EBK FUNDAMENTALS OF BIOSTATISTICS
EBK FUNDAMENTALS OF BIOSTATISTICS
8th Edition
ISBN: 9780101123402
Author: Rosner
Publisher: YUZU
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Chapter 10, Problem 1P

Consider the Physicians’ Health Study data presented in Example 10.37 (p. 411).

How many participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two-sided test with α = .05 if compliance is perfect?

Expert Solution & Answer
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To determine

Find the number of participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two-sided test with α = 0.05 and compliance is perfect.

Answer to Problem 1P

The number of participants need to enrol in each group to achieve 90% power is 18,469.

Explanation of Solution

From Example 10.37, it is known that p1=0.020,p2=0.025.

Where,

    p¯=p1+p22=0.020+0.0252=0.0225q¯=1p¯=10.0225=0.9775Δ=p1p2=0.0200.025=0.005   

From the given information, it is known that α=0.05,β=0.9.

Step-by-step procedure to obtain critical value using Excel:

  • In an empty cell of an Excel sheet, type “=NORMSINV(1-(0.05/2))”.
  • Click Enter.

The output obtained is as follows:

EBK FUNDAMENTALS OF BIOSTATISTICS, Chapter 10, Problem 1P , additional homework tip  1

Thus, z1α2=1.96.

Similarly, the value of z for 90% confidence level is obtained below:

EBK FUNDAMENTALS OF BIOSTATISTICS, Chapter 10, Problem 1P , additional homework tip  2

It can be written às follows:

z1β=z0.9=1.28

Using Equation 10.13, the sample size is computed as follows

n=2p¯q¯z1α/2+p1q1+p2q2z1β2Δ2n=2(0.0225)(0.9775)1.96+0.020(0.980)+0.025(0.975)1.282(0.05)2n=18468.5n18,469

Thus, the number of participants need to enrol in each group to achieve 90% power is 18469.

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