SPSS Example: You are interested in whether number of days of poor physical health per month
(PHYSHLTH) differs between white and non-white respondents (RACEBINARY). You are
willing to take a 1% risk of a false positive.
Null hypothesis: White and non-white respondents do not differ in terms of number of days of
poor physical health per month.
Research hypothesis: White and non-white respondents differ in terms of number of days of poor
physical health per month.
The table above shows you the sample size, mean, and standard deviation for each group.
Group Statistics
Race (1 = White; 2 =
Non-White) N Mean
Std.
Deviation
Std. Error
Mean
Days of poor physical
health past 30 days
White 1005 2.63 6.085 .192
Not White 404 2.59 6.087 .303
Independent Samples Test
Levene’s Test
for Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig.
(2-
taile
d)
Mean
Differen
ce
Std.
Error
Differen
ce
95%
Confidence
Interval of the
Difference
Lowe
r
Upp
er
Days of
poor
physical
health past
30 days
Equal
variances
assumed
.213 .644 .
101
1407 .919 .036 .358 -.667 .740
Equal
variances
not
assumed
.
101
743.7
36
.919 .036 .359 -.668 .740
First, you need to examine the results of Levene’s Test, which tells you whether you can assume
that variances within each group are equal in the population. The test statistic (F = 0.213) is
significant at 0.644, which is greater than our significance level of 0.01. Thus, we can assume
equal variances.
The t-values are the same for both rows, but you would use the top row since we can assume
equal variances. T = 0.101 which is significant at 0.919. This is greater than our significance
level of .01, and thus, we fail to reject the null hypothesis. White and non-white respondents do
not significantly differ in terms of days of poor physical health per month.
For questions 1-2, use SPSS and the data file in the Week 11 folder .To conduct a t-test, click
Analyze, Compare Means, and then Independent Samples T Test. Put the dependent variable
under “Test Variable(s)” and the independent variable under “Grouping Variable.” Afterwards,
click “Define Groups” and enter the numerical codes for the groups you want to compare. For
instance, “SEX” is coded as 1 = Male and 2 = Female. You would enter “1” for “Group 1” and
“2” for “Group 2.” You could also set a cut point if you using an interval/ratio level variable as
your grouping variable. Enter the value that is your cut point and you will compare the means of
everyone below that cut point and everyone above that cut point. For questions 1-2, you are
willing to take a 1% risk of a false positive.
- You are interested in whether days of poor mental health (MNTLHLTH) vary between
those who have completed 12 years of school or more and those who have completed
fewer than 12 years of school (EDUC).
A. State the null and research hypotheses (0.25 point).
B. Examine the results of Levene’s Test for Equality of Variances. Can you assume
that the variances for your two groups are equal? (0.25 point).
C. Provide the obtained t-value (0.25 point).
D. Make a decision regarding the null hypothesis and explain how you came to that
decision (0.25 point). - You are interested in whether hours worked in a week (HRS1) vary between males and
females (SEX).
A. State the null and research hypotheses (0.25 point).
B. Examine the results of Levene’s Test for Equality of Variances. Can you assume
that the variances for your two groups are equal? (0.25 point).
C. Provide the obtained t-value (0.25 point).
D. Make a decision regarding the null hypothesis and explain how you came to that
decision (0.25 point).
For question 3, round all answers involving calculations to two decimal places and show your
work. - You are interested in whether Black and Hispanic juveniles convicted of property crimes
differ in terms of sentence length. In your sample of Black juveniles (N = 229), you find
a mean sentence length of 31.09 months of probation (s = 15.42). In your sample of
Hispanic juveniles (N = 118), you find a mean sentence length of 40.84 months of
probation (s = 16.45). Assuming equal variances, conduct a t-test.
A. State your null and research hypotheses (0.25 point).
B. Calculate the standard error of the difference between means (0.5 point).
C. Calculate the obtained t-value (0.5 point).
D. Calculate the degrees of freedom for a t-test (0.25 point).
E. Find a critical t-value using your degrees of freedom and a significance level of .
01 (0.25 point).
F. Make a decision regarding the null hypothesis. Explain how you came to your
decision and interpret the result (0.25 point).