Statistics 101A
Professor Esfandiari
Effect of independent and dependent data on standard error
Review of material discussed so far
I
The effect of independent and dependent data on standard error
In the previous lecture we talked about the twosample and paired sample test of the
mean. We explained that in twosample tests the data are independent, whereas, in the
case of paired data such as prepost data or more generally repeated measures data or in
the case of paired data (such as twins), the data are dependent or correlated with each
other. This is an important distinction to make both from a design and a mathematical
point of view and how it impacts the calculation of standard error.
From a design point of view in the twosample case the subjects are randomly assigned to
the two groups and a subjects who appears in one group cannot appear in the other group
and the selection of one subject does not depend on the selection of any other subject.
Whereas, in the case of
“repeated measures” the same subject is measured twice. In the
case of “paired sample”, the choice of one subject is dependent on the choice of the other
subject in the pair. For instance if a twin gets selected to participate in the study,
automatically the other twin will also be in the study or if a husband gets selected to be in
the study, the wife will automatically become part of the study.
Let us take a numerical example: (control = 0, experimental = 1)
Group
Pre
post
gain
1
20
30
10
1
22
33
11
1
23
32
9
1
24
33
9
1
25
35
10
1
26
34
8
1
27
36
11
1
28
37
10
1
29
39
10
0
30
40
10
0
21
22
1
0
22
24
2
0
23
25
2
0
24
26
2
0
25
25
0
0
26
27
1
0
27
28
1
0
28
28
0
0
29
30
1
0
30
31
1
1
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 Spring '11
 esfandi
 Statistics, Standard Error, Ethnic group, Pearson productmoment correlation coefficient

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