SPSS Guide: Independent t-test
Two-Sample T-Test, Independent
SPSS Guide: Independent t-test
A clinical psychologist wonders if eating disorders are exacerbated (i.e., worsened) by peer pressures in college sororities. He compares the body weights of women within a sorority (105, 115, 90, 120, 125) to those not in a sorority (140,135,120,130,110). Is there a significant difference?
Why a Independent t-test? We have (1) two groups of participants, (2) no population information, and (3) the two subjects in the two groups are not matched.
DATA VIEW **
VARIABLE VIEW
With an independent t-test, the first column indicates the group (1=sorority, 2=other) whereas the second gives the actual data points (weight).
In the VARIABLE VIEW we click on the Values column to label "1" and "2" appropriately. This makes the output easier to read.
1. Go to the Analyze Menu, select Compare Means, then choose Independent samples t-test.
2. Put the variable the defines the two groups in the Grouping Variable box (e.g., group) and put the variable the contains the actual data points or scores in the Test Variable box (e.g., weight)
3. Click on Define Groups, then specify two groups you want to compare. Typically you'll just be comparing groups 1 and 2.
Jeff Sinn, Winthrop University, SPSS Guide - Independent T-test (rev 9/06)
Two-Sample T-Test, Independent
Statistical Hypotheses
H0: 1 ? 2 = 0 This guess says any difference is just due to sample error.
HA: 1 ? 2 0 This guess says there is a reliable difference ? a treatment effect (e.g., if you kept measuring, you'd see
that the two groups don't weigh the same).
Formula
Difference observed.
t obtained
=
(x1 - x2 ) - (?1 - ?2 ) = 111 -127
s^x1 -x2
8.216
= -1.947
t critical = ? 2.306 (from t-test table)
Difference expected.
[df = n1+n2 -2 = 8, two-tailed, =.05)]
SPSS Output
weight
group sorority
other
Group Statistics
N Mean 5 111.00
5 127.00
Std. Deviation
13.874
12.042
Std. Error Mean 6.205
5.385
Definitions
x1 = sample mean of the first group x2 = sample mean of the second group ?1 - ?2 = diff between population means (always 0) s^x1 -x2 = standard error of the difference ----------------------------- N = number of subjects in a sample Mean = x (or M) (sample mean) Std. Deviation = ^sx (standard deviation as an estimate.) Std. Error Mean = s^x (standard error of the mean as an est.) ---------------------------------------df = degrees of freedom = n1 + n2 - 2 Sig = pobt = chance diff due to sampling error Mean Diff = x1 - x2 Std. Error Diff = s^x1 -x2 ----------------------------- d = effect size, a measure of practical signif.
weight
Test for Eq of Var
Independent Samples Test t-test for Equality of Means
Sig.
Std. Error
95% Conf Int
F Sig.
t
df
2-tail Mean Diff
Diff
Lower
Upper
Eq
.094 .767 -1.947
8
.087
-16.000
8.216 -34.95
2.946
Uneq
-1.947 7.8
.088
-16.000
8.216 -35.01
3.011
Always use the first line.
Pobt is not below .05 so RETAIN the Ho hypothesis.
Difference observed. Difference expected.
Practical Significance
s^ = s^ x1 - x2 * n = 8 .216 *
d = x1 - x 2 = 111 - 127
s^
18 .3715
5 = 18 .3715 = .8709
Note: Not required!!!! Provided only so you can see calculation method. Because we did not find statistical significance, we need no calculation of practical significance. Note you must first calculate before calculating d. Note "n" is for just one group.
Summary of Statistic: Retain Ho t(8) = -1.947, n.s.
This says that the t-test with 8 degrees of freedom was not significant ? we must retain the Ho hypothesis. We must retain the possibilities that the difference between the two groups is zero.
Explanation of Study Outcome: The (research) hypothesis was not supported. The average weight of sorority women (M = 111) did not differ significantly from that of other women (M = 127),
t(8) = -1.947, n.s.
Guide to write-ups: 1. State whether the research hypothesis was supported. 2. Summarize the statistical test 3. Summarize the practical significance (if appropriate).
Jeff Sinn, Winthrop University, SPSS Guide - Independent T-test (rev 9/06)
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