then it’s possible that in the population, the true probability isn’t one third and one third and one third. A one-sample chi-square includes only one dimension, variable, or factor, such as in the example you’ll see here, and is usually referred to as a goodness-of-fit test (just how well do the data you collect fit the pattern you expected?). A two-sample chi-square includes two dimensions, variables, or factors and is usually referred to as a test of independence. For example, it might be used to test whether preference for school vouchers is not related to, or independent of, political
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