Chapter 14.1 Goodness of Fit Test

Test for Goodness of Fit: To analyze categorical data, we construct two-way tables and examine the counts or percents of the explanatory and response variables.

Proportion of M&M MINIs® Colors Observed Count, O Expected Count, E Blue   Brown Green Orange Red Yellow

  is called the chi-square statistic. It measures how well the observed counts fit the expected counts, assuming that the null hypothesis is true.

We want to compare the observed counts to the expected counts.   The null hypothesis is that there is no difference between the observed and expected counts. The alternative hypothesis is that there is a difference between the observed and expected counts.

▪ The total area under the curve is 1. The distribution of the chi-square statistic is called the chi-square distribution, c2. This distribution is a density curve. ▪       The total area under the curve is 1. ▪       The curve begins at zero on the horizontal axis and is skewed right. As the degrees of freedom increase, the shape of the curve becomes more symmetric

Using the M&M Minis® chi-square statistic, find the probability of obtaining a C2 value at least this extreme assuming the null hypothesis is true.   This is known as the “Goodness of Fit Test.”

Graph the chi-square distribution with (n – 1) = 5 degrees of freedom:   TI-83+: c2pdf (X, 5) 0 2 4 6 8 10 12 14 16 18

We would expect to obtain a C2 value at least this extreme in about _____ out of every _____ samples, assuming the null hypothesis is true.

CONDITIONS: The Goodness of Fit Test may be used when: all counts are at least 1 no more than 20% of the counts are less than 5.

Following the Goodness of Fit Test, check to see which component made the greatest contribution to the chi-square statistic to see where the biggest changes occurred.