SPSS Tutorials: definition, uses, SPSS steps and
interpretation of independent sample t-test.
Md. Sharif Hossain
What is Independent sample t-test
The Independent-Samples t Test approach automates the
estimation of the t test effect size while comparing the means for two groups
of cases. In order to ensure that any differences in reaction are caused by the
treatment (or lack of treatment) and not by other factors, the subjects for
this test should ideally be randomly assigned to two groups. If you compare the
average wage for men and women, this is not the case. The gender of a person is
not chosen at random.
The following are frequently put to the test using the
independent samples t test:
- Statistical variations between two groups' means
- Comparison of the means of two interventions, with statistics
- Differences in two change scores' means based on statistics
It should be noted that the Independent Samples t Test can
only compare the means of two groups. Comparisons between more than two groups
are impossible. You should probably perform an ANOVA if you want to compare the
means of more than two groups.
what Steps need to calculate Independent sample t-test by using IBM SPSS :
1.
From the menus choose:
Analyze > Group
comparison - parametric > Independent-samples t test
2.
Click Select variables under
the Dependent variables section
and select one or more quantitative dependent variables. A separate t test is computed for each
variable. Click OK after
selecting the variables.
3.
Click Select variable under
the Group variable section
and select a single grouping variable. The variable can be numeric or string.
Click OK after
selecting the variable.
4.
Optionally, click the link next to the group variable to specify
values for the groups that you want to compare, or to specify a cut point
value. For more information, see Independent-samples t test:
Define groups.
5.
Optionally, you can select the following options from the Additional settings menu:
o
Click Statistics to select which statistics to
include in the analysis.
o
Click Options to set the confidence interval
level and control the treatment of missing data.
o
Click Bootstrap for deriving robust estimates of
standard errors and confidence intervals for estimates such as the mean,
median, proportion, odds ratio, correlation coefficient or regression
coefficient.
The variable(s) under
consideration This is the continuous
variable whose meaning will be compared between the two groups. You may run
multiple t tests simultaneously by selecting more than one test
variable.
Grouping
Variable: The independent variable is grouped as such. The categories
(or groups) of the independent variable will define which samples will be
compared in the t test. The grouping variable must have at least two
categories (groups); it may have more than two categories, but a category
can only compare two groups, so you will need to specify which two groups
to compare. You can also use a continuous variable by specifying a cut point to
create two groups (i.e., values at or above the cut point and values below the
cut point).
Define Groups:
Click Define Groups to define the category indicators (groups)
to use in the t test. If the button is not active, make sure
that you have already moved your independent variable to the right in the Grouping
Variable field. You must define the categories of your grouping
variable before you can run the Independent Samples t Test
procedure.
Options: The
Options section is where you can set your desired confidence level for the
confidence interval for the mean difference and specify how SPSS should handle
missing values.
When finished,
click OK to run the Independent Samples t Test,
or click Paste to have the syntax corresponding to your
specified settings written to an open syntax window. (If you do not have a
syntax window open, a new window will open for you.)
How to interpret the independent sample t-test
OUTPUT
Tables
Two sections (boxes) appear in the
output: Group Statistics and Independent Samples Test.
The first section, Group Statistics, provides basic information
about the group comparisons, including the sample size (n), mean,
standard deviation, and standard error for mile times by group. In this
example, there are 166 athletes and 226 non-athletes. The mean mile time for
athletes is 6 minutes 51 seconds, and the mean mile time for non-athletes is 9
minutes 6 seconds.
The second section, Independent
Samples Test, displays the results most relevant to the Independent
Samples t Test. There are two parts that provide different
pieces of information: (A) Levene’s Test for Equality of Variances and (B)
t-test for Equality of Means.
A Levene's
Test for Equality of of Variances: This section has the test results for
Levene's Test. From left to right:
- F is the
test statistic of Levene's test
- Sig. is the
p-value corresponding to this test statistic.
The p-value of Levene's test is
printed as ".000" (but should be read as p <
0.001 -- i.e., p very small), so we we reject the null of
Levene's test and conclude that the variance in mile time of athletes is
significantly different than that of non-athletes. This tells us that we
should look at the "Equal variances not assumed" row for the t test
(and corresponding confidence interval) results. (If this test result had
not been significant -- that is, if we had observed p > α --
then we would have used the "Equal variances assumed" output.)
B t-test
for Equality of Means provides the results for the actual Independent
Samples t Test. From left to right:
- t is the
computed test statistic, using the formula for the equal-variances-assumed
test statistic (first row of table) or the
formula for the equal-variances-not-assumed
test statistic (second row of table)
- df is the
degrees of freedom, using the equal-variances-assumed
degrees of freedom formula (first row of table) or
the equal-variances-not-assumed
degrees of freedom formula (second row of table)
- Sig (2-tailed) is the
p-value corresponding to the given test statistic and degrees of freedom
- Mean Difference is the
difference between the sample means, i.e. x1 − x2; it also
corresponds to the numerator of the test statistic for that test
- Std. Error
Difference is
the standard error of the mean difference estimate; it also corresponds to
the denominator of the test statistic for that test
Note that the mean difference is calculated by
subtracting the mean of the second group from the mean of the first group. In
this example, the mean mile time for athletes was subtracted from the mean mile
time for non-athletes (9:06 minus 6:51 = 02:14). The sign of the mean
difference corresponds to the sign of the t value. The
positive t value in this example indicates that the mean mile
time for the first group, non-athletes, is significantly greater than the mean
for the second group, athletes.
The associated p value is
printed as ".000"; double-clicking on the p-value will reveal the un-rounded
number. SPSS rounds p-values to three decimal places, so any p-value too small
to round up to .001 will print as .000. (In this particular example, the
p-values are on the order of 10-40.)
C Confidence
Interval of the Difference: This part of the t-test output
complements the significance test results. Typically, if the CI for the mean
difference contains 0 within the interval -- i.e., if the lower boundary of the
CI is a negative number and the upper boundary of the CI is a positive number
-- the results are not significant at the chosen significance level. In this
example, the 95% CI is [01:57, 02:32], which does not contain zero; this agrees
with the small p-value of the significance test.
DECISION AND CONCLUSIONS
Since p < .001 is less than
our chosen significance level α = 0.05, we can reject the null
hypothesis, and conclude that the that the mean mile time for athletes and
non-athletes is significantly different.
Based on the results, we can state the
following:
- There was a
significant difference in mean mile time between non-athletes and athletes
(t315.846 =
15.047, p < .001).
- The average mile
time for athletes was 2 minutes and 14 seconds lower than the average mile
time for non-athletes.
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