Unformatted text preview: rela7on coeﬃcient) Abbreviated as li`le r Interpreta1on Sign (+ vs
) tells you about direc7on Value tells you about the strength: close to
1 or closer to 1 represents a stronger correla7on, closer to 0 represents a weaker correla7on 10 11/13/13 Which is stronger? 0.40 versus 0.45 0.80 versus
0.75
0.23 versus 0.23 Step 1: Change all scores to Z scores. Figure the mean and SD of each variable, then convert each raw score to a Z score Step 2: Figure the cross
product of the Z scores for each person, by mul7ple each person’s Z score from variable 1 by their Z score from variable 2 Step 3: Add up the cross
products of the Z scores Step 4: Divide by the number of par1cipants in the study 11 11/13/13 r = ΣZxZy
N
Sum of the cross
products of Z scores, divided by the total number of par7cipants in the study (i.e., total “sets” of scores) Find the correla7on coeﬃcient for the associa7on between number of hours slept and a person’s next day mood Number of hours slept Posi1ve mood 5 2 7 4 8 7 6 2 6 3 10 6 12 11/13/13 Step 1: Change all scores to Z scores Number of hours slept X
M (X – M)2 Z scores (Zx) = (X
M)/SD 5
2 4
2/1.63 =
1.23 7 0 0 0 8 1 1 .61 6
1 1
.61 6
1 1
.61 10 3 9 1.84 Σ = 42 SS = 16 M = 7 SD2 = 16/6 = 2.67 SD = 1.63 Step 1: Change all scores to Z scores Posi1ve mood X
M (X – M)2 Z scores (Zy) = (X
M)/SD 2
2 4
2/1.92 =
1.04 4 0 0 0 7 3 9 1.56 2
2 4
1.04 3
1 1
.52 6 2 4 1.04 Σ = 24 SS = 22 M = 4 SD2 = 22/6 = 3.67 SD = 1.92 13 11/13/13 Step 2: Figure the cross
product for each set Zx (Hours Slept) Zy (Posi1ve mood) Cross
Products of Z Scores
1.23
1.04
1.23 *
1.04 = 1.28 0 0 0 .61 1.56 0.95
.61
1.04 0.63
.61
.52 0.32 1.84...
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 Winter '13
 bernard
 Psychology, the00, a00

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