Transcript 10/01/2015

Psychology 202a
Advanced Psychological
Statistics
October 1, 2015
The Plan for Today
• What if we don’t know the sampling
distribution of a statistic?
• The Z test
• Assumptions
• The two-sample Z test
• The t test
What if we don’t know the
sampling distribution?
• The bootstrap
• Bradley Efron
• Illustration in R
Using the central limit theorem
for inference
• The one-sample Z test
M  0
.
• Z
sM
• Example: H 0 :   100.
• s = 10, n = 25, M = 105
105  100
• Z
 2.50.
2
Assumptions of the Z test
• Independent observations.
• s is known.
• Distribution is normal or sample is
sufficiently large.
• Problem: those assumptions are virtually
never actually met.
The two-sample Z test
•
Z
( M 1  M 2 )  ( 1   2 )
s M M
1
s M M 
1
2
s12
n1
.
2

s 22
n2
.
• Example: s1 = s2 = 10, n1 = n2 = 25,
M1 = 103, M2 = 108.
Two-sample Z test (cont.)
• H 0 : 1  2  0.
• s M M 
1
•
2
102
25

102
25
 8.
103  108
Z
 1.768.
8
Assumptions of the two-sample
Z test
• Independent observations within groups.
• Independent observations between
groups.
• s is known for both populations.
• Distribution is normal or sample is
sufficiently large in both populations.
The one-sample t test
• Solution to not knowing s : substitute an
estimate of the standard deviation.
•
M  0
t
.
sM
• Class example.
• The t test in SAS.