Question

# Find the expected count and the contribution to the chi-square statistic for the (Control, Disagree) cell in the two-way table below. begin{array}{|c|

Two-way tables
Find the expected count and the contribution to the chi-square statistic for the (Control, Disagree) cell in the two-way table below.
$$\begin{array}{|c|c|c|}\hline&\text{Strongly Agree}&\text{Agree}&\text{Neutral}&\text{Disagree}&\text{Strongly Disagree}\\\hline\text{Control} &38&47&2&12&11\\ \hline \text{Treatment}&60&45&9&4&2 \\ \hline \end{array}\\$$
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 ?

2020-11-27

Step 1
a) The expected frequencies are calculated by using the following formula:
$$\text{Expected frequency}=\frac{\text{Row total} \cdot \text{Column total}}{\text{Overall total}}$$
Step 2
Then, expected frequencies are calculated as follows: $$\begin{array}{|c|c|c|}\hline&\text{Strongly Agree}&\text{Agree}&\text{Neutral}&\text{Disagree}&\text{Strongly Disagree}\\\hline\text{Control} &46.9&44.0&5.3&7.7&6.2\\ \hline \text{Treatment}&51.1&48.0&5.7&8.3&6.8 \\ \hline \end{array}\\$$ The formula for finding the test statistic is obtained as follows: $$x^2=\sum \frac{(O_i-E_i)^2}{E_i}$$ The chi-square statistic is calculated as follows:
$$\begin{array}{|c|c|c|}\hline\text{Observed count (O)}&\text{Expected count (E)}&\frac{(O-E)^2}{E}\\\hline 38 &46.9&1.678\\ \hline 47&44.0&0.205 \\ \hline 2&5.3&2.021 \\ \hline 12&7.7&2.470 \\ \hline 11&6.2&3.679 \\ \hline 60&51.1&1.539 \\ \hline 45&48.0&0.188 \\ \hline 9&5.7&1.853 \\ \hline 4&8.3&2.264 \\ \hline 2&6.8&3.372 \\ \hline \text{Total}: 230&&x^2=19.269 \\ \hline \end{array}\\$$

Thus , the chi-square statistic is 19.269