Chi-square goodness of fit, homogeneity, independence and inference for regression slope.
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- What does the chi-square goodness of fit test determine?
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Whether observed data from one categorical variable fit a specified probability distribution or model.- When should you use a chi-square goodness of fit test?
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When testing whether a single categorical variable follows an expected distribution, like uniform, binomial, or a theoretical model.- What is an expected frequency in a chi-square test?
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The number of observations you would expect in each category if the null hypothesis were true.- How do you calculate the expected frequency for each category in a goodness of fit test?
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Expected frequency = (Hypothesized probability of category) * (Total number of observations).- What is the degrees of freedom formula for a chi-square goodness of fit test?
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df = number of categories minus 1.- What are the conditions required for a valid chi-square test?
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All expected frequencies must be at least 1, and at least 80 percent of expected frequencies must be at least 5.- What is the null hypothesis in a chi-square goodness of fit test?
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The observed data follow the specified distribution, or each category has the hypothesized probability.- What is the chi-square test statistic formula?
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Chi-square = sum of (Observed frequency - Expected frequency)^2 / Expected frequency for all categories.- What does the chi-square test of homogeneity test?
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Whether the distribution of a categorical variable is the same across multiple populations or groups.- When should you use a chi-square test of homogeneity?
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When comparing the distribution of one categorical variable across two or more independent samples or groups.- How does the chi-square test of homogeneity differ from the test of independence?
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Homogeneity tests whether distributions of one variable are the same across groups; independence tests whether two variables are associated within one sample.- What is the degrees of freedom formula for a chi-square test of homogeneity?
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df = (number of rows minus 1) times (number of columns minus 1).- What is the null hypothesis in a chi-square test of homogeneity?
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The distribution of the categorical variable is the same across all populations or groups.- How is data organized in a chi-square test of homogeneity?
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In a two-way table where rows represent groups or populations and columns represent categories of the variable.- How do you calculate expected frequency in a test of homogeneity?
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Expected frequency = (Row total * Column total) / (Grand total) for each cell.
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