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Inference for paired data.
If your paired data is in two separate
columns, like before in C7 and
after in C8, you can perform
inference in Minitab by going to stat, basic statistics,
paired T.
Minitab
will take the difference between the first sample and the second sample.
If I want to use before minus after,
the first sample would be the before column
and the second sample is after.
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By clicking the options button I can set the confidence level
if I'm looking for a confidence interval.
Make sure that the alternative
hypothesis is set to not equal if you are looking for confidence interval.
Instead, I want to see
if the mean difference is greater than zero.
If I wanted to see if
the mean difference was greater than five, I would change
this number to five.
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Also Minitab can produce a graph for us
without us having to take the differences. Minitab will do it
for us. Let's look at a histogram.
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Let's look at the output for the p-value.
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Make sure at the top of the output, the order is correct.
We wanted before minus after.
At the
bottom of the output we can find the hypotheses,
the test statistic,
and the p-value.
The p-value will
only go out to three decimal places in Minitab, but this does not
mean that the p-value is exactly equal to zero.
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Let's say that we already have a
column of differences in Minitab.
Let me quickly create this.
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I'll go to the calc menu and use the calculator
to manually compute the difference between before and after.
I'll store it in the new column that I just called difference.
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If this is the only part of the data that you have, one column of
differences, you can still perform the two, or the paired
t-test in Minitab.
What you need to do is first summarize
the column of differences. You can do that by going to
stat, basic statistics, display descriptive
statistics.
Enter the column of differences
and the statistics that you will need will be the mean,
the standard deviation, and the sample size.
I will uncheck the
rest of the statistics.
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We can then enter
these numbers in the paired t-test
option in Minitab. That's in the stat menu under
basic statistics.
I'll select
paired T and then instead of having the two
samples, we're going to enter the summarized data.
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Sample size, that's fifty,
mean, 10.37,
and standard deviation,
14.04.
I'll check
in the options button, we'll do a two sided test
and get a confidence interval as well.
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The only downfall with this is that we can not
produce a graph if we only have summarized data.
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We'll have to do that manually using the graph drop down menu
in Minitab.
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So here's the output from our hypothesis test.
The confidence interval appears above
the information for the hypothesis test.
Down here we can find the p-value.
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And if you wanted to create the histogram of differences,
you can do that by going to the graph menu,
select histogram,
simple is already selected,
and the variable that we want to graph is the difference
column.