Question

A louse-y situation A study published in the New England Journal of Medicine compared two medicines to treat head lice: an oral medication called ivermectin and a topical lotion containing malathion. Researchers studied 812 people in 376 households in seven areas around the world. Of the 185 households randomly assigned to ivermectin, 171 were free from head lice after 2 weeks, compared with only 151 of the 191 households randomly assigned to malathion.

a. Calculate the difference (Ivermectin – Malathion) in the proportion of households that were free from head lice in the two groups.

One hundred trials of a simulation were performed to see what differences in proportions would occur due only to chance variation in the random assignment, assuming that the type of medication doesn’t matter. The results are shown in the dotplot.

b. There is one dot at 0.09. Explain what this dot means in this context.

c. Use the results of the simulation to determine if the difference in proportions from part (a) is statistically significant. Explain your reasoning.

Short answer

(a) $0.1337$is the difference in the proportion of households that were free from head lice in the two groups.

(b) The dot signifies that the difference between two medicines.

(c) The difference in mean is not statistically significant because other factors also influence the result.

Step-by-step solution

Part (a) Step 1: Given Information

We are given that the first medicine, Ivermectin, was used and shows$171$out of$185$were free from head lice. Therefore, the proportion of Ivermectin$=\frac{171}{185}$

Second Medicine Malathion shows that$151$out of$191$was free from head lice

Therefore, the proportion of malathion$=\frac{151}{191}$

Part (a) Step 2: Explanation

The difference in the proportions of the two medicines is: proportion of Ivermectin - Proportion of Malathion.

We have, difference=$\frac{171}{185}-\frac{151}{191}$

On solving, we get a difference.$=0.1337$

Hence, $0.1337$the difference in the proportion of households that were free from head lice in the two groups.

Part (b) Step 1: Given Information

We are given the values of researchers' experiment randomly assigned to ivermectin and some were assigned to head lice and compared with malathion and we have to find out the significance of dot structure.

Part (b) Step 2: Explanation

The dot$0.09$ signifies that the chances are very small that the difference in the proportion of the two medicines is larger.

Part (c) Step 1: Given Information

We are given the values of researchers' experiments randomly assigned to ivermectin; some were assigned to head lice and compared with malathion and we have to find out if the result in part (a) is statistically significant or not.

Part (c) Step 2: Explanation

Using the results of the simulation to determine if the difference in proportions from part (a) is statistically significant, we conclude that the difference is quite significant statistically only if there is low probability that results have occurred by chance. Also the difference is less which depicts that probability of result by chance is less.