SW318 Social Work Statistics Slide 1

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Independent Samples T-Test Practice Problem 1a
This question asks whether the statement Survey
respondents who were male had completed more
years of school than survey respondents who were
female is true or not. The problem tells you the
level of significance or alpha to use for the
test, e.g. 0.05 in this problem. Note that you
have to use a one-tailed hypothesis test because
it says completed MORE years of school. Had the
question stated that males and females completed
a DIFFERENT number of years of school, we would
use a two-tailed test.
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Independent Samples T-Test Practice Problem 1b
The problem tells you what statistic to base your
answer on, in this case an independent samples
t-test. There are other statistics we might have
used, and they might even produce a different
answer. The independent samples t-test requires
that the independent variable be dichotomous and
the dependent variable be interval. sex is
dichotomous level, satisfying the requirement for
the independent variable. educ is interval
level satisfying the requirement for the
dependent variable.
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Independent Samples T-Test in SPSS (1)
The independent samples t-test assumes that the
dependent variable is normally distributed. To
test this assumption, we will check the skewness
and kurtosis for educ. Select Analyze gt
Descriptive Statistics gt Descriptives
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Independent Samples T-Test in SPSS (2)
Move the dependent variable educ to the list
box of Variable(s). Click on the Options button
to select statistics.
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Independent Samples T-Test in SPSS (3)
Make certain the check boxes for Kurtosis and
Skewness are checked. Click on the Continue
button to close the dialog box.
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Independent Samples T-Test in SPSS (4)
The skewness statistic (-.514) falls in the
acceptable range, but the kurtosis statistic
(1.899) does not. We cannot satisfy the
assumption of normality by the distribution of
the variable. However, the assumption of
normality can be satisfied for this test by the
Central Limit Theorem if both groups in the
hypotheses test have 50 or more subjects. We
will get the number of subjects in each group
defined by the independent variable in the output
for the t-test.
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Independent Samples T-Test in SPSS (5)
This problem can be solved using an independent
samples t-test in SPSS. In order to conduct it,
go to Analyze gt Compare Means gt
Independent-Samples T Test
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Independent Samples T-Test in SPSS (6)
First, in the Independent-Samples T Test window,
select and move the dependent variable educ to
the Test Variable(s) list box and move the
independent variable sex to the Grouping
Variable text box.
Second, click on Define Groups button to tell
SPSS the code numbers for the groups to
substitute for the question marks.
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Independent Samples T-Test in SPSS (7)
Recall that 1 is the value for male and 2 for
female for the variable sex. Type these values
in the Group 1 and Group 2 text boxes. If you
do not recall the code numbers for the groups,
look on the Variable View page in the SPSS Data
Editor. Click on the Continue button to close
the dialog box.
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Independent Samples T-Test in SPSS (8)
Note that the code values for the independent
(Grouping) variable replace the question marks
that were after the variable name.
Click OK to produce the output.
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Independent Samples T-Test in SPSS (9)
We still have not satisfied the assumption of
normality, so we check the number in each group.
There were 291 males and 374 females with valid
data. We satisfy the normality assumption with
the Central Limit Theorem.
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Independent Samples T-Test in SPSS (10)
The independent samples t-test assumes that the
variance measure of variability is equal for both
of the groups included in the t-test. This
assumption is tested with Levene's Test for
Equality of Variances. The Levene Test is itself
a test of the null hypothesis that the variances
of the two groups are equal. If we fail to
reject the null hypothesis because the p-value or
sig. for the statistic is greater than alpha, we
satisfy the requirement for equal variances. If
we reject the null hypothesis because the p-value
or sig. for the statistic is less than or equal
to alpha, we do not meet the requirement for
equal variances.
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Independent Samples T-Test in SPSS (11)
If we satisfy the assumption of equal variances,
we use the output on the row titled Equal
variances assumed.
If we do not satisfy the assumption of equal
variances, we use the output on the row titled
Equal variances not assumed. This calculation
is based on a formula for the t-test that takes
into account the differences in variance measures.
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Independent Samples T-Test in SPSS (12)
In this problem, the probability associated with
Levene's Test for Equality of Variances (.021) is
less than the level of significance (0.05) stated
in the problem. We reject the null hypothesis
that the variances are equal, concluding that the
Equal variances not assumed formula for the
independent samples t-test should be used for the
analysis.
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Independent Samples T-Test in SPSS (13)
Having determined which formula for the t-test to
base the hypothesis test on, we look to the
statistical output for the t-test. The research
hypothesis implied by the problem is that the
mean "highest year of school completed" educ
for survey respondents who were male is higher
than the mean for survey respondents who were
female. This is a one-tailed directional
hypothesis. The null hypothesis for this
research hypothesis would state that the mean
education for males is equal to the mean for
females. We make our decision about the null
hypothesis by comparing the probability of the
test statistic (t) to the alpha level of
significance stated in the problem.
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Independent Samples T-Test in SPSS (14)
SPSS prints out the two-tailed significance and
our research hypothesis states a direction to the
relationship, requiring us to compute the
one-tailed probability.
