Transcript T-Test (difference of means test)

T-Test (difference of means test)
T-Test =
used to compare means
between two groups.
Level of measurement:
– DV (Interval/Ratio)
– IV (Nominal—groups)
Hypotheses
Example: Gender and Income
Hr1:
The mean income for women
differs from the mean income for
men.
Hr2:
Women make less on average than
men.
or Hr3: Men make more on average than
women.
One Tailed vs. Two Tailed Test
See overhead
Can you come up with a relationship that
would require using a t-test?
How would you state the hypothesis?
What does the t-test do?
 t-Test tells us if the difference in means is due
sampling error or if the sample supports our
hypothesis that the difference reflects a true
difference in the population.
Independent vs. Dependent Samples
Independent = groups are not linked
Ex (gender): the selection of each male in the sample
is independent of the selection of each female in the
sample.
Dependent = groups are linked in some way:
Ex (couples): husbands and wives selected for a
study on marital happiness. Each male in the sample
is linked to a female in the sample.
Ex: Two groups compared on a before and after test.
Independent Samples t-test
GSS data = each individual in the sample is chosen
independently of all other individuals in the sample,
So,
use independent sample t-test
Even though the GSS is one sample, we can conduct ttest on groups (e.g. men/women) in GSS.
Formula:
t=
see board/overhead
The formula is a ratio of the difference in means
to the standard error of means (sampling error).
Standard error = the standard deviation of the
difference between means.
(Is the difference due to sampling error or does the
difference reflect a true population difference?)
Three Points About Difference
of Means
1. The larger the sample the less likely the difference
between means is due to sampling error.
2. The larger the difference between means the less
likely the difference is due to sampling errors.
3. The smaller the variance around the mean for
each group, the less likely the difference is due
to sampling error.
Equal and Unequal Variance
SPSS conducts a F test for equal variance.
Hr: Variance of sample1 is not equal to variance of sample 2.
Ho: Variance of sample 1 is equal to variance of sample 2.
F test, test for equal variance
Fail to reject Ho = Use t-test for equal variance.
Importance:
A slight change in the
calculation of the standard error.
Equal Variance = Pooled variance used in
the calculation of the
standard error.
Unequal Variance =
Calculation does
not use pooled
variance.
Interpreting GSS Output
Group Statistics
HOURS PER DAY
WATCHING TV
RESPONDENTS SEX
MALE
FEMALE
N
Mean
2.99
2.96
775
1054
Std. Deviation
2.685
2.507
Std. Error
Mean
.096
.077
Independent Samples Test
Levene's Test for
Equality of Variances
F
HOURS PER DAY Equal variances
WATCHING TV
assumed
Equal variances
not assumed
.490
Sig.
.484
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
.228
1827
.820
.028
.122
-.212
.268
.226
1600.600
.821
.028
.124
-.214
.270
Education & Age Kid Born
Group Statistics
R'S AGE WHEN
1ST CHILD BORN
recoded educ
1.00
2.00
N
1000
957
Mean
22.25
25.03
Std. Deviation
4.881
5.304
Std. Error
Mean
.154
.171
Independent Samples Test
Levene's Test for
Equality of Variances
F
R'S AGE WHEN
Equal variances
1ST CHILD BORN assumed
Equal variances
not assumed
7.249
Sig.
.007
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-12.083
1955
.000
-2.782
.230
-3.234
-2.331
-12.061
1924.139
.000
-2.782
.231
-3.235
-2.330