necessaryh
2021-01-22
Answered

How does the size of the cross-tabulation table impact the chi-square value.

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oppturf

Answered 2021-01-23
Author has **94** answers

The chi-squared data is often expressed in a cross-tabulation, where each row represents a level or category of one categorical variable, and each column represents a level or category of the other categorical variable.

The value recorded in a cell corresponding to the

Step 2

Explanation:

Suppose there are r rows, that is, there are r levels of the row variable, and c columns, that is, there are c levels of the column variable.

Since the grand total is a constant, and row total = column total = grand total,

For the cross-tabulation, the total degrees of freedom,

For a chi-squared test, there are two ways to conclude the hypothesis test- using the critical value, and using the p-value.

The critical value for the usual right-tailed test, at level of significance,

The p-value for the usual right-tailed test, for the statistic value,

Note that, the distribution of the chi-squared test statistic under the null hypothesis, which is the chi-squared distribution with

Clearly, the size of the cross-tabulation determines the degrees of freedom of the null chi-squared distribution, which, in turn, is the key point in establishing the rejection rule, and hence, forming the conclusion of the chi-squared test of significance.

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