The
t-test with SPSS |

**A Review of the t-test**

The t-test is used for testing differences between two means. In order to use
a t-test, the **same variable** must be measured in different groups, at
different times, or in comparison to a known population mean. Comparing a sample
mean to a known population is an unusual test that appears in statistics books
as a transitional step in learning about the t-test. The more common applications
of the t-test are testing the difference between independent groups or testing
the difference between dependent groups.

A t-test for independent groups is useful when the same variable has been measured in two independent groups and the researcher wants to know whether the difference between group means is statistically significant. "Independent groups" means that the groups have different people in them and that the people in the different groups have not been matched or paired in any way. A t-test for related samples or a t-test for dependent means is the appropriate test when the same people have been measured or tested under two different conditions or when people are put into pairs by matching them on some other variable and then placing each member of the pair into one of two groups.

__The t-test For Independent Groups on SPSS__

A t-test for independent groups is useful when the researcher's
goal is to compare the difference between means of two groups on the same variable.
Groups may be formed in two different ways. First, a preexisting characteristic
of the participants may be used to divide them into groups. For example, the
researcher may wish to compare college GPAs of men and women. In this case,
the **grouping variable** is biological sex and the two groups would consist
of men versus women. Other preexisting characteristics that could be used as
grouping variables include age (under 21 years vs. 21 years and older or some
other reasonable division into two groups), athlete (plays collegiate varsity
sport vs. does not play), type of student (undergraduate vs. graduate student),
type of faculty member (tenured vs. nontenured), or any other variable for which
it makes sense to have two categories. Another way to form groups is to randomly
assign participants to one of two experimental conditions such as a group that
listens to music versus a group that experiences a control condition. Regardless
of how the groups are determined, one of the variables in the SPSS data file
must contain the information needed to divide participants into the appropriate
groups. SPSS has very flexible features for accomplishing this task.

Like all other statistical tests using SPSS, the process begins with data. Consider the fictional data on college GPA and weekly hours of studying used in the correlation example. First, let's add information about the biological sex of each participant to the data base. This requires a numerical code. For this example, let a "1" designate a female and a "2" designate a male. With the new variable added, the data would look like this:

Participant |
Current GPA |
Weekly Study Time |
Sex |

Participant #01 |
1.8 |
15 hrs |
2 |

Participant #02 |
3.9 |
38 hrs |
1 |

Participant #03 |
2.1 |
10 hrs |
2 |

Participant #04 |
2.8 |
24 hrs |
1 |

Participant #05 |
3.3 |
36 hrs |
. |

Participant #06 |
3.1 |
15 hrs |
2 |

Participant #07 |
4.0 |
45 hrs |
1 |

Participant #08 |
3.4 |
28 hrs |
1 |

Participant #09 |
3.3 |
35 hrs |
1 |

Participant #10 |
2.2 |
10 hrs |
2 |

Participant #11 |
2.5 |
6 hrs |
2 |

With this information added to the file, two methods of dividing participants
into groups can be illustrated. Note that Participant #05 has just a single
dot in the column for sex. This is the standard way that SPSS indicates missing
data. This is a common occurrence, especially in survey data, and SPSS has flexible
options for handling this situation. Begin the analysis by entering the new
data for sex. Use the arrow keys or mouse to move to the empty third column
on the spreadsheet. Use the same technique as previously to enter the new data.
When data is missing (such as Participant #5 in this example), hit the **<ENTER>**
key when there is no data in the top line (you will need to **<DELETE>**
the previous entry) and a single dot will appear in the variable column. Once
the data is entered, click** Data**

To request the t-test, click **Statistics** > **Compare Means** >
**Independent Samples T Test**. Use the right-pointing arrow to transfer
COLGPA to the "

__T-Test__

**
Group Statistics**

Variable | N |
Mean |
Std. Deviation | Std. Error Mean | |

SEX | 1.00 Female | 5 | 3.4800 | .487 | .218 |

2.00 Male | 5 | 2.3400 | .493 | .220 |

**Independent Samples Test**

Levene's Test for Equality of Variances | |||

F | Sig. | ||

SEX | Equal variances assumed | .002 | .962 |

Equal Variances not assumed |

t-test for Equality of Means | |||||

t | df | Sig. (2-tailed) | Mean Difference | ||

SEX | Equal variances assumed | 3.68 | 8 | .021 | .1750 |

Equal variances not assumed | 3.68 | 8.00 | .025 | .1750 |

The output begins with the means and standard deviations for the two variables
which is key information that will need to be included in any related research
report. The "Mean Difference" statistic indicates the magnitude of
the difference between means. When combined with the confidence interval for
the difference, this information can make a valuable contribution to explaining
the importance of the results. "Levene's Test for Equality of Variances"
is a test of the homogeneity of variance assumption. When the value for *F*
is large and the *P*-value is less than .05, this indicates that the variances
are heterogeneous which violates a key assumption of the t-test. The next section
of the output provides the actual t-test results in two formats. The first format
for "Equal" variances is the standard t-test taught in introductory
statistics. This is the test result that should be reported in a research report
under most circumstances. The second format reports a t-test for "Unequal"
variances. This is an alternative way of computing the t-test that accounts
for heterogeneous variances and provides an accurate result even when the homogeneity
assumption has been violated (as indicated by the Levene test). It is rare that
one needs to consider using the "Unequal" variances format because,
under most circumstances, even when the homogeneity assumption is violated,
the results are practically indistinguishable. When the "Equal" variances
and "Unequal" variances formats lead to different conclusions, seek
consultation. The output for both formats shows the degrees of freedom (df)
and probability (2-tailed significance). As in all statistical tests, the basic
criterion for statistical significance is a "2-tailed significance"
less than .05. The .021 probability in this example is clearly less than .05
so the difference is statistically significant.

