Lab 8

1
Lab 8

• Correlation with Listwise and Pairwise Deletion

2
Reporting Correlations in APA

• r (28) .30, p lt .05
• r (28) .06, ns

3
Proc Corr

• Produces correlation matrix for specified
  (continuous) variables.
• Produces Pearson correlations (unless you request
  Spearman).
• Can perform pairwise or listwise deletion.
• Provides descriptive statistics

4
Listwise Deletion

• Proc Corr NOMISS
• Var var1 var2 var3
• Run

5
Listwise Deletion Output
6
Pairwise Deletion

• Proc Corr
• Var var1 var2 var3
• Run
• Maximizes cases per comparison.
• Comparisons will probably be based on slightly
  different cases.

7
Pairwise Deletion Output
8
Example

• 4 variables
• Commitment (commit) intention to remain in a
  relationship
• Satisfaction (satis) satisfaction with the
  relationship
• Investment size (invest) amount of time and
  personal resources that the person has put into
  the relationship
• Alternative value attractiveness of the
  alternatives to the relationship

9
Data and program

• Proc corr nomiss
• Var commit satis invest altern
• Proc corr
• Var commit satis invest altern
• Run

• Data d1
• Input _at_1 (commit) (2.) _at_4 (satis) (2.) _at_7
  (invest) (2.) _at_10 (altern) (2.)
• Cards
• 20 20 28 21
• 10 5 31
• 30 33 24 11
• 10 15 36
• 22 18 33 16
• 31 29 33 12
• 6 10 12 29
• 11 12 30
• 25 23 34 12
• 10 7 14 32

10
Descriptive Statistics with Proc Corr Listwise
(nomiss)

• The CORR Procedure
• 4 Variables commit
  satis invest altern
• Simple
  Statistics
• Variable N Mean Std Dev Sum
  Minimum Maximum
• commit 7 20.57143 9.51940 144.00000
  6.00000 31.00000
• satis 7 20.00000 9.41630
  140.00000 7.00000 33.00000
• invest 7 25.42857 9.19886 178.00000
  12.0000 34.00000
• altern 7 19.00000 8.60233 133.00000
  11.0000 32.00000

11
Listwise (nomiss) Output

• N 7 Prob gt r under H0 Rho0
• commit satis
  invest altern
• commit 1.00000 0.94826 0.81706
  -0.95251
• 0.0011
  0.0248 0.0009
• satis 0.94826 1.00000
  0.65998 -0.92796
• 0.0011
  0.1067 0.0026
• invest 0.81706 0.65998
  1.00000 -0.84669
• 0.0248 0.1067
  0.0162
• altern -0.95251 -0.92796
  -0.84669 1.00000
• 0.0009 0.0026
  0.0162

12
Descriptive Statistics with Proc Corr Pairwise

• 4 Variables commit
  satis invest altern
• Simple Statistics
• Variable N Mean Std Dev
  Sum Minimum Maximum
• commit 9 18.33333 9.36750 165.000
  6.00000 31.00000
• satis 9 18.00000 9.08295
  162.000 7.00000 33.00000
• invest 9 22.00000 10.77033
  198.000 5.00000 34.00000
• altern 10 23.00000 9.64941
  230.000 11.00000 36.00000

13
Pairwise (default) Output

• Prob gt r under H0 Rho0 Number of
  Observations
• commit satis
  invest altern
• commit 1.00000 0.95266 0.82621
  -0.96011
• 0.0003
  0.0115 lt.0001
• 9 8
  8 9
• satis 0.95266 1.00000
  0.71057 -0.91786
• 0.0003
  0.0482 0.0005
• 8 9
  8 9
• invest 0.82621 0.71057
  1.00000 -0.85022
• 0.0115 0.0482
  0.0037
• 8 8
  9 9
• altern -0.96011 -0.91786
  -0.85022 1.00000
• lt.0001 0.0005
  0.0037
• 9 9
  9 10

14
Correlation w/ Categorical Vars

• Can separate analysis by categorical variables.
  Will give independent samples correlations.
• Just like the BY statement in Proc GLM.
• Proc Corr
• var Var1 Var2 Var2
• by categoricalVariable
• Run

15
Example with Gender added, 1female, 2male

• Proc corr
• Var commit satis invest altern
• By gender
• Run

• Data d1
• Input _at_1 (commit) (2.) _at_4 (satis) (2.) _at_7
  (invest) (2.) _at_10 (altern) (2.) _at_13 (gender)
  (1.)
• Cards
• 20 20 28 21 1
• 10 5 31 1
• 30 33 24 11 1
• 10 15 36 1
• 22 18 33 16 1
• 31 29 33 12 2
• 6 10 12 29 2
• 11 12 30 2
• 25 23 34 12 2
• 10 7 14 32 2

