Transcript PowerPoint

Statistic for the day:
The average distance that food
travels to get to your table: 1300
miles
Assignment:
Read Chapter 3
Or
Review for Midterm #3
These slides were created by Tom Hettmansperger and in some cases
modified by David Hunter
perfect pitch
These slides were created by Tom Hettmansperger and in some cases
modified by David Hunter
perfect pitch (closeup)
A study to see if perfect pitch (the ability to reproduce
music notes without reference to a standard) is related
to a physical structure in the brain.
Structure is called the planum temporale ( PT )
Using brain scans the PT surface area in mm2 was
measured for three groups:
•musicians with perfect pitch
•musicians without perfect pitch
•non-musicians without perfect pitch
A measure of asymmetry in the PT was computed
for each subject:
LR
dPT 
( L  R) / 2
The researchers found:
•musicians with perfect pitch: mean dPT = -.57
•musicians without perfect pitch: mean dPT = -.23
Question: Are the dPT means close or not? Is
there a difference between musicians with and
without perfect pitch?
Equivalently we ask:
Is the difference in means:
-.57 – (-.23) = -.34 close to 0?
What additional information do we need to
answer the questions?
Answer:
We must know either
The sample standard deviation and sample size for
each sample. Then compute the SEM for each sample.
Remember: SEM = SD/sqrt(sample size)
OR
Be given the SEM directly and not have to compute it.
In either case we can then use the Pythagorean theorem
to find the standard deviation of the difference in means.
sqrt[( SEM 1)2 + (SEM 2)2]
To find standard deviation of difference
Sample Mean 1
Sample Mean 2
sample size 1
sample size 2
sample standard
sample standard
deviation 1: SD 1
deviation 2: SD 2
SEM 1:
SEM 2
(SD 1)/sqrt(sample size 1) (SD 2)/sqrt(sample size 2)
Standard deviation of the difference of sample
mean 1and sample mean 2:
sqrt [ (SEM 1)2 + (SEM 2)2]
means
musicians
perf pitch
-.57
musicians
no perf pitch
-.23
sample
size
SD
11
19
.21
.17
SEM
.019
.039
Pythagoras
SD of difference
sqrt(.0192 + .0392) = .043
Diff in means = -.57 – (-.23) = -.34
So: -.34 + 2x(.043) or -.34 + .086 or -.43 to -.26
Conclusion: They are not close. There is a difference.
Normal Curve of the difference of means with
center at -.34 and standard deviation of the
difference = .043
Frequency
10
5
95%
0
-0.44
-0.42
-0.40
-0.38
-0.36
-0.34
-0.32
-0.30
-0.28
-0.26
-0.24
0 is not close
diff in means
means
musicians
perf pitch
-.57
non-musicians
-.23
sample
size
SD
11
30
.21
.24
SEM
.019
.044
Pythagoras
SD of difference
sqrt(.0192 + .0442) = .048
Diff in means = -.57 – (-.23) = -.34
So: -.34 + 2x(.048) or -.34 + .096 or -.44 to -.24
Conclusion: They are not close. There is a difference.
means
musicians
no perf pitch
-.23
nonmusicians
-.23
sample
size
SD
19
30
.17
.24
SEM
.039
.044
Pythagoras
SD of difference
Diff in means = -.23 – (-.23) = 0
Conclusion: They are close. There is no difference
General conclusions:
There is a significant difference between the asymmetry
of the PT for musicians with perfect pitch and both
musicians without perfect pitch and non-musicians.
This strongly suggests that there is a relationship
between the physical structure of the PT in the
brain and perfect pitch ability.
Questions:
1. Do PSU women carry more change than men?
2. Is there a greater proportion of women who carry
change than for men?
How to formulate question 1 in statistical terms:
Is the mean amount of change carried by PSU women
greater than the mean amount of change carried by men?
Take samples of change from women and men and
compare the sample means.
To find standard deviation of difference
Sample Mean 1
Sample Mean 2
sample size 1
sample size 2
sample standard
sample standard
deviation 1: SD 1
deviation 2: SD 2
SEM 1:
SEM 2
(SD 1)/sqrt(sample size 1) (SD 2)/sqrt(sample size 2)
Standard deviation of the difference of sample
mean 1and sample mean 2:
sqrt [ (SEM 1)2 + (SEM 2)2]
Stat 100: Men vs. Women
Variable
-------Age
GPA
Credits
Studyhrs
Phonmins
Jeans
CDs
Cigpacks
Sex
-----Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
N
--133
101
133
98
136
100
136
101
127
96
136
98
135
101
136
101
Mean
-----19.624
19.584
3.2186
2.9863
15.566
15.250
2.941
2.149
150.0
91.1
9.529
5.684
85.4
93.7
0.419
1.108
StDev
-----3.320
1.669
0.4912
0.5322
2.073
1.833
1.761
3.638
177.9
111.2
6.092
3.283
116.3
122.7
1.227
2.300
SE Mean
------0.288
0.166
0.0426
0.0538
0.178
0.183
0.151
0.362
15.8
11.4
0.522
0.332
10.0
12.2
0.105
0.229