A second method of performing an independent groups t-test with SPSS is to
use a noncategorical variable to divide the test variable (college GPA in this
example) into groups. For example, the group of participants could be divided
into two groups by placing those with a high number of study hours per week
in one group and a low number of study hours in the second group. Note that
this approach would begin with exactly the same information that was used in
the correlation example. However, converting the Studyhrs data to a categorical
variable would cause some detailed information to be lost. For this reason,
caution (and consultation) is needed before using this method. To request the
analysis, click __S__tatistics**>** **Compare Means** **>**
**Independent Samples T Test...**. Colgpa will remain the "Test
Variable(s)" so it can be left where it is. Alternately, other variables
can be moved into this box. Click "Sex(1,2)" to highlight it and remove
it from the "Grouping Variable" box by clicking the bottom arrow which
now faces left because a variable in the box has been highlighted. Next, highlight
"Studyhrs" and move it into the "Grouping Variable" box.
Now click

**Group Statistics**

Studyhours | N | Mean | Std.Deviation | Std. Error Mean | |

COLGPA College GPA for Fall 1997 | Studyhours >= 20.00
Studyhours < 20.00 |
6
5 |
3.4500
2.3400 |
.4416
.4930 |
.1803
.2205 |

The "Group Statistics" table provides the means and standard deviations along with precise information regarding the formation of the groups. This can be very useful as a check to ensure that the cutpoint was selected properly and resulted in reasonably similar sample sizes for both groups. The remainder of the output is virtually the same as the previous example.

__The t-test For Dependent Groups on SPSS__

The t-test for **dependent** groups requires a different way of approaching
the data. For this type of test, each case is assumed to have two measures of
the same variable taken at different times. Each "Case" would therefore
consist of a **single person**. This would be what is called a repeated measures
design. Alternately, each case could contain the same information about two
**different** individuals who have been paired or matched on a variable.
In the repeated measures situation, one might collect GPA information at two
different points in the careers of a group of students. The table below shows
how this situation might appear in the fictional example. In this case, GPA
data have been collected at the end of each participant's
first year (Colgpa1) and senior year (Colgpa2).

Participant |
Colgpa1 |
Weekly Study Time |
Sex |
Colgpa2 |

Participant #01 |
1.8 |
15 hrs |
2 |
. |

Participant #02 |
3.9 |
38 hrs |
1 |
3.88 |

Participant #03 |
2.1 |
10 hrs |
2 |
2.80 |

Participant #04 |
2.8 |
24 hrs |
1 |
3.20 |

Participant #05 |
3.3 |
36 hrs |
. |
3.60 |

Participant #06 |
3.1 |
15 hrs |
2 |
3.57 |

Participant #07 |
4.0 |
45 hrs |
1 |
4.00 |

Participant #08 |
3.4 |
28 hrs |
1 |
3.35 |

Participant #09 |
3.3 |
35 hrs |
1 |
3.66 |

Participant #10 |
2.2 |
10 hrs |
2 |
2.55 |

Participant #11 |
2.5 |
6 hrs |
2 |
2.67 |

One thing to note about the new data is that the GPA of the first participant is missing. Given the 1.8 GPA at the first assessment, it seemed reasonable that this person might not remain in college for the entire four years. This is a common hazard of repeated measures designs and the implication of such missing data needs to be considered before interpreting the results.

To request the analysis, click __S__tatistics**>** **Compare
Means**

**Paired Samples Statistics**

Mean |
N |
Std. Deviation | Std. Error Mean | ||

Pair 1 | Colgpa1
Colgpa2 |
3.0600
3.3280 |
10
10 |
.6552
.5091 |
.2072
.1610 |

**Paired Samples Correlations**

N | Correlation | Sig. | |

Pair 1 Colgpa1 - Colgpa2 | 10 | .944 | .000 |

**Paired Samples Test**

Paired Differences |
t |
|||||

95% Confidence Interval of the Difference |
||||||

Mean | Std. Deviation | Std. Error Mean | Lower | Upper | ||

Pair 1 Colgpa1 - Colgpa2 | -.2680 | .2419 | 7.649E-02 | .4410 | -9.50E-02 | -3.504 |

**
Paired Samples Test**

df | Sig. (2-tailed) | |

Pair 1 Colgpa1 - Colgpa2 | 9 | .007 |

The output is similar to the independent groups t-test. The first table of
the output shows the means and standard deviations for the two groups and the
second table shows the correlation between the paired variables. The next table
shows the mean of the differences, standard deviation of the differences, standard
error of the mean, the confidence interval for the difference, and the obtained
value for t. The 2-tailed Sig[nificance] which is stated as a probability
is shown in the last table. As usual, probabilities **less than** .05 indicate
that the null hypothesis should be rejected. In this case, the interpretation
would be that GPA increased significantly from firstyear to senior year, __t__(9)
= 3.50, __p__ = .007.

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