that once you know the chi-square value and the number of degrees of freedom, you can calculate the probability of getting that value of chi-square using the chi-square distribution. The distribution of the test statistic under the null hypothesis is approximately the same as the theoretical chi-square distribution. If you had observed \(760\) smooth-winged flies and \(240\) wrinkled-wing flies, which is closer to the null hypothesis, your chi-square value would have been smaller, at \(0.53\) if you'd observed \(800\) smooth-winged and \(200\) wrinkled-wing flies, which is further from the null hypothesis, your chi-square value would have been \(13.33\). Entering these numbers into the equation, the chi-square value is \(2.13\). You observe \(770\) flies with smooth wings and \(230\) flies with wrinkled wings the expected values are \(750\) smooth-winged and \(250\) wrinkled-winged flies. To give an example, let's say your null hypothesis is a \(3:1\) ratio of smooth wings to wrinkled wings in offspring from a bunch of Drosophila crosses. ![]() ![]() \]Īs with most test statistics, the larger the difference between observed and expected, the larger the test statistic becomes.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |