Statistics Dictionary
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MatchedPairs tTest
A matchedpairs ttest is used to test whether there is a
significant mean difference between two sets of
paired data.
Here is how to use the test.

Define paired differences.
Define a new variable d, based on the difference between paired values
from two data sets.
d = x_{1}  x_{2}
where x_{1} is the value of variable x in the first data set,
and x_{2} is the value of variable from the second data set that is
paired with x_{1}.

Define hypotheses.
The table below shows three sets of null and alternative hypotheses.
Each makes a statement about how the true difference in population values
μ_{d} is related to some hypothesized value
M.
(In the table, the symbol ≠ means " not equal to ".)
Set

Null hypothesis 
Alternative hypothesis 
Number of tails 
1

μ_{d} = M

μ_{d} ≠ M

2 
2

μ_{d} > M

μ_{d} < M

1 
3

μ_{d} < M

μ_{d} > M

1 

Specify significance level. Often, researchers choose
significance levels
equal to
0.01, 0.05, or 0.10; but any value between 0 and
1 can be used.

Find degrees of freedom. The
degrees of freedom
(DF) is:
DF = n  1
where n is the number of paired observations.

Compute test statistic. The test statistic is a t statistic (t) defined by
the following equation.
t = (d
 M )
/ [ s_{d} /sqrt(n) ]
where
d is the sample mean difference between
paired observations,
M is the hypothesized mean difference (from the null hypothesis), and
s_{d} is the
standard deviation
of the differences
(i.e., of the d values).

Compute Pvalue. The Pvalue is the probability of observing a
sample statistic as extreme as the test statistic. Since the
test statistic is a t statistic, use the
t Distribution Calculator
to assess the probability associated with the t statistic, having
the degrees of freedom computed above.

Evaluate null hypothesis. The evaluation involves comparing the Pvalue to the
significance level,
and rejecting the null hypothesis when the Pvalue is less than
the significance level.
The matchedpairs ttest can be used with large or
small samples.