Question

Find the expected count and the contribution to the chi-square statistic for the (Group 1, No)

Two-way tables
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asked 2021-01-16

Find the expected count and the contribution to the chi-square statistic for the (Group 1, No) cell in the two-way table below.

\(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &56 & 42 & 98\\ \hline \ \text{Group 2}&135&67&202 \\ \hline \text{Group 3}&66&23&89 \\ \hline \text{Total}&257&132&389 \\ \hline \end{array}\)
Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Expected count =?
contribution to the chi-square statistic = ?

Answers (1)

2021-01-17
Step 1
Observed values with marginal totals:
\(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}&\text{Total}\\\hline\text{Group 1} &56 & 42 & 98\\ \hline \ \text{Group 2}&135&67&202 \\ \hline \text{Group 3}&66&23&89 \\ \hline \text{Total}&257&132&389 \\ \hline \end{array}\)
Step 2
Expected values:
Expected values are the product of the column and row total divided by the table total. \(\begin{array}{|c|c|c|}\hline&\text{Yes}&\text{No}\\\hline\text{Group 1} &\frac{257\times98}{389}=64.7 & \frac{132\times98}{389}=33.2\\ \hline \text{Group 2}&\frac{257\times202}{389}=133.5&\frac{132\times202}{389}=68.5 \\ \hline \text{Group 3}&\frac{257\times89}{389}=58.8&\frac{132\times89}{389}=30.2 \\ \hline \end{array}\)
Step 3
The expected count for (Group 1, No) is as follows:
\(\text{Expected count}=\frac{132 \times 98}{389}\)
\(=33.2545\)
\(\approx33.3\) The contribution to test statistic is as follows: \(\text{contribution to chi-square}=\frac{(O-E)^2}{E}\)
\(=\frac{(42-33.2545)^2}{33.2545}\)
\(=2.29995\)
\(\approx2.300\)
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