Q.48 - The Practice of Statistics for AP

Question

Removing warts A recently reported study looked at the use of oral zinc supplements to get rid of warts. The treatment group took an oral zinc supplement. Of these $32$ people, $19$ were rid of their warts after one month, and $6$ additional patients were rid of them after two months. The $23$ subjects in a control group were given a placebo. Of these, $1$ was rid of his warts after one month and $2$ additional patients were rid of their warts after two months. The reported results of the study included this table.

(a) The researchers say they did a chi-square test on this table. Explain why that makes no sense. Then make a correct two-way table displaying the results of the experiment. 

(b) Explain why it is not appropriate to use a chi-square test in this setting even with the correct two-way table. 

Step-by-Step Solution

Answer

a). Independent requirement has been not met.

b). Not proven to satisfy the random criterion.

Part (a) Step 1:Given Information

Part (a) Step 2: Explanation

There are $32$ participants from the treatment who are not given full details. Group and $23$ of the observed experimental group. So, the use of Chi-square makes no sense. The above-mentioned table exam.

Below is the product of the two-way table from the previous experiment:

Part (b) Step 3: Given Information

Part (b) Step 4: Explanation

The expected count for any cell when $H_0$ is true is

For the expected count

$\text{ Expected count }=\frac{\text{ Raw Total }\times \text{ Column Total }}{\text{ Table Total }}$

Since at least $5$ are not all expectations. So, in this situation, a chi-square test should not be carried out.