We now show how to construct the table of expected values (i.e. To accomplish this we use the fact (by Definition 3 of Basic Probability Concepts) that if A and B are independent events then P( A ∩ B) = P( A) ∙ P( B). We also assume that the proportions for the sample are good estimates for the probabilities of the expected values. We use the chi-square test, and so need to calculate the expected values that correspond to the observed values in the table above. H 0: Highest level of schooling attained is independent of parents’ wealth Based on the data collected is the person’s level of schooling independent of their parents’ wealth?įigure 1 – Observed data and expected values for Example 1 The results are summarized on the left side of Figure 1 (Observed Values).

Instead you need to use the equivalent function, CHITEST.Įxample 1: A survey is conducted of 175 young adults whose parents are classified either as wealthy, middle class or poor to determine their highest level of schooling (graduated from university, graduated from high school or neither). The ranges R1 and R2 must have the same size and shape and can only contain numeric values.įor versions of Excel prior to Excel 2010, the CHISQ.TEST function doesn’t exist. For R1 = the array of observed data and R2 = the array of expected values, we haveĬHISQ.TEST(R1, R2) = CHISQ.DIST( x, df) where x is calculated from R1 and R2 as in Definition 2 of Goodness of Fit and df = (row count – 1) (column count – 1). In these cases df = (row count – 1) (column count – 1).Įxcel Function: The CHISQ.TEST function described in Goodness of Fit can be extended to support ranges consisting of multiple rows and columns. Such data are organized in what are called contingency tables, as described in Example 1.

The method described in Goodness of Fit can also be used to determine whether two sets of data are independent of each other.

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