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Stats for Correlations: Means, Deviations, Covariances, Pearson Correlation, Study notes of Mathematical Statistics

Alliance UniversityMathematical Statistics

The concepts of means, standard deviations, covariances, and pearson correlation in statistics. It covers the computation of these statistics, including the use of user-specified treatments for missing values. The document also discusses the significance level of pearson correlation and provides references.

Typology: Study notes

2011/2012

Uploaded on 10/31/2012

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1
CORRELATIONS
The user-specified treatment for missing values is used for computation of all
statistics except, under certain conditions, the means and standard deviations.
Notation
The following notation is used throughout this chapter unless otherwise specified:
N Number of cases
Xkl Value of the variable k for case l
wl Weight for case l
Wk Sum of weights of cases used in computation of statistics for variable k
Wkj Sum of weights of cases used in computation of statistics for variables k and j
Statistics
Means and Standard Deviations
X
wX
W
SwXXWW
k
lkl
l
N
k
kl
l
N
kk k
kl
=
=โˆ’
๎˜
๎˜‚
๎˜ƒ๎˜„
๎˜…
๎˜†โˆ’
=
=
โˆ‘
โˆ‘
1
2
1
21
16
Note: If no treatment for missing values is specified (default is pairwise), means
and standard deviations are computed based on all nonmissing values for each
variable. If missing values are to be included or listwise is chosen, that option is
used for means and standard deviations as well.
pf2

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Download Stats for Correlations: Means, Deviations, Covariances, Pearson Correlation and more Study notes Mathematical Statistics in PDF only on Docsity!

1

CORRELATIONS

The user-specified treatment for missing values is used for computation of all statistics except, under certain conditions, the means and standard deviations.

Notation

The following notation is used throughout this chapter unless otherwise specified:

N (^) Number of cases X (^) kl Value of the variable^ k^ for case^ l wl Weight for case^ l Wk Sum of weights of cases used in computation of statistics for variable^ k

Wkj Sum of weights of cases used in computation of statistics for variables^ k^ and^ j

Statistics

Means and Standard Deviations

X

w X

W

S w X X W W

k

l kl l

N

k

k l l

N kl k^ k^ k

=

=

1

2 1

I T

Note: If no treatment for missing values is specified (default is pairwise), means and standard deviations are computed based on all nonmissing values for each variable. If missing values are to be included or listwise is chosen, that option is used for means and standard deviations as well.

2 CORRELATIONS

2

Cross-product Deviations and Covariances

The cross-product deviation for variables i and j is

Cij w Xl il X (^) jl w X w X W l

N l il l

N l jl l

N = โˆ’ ij

%

'

& &

(

0

) )

%

'

& &

(

0

) ) = = =

โˆ‘ โˆ‘ โˆ‘ 1 1 1

The covariance is

S

C

ij W

ij ij

Pearson Correlation

r

C

C C

ij

ij ii jj

Significance Level of r

The significance level for rij is based on

t r

W

r

ij

ij ij

which, under the null hypothesis, is distributed as a t with Wij โˆ’ 2 degrees of freedom. By default, the significance level is two-tailed.

References

Blalock, H. M. 1972. Social statistics. New York: McGraw-Hill.