Page 227 - Statistics for Dummies

Chapter 13: Confidence Intervals: Making Your Best Guesstimate
Estimating the Difference
of Two Proportions
When a characteristic, such as opinion on an issue (support/don’t support),
of the two groups being compared is categorical, people want to report on
the differences between the two population proportions — for example, the 211
difference between the proportion of women who support a four-day work
week and the proportion of men who support a four-day work week. How do
you do this?
You estimate the difference between two population proportions, p – p , by
1 2
taking a sample from each population and using the difference of the two
sample proportions, , plus or minus a margin of error. The result is called
a confidence interval for the difference of two population proportions, p – p .
1 2
The formula for a CI for the difference between two population proportions
is , where and n are the sample propor-
1
tion and sample size of the first sample, and and n are the sample proportion
2
and sample size of the second sample. z* is the appropriate value from the stan-
dard normal distribution for your desired confidence level. (Refer to Table 13-1
for z*-values.)
To calculate a CI for the difference between two population proportions, do
the following:

1. Determine the confidence level and find the appropriate z*-value.
Refer to Table 13-1.
2. Find the sample proportion for the first sample by taking the total
number from the first sample that are in the category of interest
and dividing by the sample size, n . Similarly, find for the second
1
sample.
3. Take the difference between the sample proportions, .
4. Find and divide that by n . Find and divide that
1
by n . Add these two results together and take the square root.
2
5. Multiply z* times the result from Step 4.
This step gives you the margin of error.

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