Does sample size affect goodness-of-fit?
All measures of goodness-of-fit suffer the same serious drawback. When the sample size is small, only the most aberrant behaviors will be identified as lack of fit. On the other hand, very large samples invariably produce statistically significant lack of fit.
What should be done when categories have expected frequencies less than 5 so that the goodness-of-fit test may be applicable?
For the chi-square approximation to be valid, the expected frequency should be at least 5. This test is not valid for small samples, and if some of the counts are less than five, you may need to combine some bins in the tails.
When to use the goodness of fit test?
11.2 – Goodness of Fit Test A chi-square goodness-of-fit test can be conducted when there is one categorical variable with more than two levels. If there are exactly two categories, then a one proportion z test may be conducted. The levels of that categorical variable must be mutually exclusive.
When to reject the null hypothesis in goodness of fit test?
In a goodness-of fit test, if the p-value is 0.0113, in general, do not reject the null hypothesis.
What are the degrees of freedom for goodness of fit?
Degrees of freedom for a chi-square goodness-of-fit test are equal to the number of groups minus 1. The distribution plot below compares the chi-square distributions with 2, 4, and 6 degrees of freedom. To find the p-value we find the area under the chi-square distribution to the right of our test statistic.
When does the variable size correspond to small?
The variable size corresponds to small if the length of the petal is smaller than the median of all flowers, big otherwise: For this example, we have a sample of 150 flowers and we want to test whether the proportion of small flowers is the same than the proportion of big flowers (measured by the variable size ).