The most common use is a nominal variable with only two values (such as male or female, left or right, green or yellow), in which case the test may be called the exact binomial test. You use the exact test of goodness-of-fit when you have one nominal variable. This is because the predictions of the null hypothesis are so simple that the probabilities can easily be calculated. There is no test statistic instead, you directly calculate the probability of obtaining the observed data under the null hypothesis. This is the P value.Įxact tests, such as the exact test of goodness-of-fit, are different.
Use a mathematical function to estimate the probability of getting a test statistic as extreme as the one you observed, if the null hypothesis were true. 
Calculate a number, the test statistic, that measures how far the observed data deviate from the expectation under the null hypothesis. Most statistical tests take the following form: The main goal of a statistical test is to answer the question, "What is the probability of getting a result like my observed data, if the null hypothesis were true?" If it is very unlikely to get the observed data under the null hypothesis, you reject the null hypothesis. You use the exact test of goodness-of-fit when you have one nominal variable, you want to see whether the number of observations in each category fits a theoretical expectation, and the sample size is small.
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