Usually, social researchers
use the T-Test to test for significant differences between
means observed for two But occasionally,
researchers will want to determine whether there is a
significant change in the scores of the same cases on the
same variables over time. In this instance, the standard
T-Test for Independent Samples does not apply. Consider the situation of
voting turnout in American states in elections since 1980.
Different stories could be
told for each of these elections, but let's concentrate on
the turnout data for 1980 and 1984. The 1980 election,
between incumbent president Jimmy Carter and challenger
Ronald Reagan also had a third candidate, John Anderson--who
had been a Republican party leader but who ran as an
Independent. Reagan was elected in 1980
and ran for re-election in 1984 against Walter Mondale, but
there was no third party candidate in 1984. The mean voting
turnout in 1984--when calculated across all the
states--dropped compared with 1980. Some say that turnout
dropped because there was no third party candidate. Others
say that the observed differene between means of only 1.1%
points (55.7-54.6) could have been attributable to
chance.
Treating the 51 states as
"Independent" in computing the T-Test produces a But suppose that some
systematic process was going on. Suppose that
Pair 1 % turnout in 1980 election % turnout in 1984 election Paired Differences When states are matched on
their turnout levels in 1980 and 1984, a

**The Paired Samples
T-Test in Research**
**independent** groups, such as
Democrats v. Republicans, or men v. women, or white v.
black, and so on. These groups are *independent* in the
sense that cases in one group are not **matched** with
cases in the other group.

**% turnout in presidential elections by
states**

Perhaps we could do a standard T-Test to check this out.
Let's compute the **T-Test for Independent
Samples:**
**test
statistic** (**t**) less than one. A test statistic
this small falls far short of significance at the customary
.05 level, so it suggests that the observed difference in
states' voting turnout between 1980 and 1984 is unlikely to
have occurred by chance.*most*
states tended to demonstrate a slightly lower voting turnout
rate between 1980 and 1984--perhaps dropping by about one
point. Perhaps this systematic change is lost by only
calculating the means for each year.

In fact, because the states are **matched on repeated
measures**, we must use the **Paired Samples T-Test**
in SPSS, which produces this very different
result:

**Paired Samples Statistics**

**Paired Samples Test: % turnout in 1980
election - % turnout in 1984 election**
**t**
**df**
**Sig. (2-tailed)**
**0.002****paired samples T
Test** shows that the changes from one year to the next
were small, but systematic. Such systematic shifts downward
in voting turnout would have occurrred **fewer** than 1
time out of 100, if the shifts were purely due to change
variation.