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Chapter 10: Problem 62

Suppose you are testing two different injections by randomly assigning them to children who react badly to bee stings and go to the emergency room. You observe whether the children are substantially improved within an hour after the injection. However, one of the expected counts is less than 5 .

Short Answer

Expert verified
To determine a significant difference in the effectiveness of the two injections, use a Fisher's Exact test given one expected count is less than 5. If the p-value is less than 0.05, the difference is statistically significant; else, it's not.

Step by step solution

01

Define the Problem

You are trying to determine if there's a significant difference in the effectiveness of two injections for children who react badly to bee stings. The outcome (dependent variable) is whether the children improved or not within an hour after the injection, and the independent variable is the type of injection.
02

Tabulate the Data

Since it's a comparative study between two groups, it's recommended to at first put the data into a 2x2 table, also known as a contingency table. The rows of your table should represent the injection types, and the columns should represent 'improved' and 'not improved'.
03

Calculate Fisher's Exact P-value

Next, apply Fisher's exact test to the data in the contingency table to find the p-value. This will tell you if the observed number of successes (children who were improved) is statistically different from what would be expected by chance alone for each injection. Use a statistical software or a Fisher's exact test calculator, input the contingency table values and get the p-value.
04

Interpret the P-value

If the p-value is less than the significance level (usually 0.05), then conclude that there is a significant difference in the effectiveness of the two injections. Otherwise, if the p-value is greater than 0.05, conclude that there is not a statistically significant difference in the effectiveness of the two injections.

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