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Unformatted text preview: Quantitative Methods in
Psychology
July 29th, 2009: ttest week
Jeff Vietri
Corresponding to chapter 11 in the text Today's Agenda
• Answer any questions about homework
• Introduce pairedsamples ttest
• Compare ttests Repeatedsample ttest
Repeatedsample
• Since human behavior is so variable,
Since
researchers want to eliminate as many
confounds and nuisance variables as
possible
possible Variability across Ps
• There are times when our individuals will be
so different on the DV that an independentsamples test lacks sensitivity to pick up
differences
– Think of an intervention where each sample
includes people who are at the extremes on the
DV
• Harvard grads & HS dropouts in academic
achievement
• Track stars & couch potatoes in a test of running
shoes – Given withingroup variability, we are unlikely
to detect the differences made by the
intervention Example
Example
• I want to test the effects of sleep on memory
want
in humans.
in
• Randomly sample people to be included in my
Randomly
study
study
• Randomly assign people to either be in my sleep
Randomly
deprivation (experimental) condition or control
condition
condition
• I find no significant difference on memory
find
between the two groups
between Example
Example
• Perhaps, sleep deprivation does not affect
Perhaps,
memory (H0 is true).
(H0
• Perhaps, by chance the people in my sleep
Perhaps,
deprivation group had better memories to begin
with than my control group, and it compensated
for the decrease in memory caused by sleep
deprivation (H0 is not true, but individual
differences masked the effect of treatment).
differences
• I assumed the groups are the same for all
assumed
relevant variables at the beginning of the study
but that might not be true
but Repeated measures
Repeated
• Subject variables could be confounding
Subject
experimental variables
• A more effective way is to do my study is
more
to eliminate these subject variables by
measuring the same individual both with
and without treatment
and • Repeated measures (withinsubject
design) Subjects are compared against
design)
themselves if data is collected at two
different times
different
• In contrast with independent samples
In
(betweensubject design)
(betweensubject
• A similar method: Matched subject
– Each subject in one group matched with a
Each
subject in the other group (e.g., baseline
memory)
memory) • This design dramatically reduces error (of
This
measurement) and increases the power of
a study
study Repeated measures
Repeated
• Each individual is compared with him/her self
Each
(or a matched subject who is similar) to
eliminate subject variables as confounds
eliminate
• We analyze the difference scores. Then, treat
We
these difference scores as raw scores in onethese
sample ttest .
t= M D − µD
t=
sM D Statistic – Parameter
Amount of error
Null
hypothesis
states it is 0 sM D = sD
n Repeated Samples tTest
Repeated Repeated Samples tTest
Repeated
• Do students learn differently
Do
when texting?
when
Student
1
2
3
4
5
6
7 No SMS
5
6
8
9
6
7
12 SMS
4
6
7
6
7
6
9 M D − µD
t=
sM D sM D = sD
n = sD 2
n • MD = mean of the difference scores
– Add all difference scores and divide by the number of
Add
difference scores
difference • Df = n1
• Note that this is the number of pairs of difference
Note
scores!
scores!
• sMD = estimated standard error of the difference
scores
scores
– Standard deviation of the difference scores (sD)
divided by the square root of nD
divided
– Once you create all the difference scores, you can
Once
treat them as regular scores and find their
SS and s2 and s.
SS A researcher obtains t = 2.35 for a repeatedresearcher
measures study using a sample of n = 8
measures
participants. Based on this t value, what is the
correct decision?  FIRST, α = .05 , THEN α = .01
correct • A sample of n = 16 high school students took the
sample
SAT before and after a special training course. For
each student, the difference between the first score
and the second score was measured, and the
results showed that their SAT scores averaged MD =
results
18 points higher after the course with SS = 6000. On
SS
the basis of this sample, can you conclude that there
was a significant difference after taking the training
course? Use a twotailed test at the .05 level of
significance.
significance. Repeated Samples tTest
• Advantages
– Need less participants since uses participants
Need
more efficiently
more
– Good at studying changes over time
– Reduces/eliminates individual differences • Assumptions
– Independent observations
– Distribution of difference scores must be
Distribution
normal
normal Repeated Samples tTest
Repeated
• If can control or eliminate other sources of
If
variability then do it
variability
• Reducing variability within groups is
Reducing
important
important
• Use your brain if you're conducting
Use
research; are you introducing confounds
by your design?
by
– order/maturity effects • Can you eliminate them somehow?
– Counterbalanced designs? Summary
Summary
If we know the population parameters (µ and σ): Singlesample ztest
Singlesample
If we know µ, but not σ:
but Singlesample ttest
Singlesample If we don't know µ/want to compare two unrelated If
µ/
samples Independentsamples ttest
Independentsamples If we don't know µ/want to compare pairs of scores
If
µ/ Pairedsamples ttest ...
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 Fall '11
 Staff
 Psychology

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