16
Female (gender 1) Descriptive Statistics

• --------------------------- gender1
  -----------------------------
• 4 Variables commit
  satis invest altern
• Simple
  Statistics
• Variable N Mean Std Dev Sum
  Mini Maxi
• commit 4 20.500 8.22598 82.0
  10.00 30.00
• satis 4 20.250 9.53502 81.0
  10.00 33.00
• invest 5 21.000 11.11306 105.0
  5.00 33.00
• alte 5 23.000 10.36822 115.00
  11.00 36.00

17
Female (gender 1) Correlation Output

• Prob gt r under H0 Rho0 Number of
  Observations
• commit satis
  invest altern
• commit 1.00000 0.95135
  0.69889 -0.98468
• 0.1994
  0.3011 0.0153
• 4 3
  4 4
• satis 0.95135 1.00000
  0.32591 -0.87387
• 0.1994
  0.6741 0.1261
• 3 4
  4 4
• invest 0.69889 0.32591
  1.00000 -0.73770
• 0.3011 0.6741
  0.1548
• 4 4
  5 5
• altern -0.98468 -0.87387 -0.73770
  1.00000
• 0.0153 0.1261
  0.1548
• 4 4
  5 5

18
Female (gender 1) Descriptive Statistics

• Variable N Mean Std Dev Sum Min
  Maximum
• commit 5 16.60000 10.78425 83.00 6.000
  31.00000
• satis 5 16.20000 9.36483 81.00
  7.00 29.00000
• invest 4 23.25000 11.87083 93.00 12.00
  34.00000
• altern 5 23.00000 10.09950 115.0 12.00
  32.00000

19
Female (gender 1) Correlation Output

• Number of Observations
• commit satis
  invest altern
• commit 1.00000 0.96888 0.96849
  -0.94798
• 0.0066
  0.0315 0.0141
• 5 5
  4 5
• satis 0.96888 1.00000
  0.94622 -0.96479
• 0.0066
  0.0538 0.0079
• 5 5
  4 5
• invest 0.96849 0.94622
  1.00000 -0.98271
• 0.0315 0.0538
  0.0173
• 4 4
  4 4
• altern -0.94798 -0.96479
  -0.98271 1.00000
• 0.0141 0.0079
  0.0173
• 5 5
  4 5

20
Plotting scatterplots

• Proc plot
• Plot commitsatis commitaltern commitinvest
• Run

• Data d1
• Input _at_1 (commit) (2.) _at_4 (satis) (2.) _at_7
  (invest) (2.) _at_10 (altern) (2.)
• Cards
• 20 20 28 21
• 10 5 31
• 30 33 24 11
• 10 15 36
• 22 18 33 16
• 31 29 33 12
• 6 10 12 29
• 11 12 30
• 25 23 34 12
• 10 7 14 32

21
Scatterplot commitsatis

• Plot of commitsatis. Legend A 1 obs, B 2
  obs, etc.
• (NOTE 2 obs had missing values.)
• commit
• 30 A
  A
• A
• A
• 20 A
• 10 A A
• A
• 0
• 
  
• 0 10 20 30
  40
• satis

22
Scatterplot commitaltern

• Plot of commitaltern. Legend A 1 obs, B 2
  obs, etc.
• (NOTE 1 obs had missing values.)
• commit
• 30 A A
• A
• A
• 20 A
• 10 A A A
• A
• 0
• 
  
• 10 15 20 25 30
  35 40
• altern

23
Scatterplot commitaltern

• Plot of commitinvest. Legend A 1 obs, B
  2 obs, etc.
• (NOTE 2 obs had missing values.)
• commit
• 30 A
  A
• 
  A
• 
  A
• 20 A
• 10 A A
• A
• 0
• 0 10 20 30
  40
• invest

24
Comparing Dependent Correlations

• Use the Hotelling-William test when one variable
  is in common (Example in lecture notes)
• Use the Steiger test when no variables are in
  common (Example in lecture notes)

25
In Class Example

• Download lab8.sas from Brannicks website.
• 3 variables
• Age, age
• Score on a knowledge test, knwldge
• Score on an iq test, iq
• Perform a proc corr, listwise and pairwise.
• Are there significant differences in the
  variables and are the pairwise and listwise
  results different?