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Chi-Squaregoodnessoffit

Chi-Squaregoodnessoffit - Chi-Square Goodness of Fit Test...

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Chi-Square Goodness of Fit Test DEFINITIONS Qualitative variables are those which classify the units into categories. The categories may or may not have a natural ordering to them. Qualitative variables are also called categorical variables. Quantitative variables have numerical values that are measurements (length, weight, and so on) or counts (of how many). Arithmetic operations on such numerical values do have meaning. Analysis of Count Data Three tests If we have qualitative data on just one variable, a test of goodness- of-fit is used to assess if the qualitative data “fit” or are consistent with a particular discrete model for the percentages in each category. The null hypothesis would state the hypothesized discrete model. A test of homogeneity is used to assess if two or more populations are homogeneous or alike with respect to the distribution for some categorical variable. The null hypothesis is that the distributions are the same across the two or more populations. A test of independence determines if two qualitative variables are related or not for a given population. The null hypothesis is that the two variables are independent, that there is no apparent association. Big Idea for Chi-Square Tests
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1. The data consist of observed counts —that is, how many of the items or subjects fall into each category. 2. We will compute expected counts under H 0 , that is, the counts that we would expect to see for each category if the corresponding null hypothesis were true. 3. We will compare the observed and expected counts to each other via a test statistic that will be a measure of how close the observed counts are to the expected counts under 0 H . So if this “distance” is large, we have some support for rejecting 0 H . The test statistic that is computed for all three tests is called a chi- square test statistic . THE CHI-SQUARE STATISTIC Chi-Square Test Statistic : DEFINITIONS The observed counts are the data, the number of observations that fall into each category or cell.
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