To compute the one-tailed probability, the SPSS
2-tailed significance is divided in half 0.975
/ 2 0.4875
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Independent Samples T-Test in SPSS (15)
Since the one-tailed probability of the t
statistic (t.031) was p0.4875, greater than the
alpha of 0.05, the null hypothesis of equal means
was not rejected, and we do not have support for
the research hypothesis. Based on our analysis,
we can not support the statement that survey
respondents who were male had completed more
years of school than survey respondents who were
female, so the answer to the question is false.
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Independent Samples T-Test Practice Problem 2
This question cannot be answered by an
independent samples t-test because the
independent samples t-test requires that the
independent variable be dichotomous and the
dependent variable be interval. sex is
dichotomous level, satisfying the requirement for
the independent variable. However, marital is
nominal level which does not satisfy the
requirement. The answer to the question is
incorrect application of a statistic.
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Independent Samples T-Test Practice Problem 3
This question can be answered using an
independent samples t-test because sex is
dichotomous level, satisfying the requirement for
the independent variable. The dependent
variable in the t-test is required to be interval
level and rincom98 is ordinal level. However,
we can fall back on the convention of using
ordinal variables with interval level statistics,
and add a caution to any true findings.
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Independent Samples T-Test in SPSS (1)
The independent samples t-test assumes that the
dependent variable is normally distributed. To
test this assumption, we will check the skewness
and kurtosis for rincom88. Select Analyze gt
Descriptive Statistics gt Descriptives
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Independent Samples T-Test in SPSS (2)
Move the dependent variable rincom98 to the
list box of Variable(s). Click on the Options
button to select statistics.
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Independent Samples T-Test in SPSS (3)
Make certain the check boxes for Kurtosis and
Skewness are checked. Click on the Continue
button to close the dialog box.
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Independent Samples T-Test in SPSS (4)
rincom98 satisfied the criteria for a normal
distribution. The skewness of the distribution
(-.690) was between -1.0 and 1.0 and the
kurtosis of the distribution (-.245) was between
-1.0 and 1.0.
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Independent Samples T-Test in SPSS (5)
This problem can be solved using an independent
samples t-test in SPSS. In order to conduct it,
go to Analyze gt Compare Means gt
Independent-Samples T Test
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Independent Samples T-Test in SPSS (6)
Select and move rincom98 to Test Variable(s)
box and make sure sex is still in the Grouping
Variable box and the code numbers for sex are
entered. Then, click OK.
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Independent Samples T-Test in SPSS (7)
The probability associated with Levene's Test for
Equality of Variances (.487) is greater than the
level of significance (0.05), indicating that the
'Equal variances assumed' formula for the
independent samples t-test should be used for the
analysis.
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Independent Samples T-Test in SPSS (8)
The research hypothesis that the average "income"
rincom98 for survey respondents who were male
is higher than the average for survey respondents
who were female, is a one-tailed directional
test. The SPSS 2-tailed significance is divided
in half (.000 / 2 0.0000). Since the
probability of the t statistic (t4.691) was
plt0.0001, less than or equal to the alpha of
0.05, the null hypothesis of equal means was
rejected and the research hypothesis was
supported.
When SPSS prints out a probability of 0.000, the
number is not equal to zero, but contains zeroes
in the first three decimal places. We will
correct this by stating it as plt0.001.
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Independent Samples T-Test in SPSS (9)
To make certain that the relationship stated in
the research hypothesis is correct, we compare
the means of the two groups to verify that the
direction is correctly stated. The research
hypothesis stated that males had higher salaries.
The mean for males (15.16) is higher than the
mean for females (12.68). The comparison is
correctly stated in the question. The answer to
the problem is true with caution, including the
caution because the dependent variable was
ordinal.
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Steps in solving independent samples t-test
problems - 1
The following is a guide to the decision process
for answering homework problems about
independent samples t-test problems
Is the dependent variable ordinal or interval
level and independent variable dichotomous?
Incorrect application of a statistic
No
Yes
Compute the skewness, and kurtosis for the
variable to test assumption of normality.
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Steps in solving independent samples t-test
problems - 2
Assumption of normality satisfied? (skew,
kurtosis between -1.0 and 1.0)
Yes
No
Sample size 50 in each group to apply Central
Limit Theorem?
No
Incorrect application of a statistic
Yes
Compute the Independent Samples T-Test
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Steps in solving independent samples t-test
problems - 3
Is the p-value for the Levenes test for equality
of variances lt alpha?
Yes
No
Use Equal variances assumed formula for the
t-test.
Use Equal variances not assumed formula for
the t-test.
Is the research hypothesis one-tailed or
two-tailed?
One-tailed
Two-tailed
Divide the p-value for the t-test by two.
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Steps in solving independent samples t-test
problems - 4
No
Is the p-value lt alpha?
False
Yes
Comparison of means correctly stated?
No
False
Yes
Is the variable ordinal level?
No
True
Yes
True with caution