Question

Preventing strokes Refer to Exercise $38$. Which treatment seems to be most effective? Least effective? Justify your choices.

Short answer

The most effective treatment is both Aspirin and Dypiridamole and the least effective is Placebo.

Step-by-step solution

Given information

We need to find the most effective and least effective treatment to prevent stroke.

Explanation

We know that

Expected frequencies are a product of row and column total divided by table total. So,

ROW AND COLUMN NUMBER	EXPECTED FREQUENCY
$E_{11}$	$205.81$
$E_{12}$	$1443.19$
$E_{21}$	$205.81$
$E_{22}$	$1443.19$
$E_{31}$	$206.44$
$E_{32}$	$1447.56$
$E_{41}$	$205.94$
$E_{42}$	$1444.06$

The expected frequency of the number of successes deviates the most from the observed frequency, but the expected frequency for the treatment is higher than the observed frequency (expected $205.94$and observed $157$). As a result, the treatment of both is the most successful.

We see that for the treatment Placebo, the expected frequency of the number of successes differs the greatest from the observed frequency, whereas the expected frequency is lower than the observed frequency (expected $205.81$and observed $250$). As a result, the Placebo appears to be the least effective treatment.