What Chi-square is
Chi-square is a statistical method used to compare observed data to expected results. It is used to test the hypothesis that two variables are independent of each other. It is also used to test the goodness-of-fit of a set of observed values to expected values.
Steps for Chi-square:
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State the null hypothesis: This is the hypothesis that the two variables are independent of each other.
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Calculate the expected frequencies: This is the expected frequency of each combination of variables.
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Calculate the Chi-square statistic: This is the sum of the squared differences between the observed and expected frequencies.
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Calculate the degrees of freedom: This is the number of categories minus one.
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Find the critical value: This is the value at which the Chi-square statistic is significant.
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Compare the Chi-square statistic to the critical value: If the Chi-square statistic is greater than the critical value, then the null hypothesis is rejected and the two variables are not independent.
Examples
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Chi-square is commonly used to determine if there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.
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Chi-square is also used to identify if two categorical variables are related.
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Chi-square can be used to assess the relationship between a categorical independent variable and a categorical dependent variable.
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Chi-square is also used to test the goodness of fit of an observed data set to a theoretical one.
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Chi-square is often used to determine whether observed differences between sub-groups of a sample are statistically significant.