STAT141 Lecture Notes - Marginal Distribution, Contingency Table, Test Validity
8 Apr 2014
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Notation: k = # of categories of a qualitative variable pi = true proportion of category i; i = 1, , k (note: ip. A random sample of size n will provide sample statistics of observed counts . These values can compare against expected counts of npi for each category. H0 can collectively test the validity of each pi. Def"n: the goodness-of-fit test uses the chi-square statistic, 2, is computed by. 2 where obs = observed count , exp = expected count , and you sum over all categories. Sizeable differences between obs and exp of specific categories lead to large values of 2 and subsequent rejection of h0. For formal rejection/non-rejection, we need a formal test. Aside: the chi-squared distribution has the following properties: Like the t-distribution, it has only one parameter, df, that can take on any positive integer value. Skewed to the right for small df but becomes more symmetric as df increases.
