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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 reproducemusic notes without reference to a standard) is relatedto a physical structure in the brain.

Structure is called the planum temporale ( PT )

Using brain scans the PT surface area in mm2 wasmeasured for three groups:

•musicians with perfect pitch•musicians without perfect pitch•non-musicians without perfect pitch

A measure of asymmetry in the PT was computedfor each subject:

2/)( RLRLdPT

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 theoremto find the standard deviation of the difference in means.

sqrt[( SEM 1)2 + (SEM 2)2]

Sample Mean 1Sample Mean 1 Sample Mean 2Sample Mean 2

sample size 1sample size 1 sample size 2sample size 2

sample standardsample standarddeviation 1: SD 1deviation 1: SD 1

sample standardsample standarddeviation 2: SD 2deviation 2: SD 2

SEM 1:SEM 1:(SD 1)/sqrt(sample size 1)(SD 1)/sqrt(sample size 1)

SEM 2SEM 2(SD 2)/sqrt(sample size 2)(SD 2)/sqrt(sample size 2)

Standard deviation of the difference of sample Standard deviation of the difference of sample mean 1and sample mean 2:mean 1and sample mean 2:

sqrt [ (SEM 1)sqrt [ (SEM 1)22 + (SEM 2) + (SEM 2)22]]

To find standard deviation of difference

musiciansmusiciansperf pitchperf pitch

musiciansmusiciansno perf pitchno perf pitch

meansmeans -.57-.57 -.23-.23

samplesamplesizesize

1111 1919

SDSD .21.21 .17.17

SEMSEM .019.019 .039.039

PythagorasPythagoras SD of differenceSD of differencesqrt(.019sqrt(.01922 + .039 + .03922) = .043) = .043

Diff in means = -.57 – (-.23) = -.34So: -.34 + 2x(.043) or -.34 + .086 or -.43 to -.26 Conclusion: They are not close. There is a difference.

-0.44 -0.42 -0.40 -0.38 -0.36 -0.34 -0.32 -0.30 -0.28 -0.26 -0.24

0

5

10

Freq

uenc

y

Normal Curve of the difference of means withcenter at -.34 and standard deviation of thedifference = .043

diff in means

95%

0 is not close

musiciansmusiciansperf pitchperf pitch

non-musiciansnon-musicians

meansmeans -.57-.57 -.23-.23

samplesamplesizesize

1111 3030

SDSD .21.21 .24.24

SEMSEM .019.019 .044.044

PythagorasPythagoras SD of differenceSD of differencesqrt(.019sqrt(.01922 + .044 + .04422) = .048) = .048

Diff in means = -.57 – (-.23) = -.34So: -.34 + 2x(.048) or -.34 + .096 or -.44 to -.24 Conclusion: They are not close. There is a difference.

musiciansmusiciansno perf pitchno perf pitch

non-non-musiciansmusicians

meansmeans -.23-.23 -.23-.23

samplesamplesizesize

1919 3030

SDSD .17.17 .24.24

SEMSEM .039.039 .044.044

PythagorasPythagoras SD of differenceSD of difference

Diff in means = -.23 – (-.23) = 0Conclusion: They are close. There is no difference

General conclusions:

There is a significant difference between the asymmetryof the PT for musicians with perfect pitch and bothmusicians without perfect pitch and non-musicians.

This strongly suggests that there is a relationship between the physical structure of the PT in thebrain and perfect pitch ability.

Questions:

1. Do PSU women carry more change than men?

2. Is there a greater proportion of women who carrychange than for men?

How to formulate question 1 in statistical terms:

Is the mean amount of change carried by PSU womengreater than the mean amount of change carried by men?

Take samples of change from women and men and compare the sample means.

Sample Mean 1Sample Mean 1 Sample Mean 2Sample Mean 2

sample size 1sample size 1 sample size 2sample size 2

sample standardsample standarddeviation 1: SD 1deviation 1: SD 1

sample standardsample standarddeviation 2: SD 2deviation 2: SD 2

SEM 1:SEM 1:(SD 1)/sqrt(sample size 1)(SD 1)/sqrt(sample size 1)

SEM 2SEM 2(SD 2)/sqrt(sample size 2)(SD 2)/sqrt(sample size 2)

Standard deviation of the difference of sample Standard deviation of the difference of sample mean 1and sample mean 2:mean 1and sample mean 2:

sqrt [ (SEM 1)sqrt [ (SEM 1)22 + (SEM 2) + (SEM 2)22]]

To find standard deviation of difference

Stat 100: Men vs. WomenVariable Sex N Mean StDev SE Mean-------- ------ --- ------ ------ ------- Age Female 133 19.624 3.320 0.288 Male 101 19.584 1.669 0.166 GPA Female 133 3.2186 0.4912 0.0426 Male 98 2.9863 0.5322 0.0538 Credits Female 136 15.566 2.073 0.178 Male 100 15.250 1.833 0.183 Studyhrs Female 136 2.941 1.761 0.151 Male 101 2.149 3.638 0.362 Phonmins Female 127 150.0 177.9 15.8 Male 96 91.1 111.2 11.4 Jeans Female 136 9.529 6.092 0.522 Male 98 5.684 3.283 0.332 CDs Female 135 85.4 116.3 10.0 Male 101 93.7 122.7 12.2 Cigpacks Female 136 0.419 1.227 0.105 Male 101 1.108 2.300 0.229