Introduction to MINITAB in the Saint Mary's Microcomputer
Lab
IX. Inference on difference of means
(Independent samples from two populations)
Hypothesis tests and Confidence Interval calculations are carried
out with the same command.
You need to know which way the data are entered. There are two
possibilities:
1. The data for the two samples are in separate
columns (typical if you did an experiment or observation
just for this variable)
2. The data for the two samples are in the same
column, with another column containing a code saying which
sample the individual is in [Typical if the data are from a large
experiment or study in which many variables are observed on each
individual] Procedures for both cases will be disucssed here.
1. If the data are in two separate columns - one for each sample
.
Naming the columns will be a great help here, because
you will need to remember which population (which sample) you
have first in your alternative hypothesis or in calculating the
difference for the confidence interval.
- 1. Select Stat>Basic Statistics>2-Sample t.
- 2. Select (click on the circle next to) "Samples in
different columns "
- 3. With the cursor in the box labeled " First "
, select (double-click or highlight & then click " Select
") the name (or column) of your first variable (or type
the name in the box). Remember that the order matters (must match
your alternative hypothesis, or the order in which you want to
state your results, for estimation - this is your "X1",
if you haven't used better names).
- 4. With the cursor in the box labeled " Second ",
select the name of your second variable (or type its name in
the box - this is your "X2").
- 5. Click on the "Options" button
- 6. If you want a confidence interval for the difference between
the means: type in the confidence level in the "Level"
box and make sure the "Alternative" is
set to "not equal"
- 7. If you want to perform a test on the mean difference:
select the alternative hypothesis ("less than" "not
equal" or "greater than" in the "Alternative"
box - for the one-sided alternatives, make sure the alternative
says what you mean (the "First" and "Second"
labels matter)
- 8. If you want to test a null hypothesis of the form "Mu(1)
- Mu(2) = K" (rather than the usual Mu(1) = Mu(2)) enter
K in the "Test Mean" box (usually you will leave
this at 0.0)
- 9. Click "OK" for the "options" window
and "OK" for the "2-sample t" window.
Output in the Session window::
- A heading "Two-Sample T-Test and CI: [First sample],[Second
sample]"
- A second text line "Two sample T for [first column]
vs [second column]"
- A table with data on the two samples: First a heading line
identifying the numbers below
- For each variable: the variable name, the sample size (labeled
"N"), the sample mean (labeled "Mean"), Sample
standard deviation (labeled "StDev") and the (sample)
standard error of the mean (StDev/sqrt(N) - labeled "SE
Mean).
A statement of which way the comparison is done: "Difference
= mu[First] - mu[Second]"
A line "Estimate of difference: [number]" - this is
the difference in the sample means (order as specified in the
line above).
A line with the confidence interval:
For a standard confidence interval (or if the test is "not
equal") "C% confidence interval for difference: ([Lower
limit], [Upper limit])
If you performed a test with alternative "greater than"
or "less than" : "C% lower bound [or upper bound]
for difference [value] " This is the value for which we
can say "We can say, with C% confidence that the mean is
no less than [no more than] [value]" - this is the cutoff
for a one-sided confidence interval (all the risk on one side).
"T-Test of difference = 0 [or K, if you put in a K] (vs
{">" or "<" or "not ="}):
T-value = [number] P-value = [number] DF = [number]" [Degrees
of freedom may not be a whole number - Minitab uses the exact
calculation rather than our rough rule of thumb]
The printout does not give a yes or no answer - you must determine
that, based on the t- or p-value and your decision criteria.
2. If the data are all in one column, identified by codes
in another column:
- 1. Select Stat>Basic Statistics>2-Sample t.
- 2. Select (click on the circle next to) "Samples in
one column"
- 3. With the cursor in the box labeled "Samples"
, select (double-click or highlight & then click "Select
") the name (or column) of the column containing the values
of the variable you want to test on.
- 4. With the cursor in the box labeled " Subscripts",
select the name of the column that identifies which group the
individual is in..
5. Click on the "Options" button
- 6. If you want a confidence interval for the difference between
the means: type in the confidence level in the "Level"
box and make sure the "Alternative" is
set to "not equal"
- 7. If you want to perform a test on the mean difference:
select the alternative hypothesis ("less than" "not
equal" or "greater than" in the "Alternative"
box - for the one-sided alternatives, make sure the alternative
says what you mean (the "First" and "Second"
labels matter) Note: The first entry in the "Subscripts"column
will determine which group is considered "first"
and which is "second". This matters if you are testing
for "Less than" or "Greater than" - so look
at the data to make sure the order the program will use matches
the order in your alternative hypothesis.
- 8. If you want to test a null hypothesis of the form "Mu(1)
- Mu(2) = K" (rather than the usual Mu(1) = Mu(2)) enter
K in the "Test Mean" box (usually you will leave
this at 0.0)
- 9. Click "OK" for the "options" window
and "OK" for the "2-sample t" window.
Output in the Session window::
- A heading "Two-Sample T-Test and CI: [Variable tested],[Variable
indicating groups]"
- A second text line "Two sample T for [Variable]"
- A table with data on the two groups: First a heading line
identifying the numbers below
- For each group: the value (for the "subscript"
variable) that identifies the group, the sample size (labeled
"N"), the sample mean (labeled "Mean"), Sample
standard deviation (labeled "StDev") and the (sample)
standard error of the mean (StDev/sqrt(N) - labeled "SE
Mean).
A statement of which way the comparison is done: "Difference
= mu[First label] - mu[Second label]"
A line "Estimate of difference: [number]" - this is
the difference in the sample means (order as specified in the
line above).
A line with the confidence interval:
For a standard confidence interval (or if the test is "not
equal") "C% confidence interval for difference: ([Lower
limit], [Upper limit])
If you performed a test with alternative "greater than"
or "less than" : "C% lower bound [or upper bound]
for difference [value] " This is the value for which we
can say "We can say, with C% confidence that the difference
in the means (First - Second) is no less than [no more than]
[value]" - this is the cutoff for a one-sided confidence
interval (all the risk on one side).
"T-Test of mean difference = 0 [or K, if you put in a
K] (vs {">" or "<" or "not ="}):
T-value = [number] P-value = [number] DF = [number]"
The printout does not give a yes or no answer - you
must determine that, based on the t- or p-value and your decision
criteria.
Last update 8/18/2000
Maintained by cpeltier@saintmarys.edu