psy 230 ch100 (1)
TRANSCRIPT
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Ways to collect two sets of data: Independent Measures (Between-Subjects) design:
Group 1 VS. Group 2
Repeated Measures (Within-subjects) design:
Time 1 VS. Time 2
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Notation for Independent
Samples Design Null Hypothesis (H0)
No difference between group means
H0: 12 = 0
Alternative Hypothesis (H1)
There is a difference between groups
H1:12 0
Group 1 Group 2
n1 n2
M1 M2
1 2
SS1 SS2
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Formulas for Independent-
Measures Hypothesis Test Single sample t-test:
t= M
sM
Two sample (independent measures) t-test:
t= (M1M2) (12)S(M1M2)
t= (M1M2)S(M1M2)
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Calculating Estimated Standard
Error Single sample t-test:
sM
= s2
n
Two sample (independent measures) t-test:
S(M1M2) = s2 s2 n1 n2
1 2+
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Pooled Variance
Used when sample sizes are different
Single sample t-test:
s2 = SS
df
Two sample (independent measures) t-test:
s2 = SS1 + SS2df1 + df2
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An example of the reason for
pooled variance. Equal Sample Sizes:
Sample 1: n = 6, SS= 50
Sample 2: n = 6, SS= 30
Unequal Sample Sizes:
Sample 1: n = 3, SS= 20 Sample 2: n = 9, SS= 48
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Computing t-statistic for
Independent Samples
t= (M1M
2) (
1
2)
S(M1M2)
t= data hypothesis
error
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Lets practice.
We are testing the effects of orange juice on
mathematical ability. Determine whether
there is a significant difference between the
groups in average math score.
OJ Group No OJ Group
n=10 n=10M=26 M=18
SS=200 SS=160
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Step 1: State Hypotheses and
select alpha levelHypotheses:
H0:12 = 0 H1:12 0
= .05
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Step 2: Set Criteria for a Decision
(Critical Region)a) Find the degrees of freedom
b) Use the t Distribution Table (p. 531) tofind the t-values that define the critical
region
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Step 3: Collect Data and
Compute Sample Statisticsa) Find the pooled variance for the 2 samples
b) Used the pooled variance to compute the
standard error
c) Compute the tstatistic
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Step 4: Make a Decision Accept or reject the null hypothesis??
-2.101 2.101
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Measuring Effect Size for
Independent Measuresr2 = variability accounted for
total variability
r2 = ___t2___
t2 + df
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Writing it up...Give the facts:
The group who drank orange juice scored higher on
the math test (M= 26, SD = 4.71) than the group thatdid not drink orange juice (M= 26, SD = 4.71).
State what the facts mean in terms of significance:
This difference was significant, t(18) = 4.00, < .05,
r2 = .47.
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More practice with a one-tailed test Psychologists predict that girls have higher verbal
scores at age 5 than boys. What value of t would
be necessary to conclude that girls scoresignificantly higher using a one-tailed test with
= .01?
Girls Boys
n=5 n=5
M=83 M=71
SS=200 SS=120
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Think about sample variance How does sample variance influence ourt-
statistics and treatment effects (dorr2)
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Independent tTest Assumptions Scores in the two groups are independent
(not related)
Sample data are normally distributed
Variances of the two groups are about equal
(homogenous)
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One more practiceWe would like to know if people respond more
quickly to red lights or green lights. Determine
whether there is a significant difference betweenthe groups in reaction time (in milliseconds):
Green Light Reaction Time: 432, 408, 388, 370,
523, 354, 603, 445Red Light Reaction Time: 452, 429, 391, 368, 546,
352, 592, 478, 679, 483
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Chapter 10 Homework
Submit the following problems from the end
ofChapter 10:
1, 3, 6, 10, 14, 16, 18, 20, 24
SHOW YOUR WORK!!!!
Due atthe beginningof class tomorrow!
PSY 230 - ROH
LFIN
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