A “quick” step backwards
Blanched Formula
• Good way to calculate r if the means and standard deviations are already provided.
• It is very time consuming to calculate these statistics if they are not already provided
• If means and standard deviations are not given, use the raw-score formula
Raw-Score Formula
r =
Step 1: Set up table
SmileY
TalkX
Y2 X2 XY
Jerry 9 5Elan 2 1George 5 3Newman 4 4Kramer 3 2
Step 2: Square Y
SmileY
TalkX
Y2 X2 XY
Jerry 9 5 81Elan 2 1 4George 5 3 25Newman 4 4 16Kramer 3 2 9
Step 3: Square X
Smile Y
Talk X
Y2 X2 XY
Jerry 9 5 81 25 Elan 2 1 4 1 George 5 3 25 9 Newman 4 4 16 16 Kramer 3 2 9 4
Step 4: Multiply XY
Smile Y
Talk X
Y2 X2 XY
Jerry 9 5 81 25 45 Elan 2 1 4 1 2 George 5 3 25 9 15 Newman 4 4 16 16 16 Kramer 3 2 9 4 6
Step 5: Sum
SmileY
TalkX
Y2 X2 XY
Jerry 9 5 81 25 45Elan 2 1 4 1 2George 5 3 25 9 15Newman 4 4 16 16 16Kramer 3 2 9 4 6
23 15 135 55 84
Step 6: Plug in values
r =
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Step 6: Plug in values
r =15
15
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Step 6: Plug in values
r =23
23
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
15
15
Step 6: Plug in values
r =84
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
23
23
15
15
Step 6: Plug in values
r =84
55
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
23
23
15
15
Step 6: Plug in values
r =84
135
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
55
23
23
15
15
Step 6: Plug in values
r =84(5)
(5) (5)
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
13555
23
23
15
15
Step 7: Solve!
r =84(5)
(5) (5)
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
13555
23
23
15
15
Step 7: Solve!
r =23 225
84(5)
(5) (5)225 529
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
13555
2315
Step 7: Solve!
r =23
23
15
225
23
275 675
420 345
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
225 529
Step 7: Solve!
r =23
23
15
225
23420 345
50 146
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Step 7: Solve!
r =23
23
15
225
23
146 507300
75
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Step 7: Solve!
r =23
23
15
225
23
146 507300
75
85.44
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Step 7: Solve!
.88 =23
23
15
225
23
146 507300
75
85.44
Y = 23 Y2 = 135
X =15 X2 = 55
XY = 84 N = 5
Practice
AlcoholX
Nose TouchesY
Norm 6 5
Cliff 8 1
Sam 4 4
Woody 2 9
Practice
AlchX
NoseY
X2 Y2 XY
Norm 6 5Cliff 8 1Sam 4 4Woody 2 9
Practice
AlchX
NoseY
X2 Y2 XY
Norm 6 5 36 25 30Cliff 8 1 64 1 8Sam 4 4 16 16 16Woody 2 9 4 81 18
20 19 120 123 72
Practice
r =
X = 20 X2 = 120
Y =19 Y2 = 123
XY = 72 N = 4
20
20
19
19
72
120 123
(4)
(4) (4)
Practice
r =
X = 20 X2 = 120
Y =19 Y2 = 123
XY = 72 N = 4
20
20
19
19120 123(4) (4)
-92
Practice
r =
X = 20 X2 = 120
Y =19 Y2 = 123
XY = 72 N = 4
20 19-92
80 131
Practice
-.90 =
X = 20 X2 = 120
Y =19 Y2 = 123
XY = 72 N = 4
20 19-92
80 131102.37
Practice
• Page 116 -- # 21
Practice• Interpret the following:
• 1) The correlation between vocational-interest scores at age 20 and at age 40 was .70.
• 2) Age and IQ is correlated -.16.
• 3) The correlation between IQ and family size is -.30.
• 4) The correlation between sexual promiscuity and dominance is .32.
• 5) In a sample of males happiness and height is correlated .11.
Practice
• Page 97 # 5
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