Introduction to MINITAB in the Saint Mary's Microcomputer
Lab
XII. Inference on the difference between two proportions
Hypothesis tests and Confidence Interval calculations are carried
out with the same command. Minitab will not check whether the
conditions for using the test are met but will simply carry out
the calculations. Checking appropriatness is your job.
Minitab will perform tests or calculate confidence intervals
for proportions either from Summarized data (you enter the sample
size/number of trials and the number of successes for each sample)
or from raw data (Data in columns of 1's - each representing a
success - and 0's - each representing a failure).
Procedure
To calculate a confidence interval for the difference betweeen
two proportions or to carry out a significance test on a dfference
between two proportions. Some steps will vary, depending on how
you enter the data.
- 1. Select Stat>Basic Statistics>2Proportions
- 2. Locate the data:
If the data are all in one column of 1's (successes) and
0's (failures) with another column ("subscripts")
identifying which population each comes from then click on
the "Samples in one column" button, select the column
containing the data (successes & failures) for the "Samples"
box and the column containing the identifiers (subscripts) for
the "Subscripts" box.
If the data are in two columns of 1's & 0's (one column
for each sample) then click on the "Samples in different
columns" button and enter the column for your first sample
in the "First" box, column for your second column in
the "Second" box. Remember the order - it will affect
how you read your results. Naming the columns will help, here.
If you will enter summary data (sample size and number of
successes) for each sample click on the "Summarized
data" button, and enter the number of trials (sample size
- n) and number of successes for each sample in the boxes. Remember
the order - it will affect how you set up tests and how you read
results.
- 3. Click on the "Options" button (so you
can set the confidence level and/or set up the null and alternative
hypothesis.)
- 4. If you want a confidence interval estimate for the difference
in the proportions, enter the confidence level (as a percent
- 95% as "95", not ".95") in the "Level"
box and be sure the "Alternative" is
set to "not equal"
If you want to perform a test, set the alternative hypothesis
("less than", "greater than", or "not
equal") in the "Alternative" box. If you want
to test for a specific difference K (rather than simply on proportion
is greater than, less than, different from the other) you can
enter this value K (as a proportion - difference of 5 percentage
points would be .05, not 5) in the "Test difference"
box (usually you will leave this as 0 - the null hypothesis "p1-p2
= 0" is the same as "p1=p2").Be sure the direction
of your test says what you want with the order of your samples.
- 5. Click "OK" for the "Options" window
and "OK" for the "2proportions" window.
Output in the Session window. Form depends on how the
data were entered:
A. For data entered in two columns (of 0's & 1's)
the program will show:
- A heading "Test and CI for two proportions: [first sample],[second
sample]"
- A line "Success = 1" to remind you how "success"
was indicated.
- A table with data on the two samples (labeled at the top):
For each sample:
- Variable (column number, if you didn't name them), number
of successes (X) number of trials (N) and sample p (p-hat).
- A line "Estimate of p(first sample) - p(second sample):
[value of p-hat[first] - p-hat [second] ]
- A confidence interval (if alternative was "not equal")
- "C% confidence interval for p(first) - p(second)":
([lower bound],[upper bound]) or or cutoff (one-sided
confidence interval) (if alternative was "less than"
or "greater than")"C% upper [or lower] bound for
p(first) - p(second)":[cutoff for one-sided confidence interval]
- A text line "Test for p(first) - p(second) = 0 [or K,
if you entered a K value] (vs [alternative]): Z = [z-value of
test], P-Value = [p-value]"
B. If two-proportion data were entered in summary form
the program will show:
- A heading "Test and CI for two proportions"
- Atable repeating the data entered, plus the sample proportions:
For each sample:
- Sample number (1 or 2) number of successes (X) number of
trials (N) and sample p (p-hat).
- A line "Estimate of p(1) - p(2): [value of p-hat[first]
- p-hat [second] ]
- A confidence interval (if alternative was "not equal")
- "C% confidence interval for p(1) - p(2)": ([lower
bound],[upper bound]) or or cutoff (one-sided confidence
interval) (if alternative was "less than" or "greater
than")"C% upper [or lower] bound for p(1) - p(2)":[cutoff
for one-sided confidence interval]
- A text line "Test for p(1) - p(2) = 0 [or K, if you
entered a K value] (vs [alternative]): Z = [z-value of test],
P-Value = [p-value]"
C. For data entered in one column, with an indicator variable
(subscript) in another column the program will show:
- A heading "Test and CI for two proportions:[sample column],
[subscript column]"
- A line "Success = 1" to remind you how "success"
was indicated.
- A table with data on the two samples (labeled at the top):
For each sample:
- Value of the subscript that identifies the sample [Note
smaller subscript value will give the "first" sample],
number of successes (X) number of trials (N) and sample p (p-hat).
- A line "Estimate of p(subscript for first sample) -
p(subscript for second sample): [value of p-hat[first] - p-hat
[second] ]
- A confidence interval (if alternative was "not equal")
- "C% confidence interval for p(first subscript) - p(second
subscript)": ([lower bound],[upper bound]) or or
cutoff (one-sided confidence interval) (if alternative was "less
than" or "greater than")"C% upper [or lower]
bound for p(first subscript) - p(second subscript)":[cutoff
for one-sided confidence interval]
- A text line "Test for p(first subscript) - p(second
subscript) = 0 [or K, if you entered a K value] (vs [alternative]):
Z = [z-value of test], P-Value = [p-value]"
The printout does not give a yes or no answer for the
test - you must determine that, based on the p-value and your
decision criteria.
Last update 11/27/2000
Maintained by cpeltier@saintmarys.edu