Variability Range, variance, standard deviation Coefficient of variation (S/M): 2 data sets Value of standard scores? Descriptive Statistics III REVIEW.
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• Variability• Range, variance, standard deviation
• Coefficient of variation (S/M): 2 data sets• Value of standard scores?
Descriptive Statistics IIIREVIEW
2SS
S
MXZ
zT 1050
1
2
2
n
MXS
)(50 percentilezp
Correlation and Prediction
HPHE 3150Dr. Ayers
Variables
Independent(categorical: name)
• Presumed cause• Antecedent• Manipulated by researcher• Predicted from• Predictor• X
Dependent(ordinal/continuous: #)
• Presumed effect• Consequence• Measured by researcher• Predicted• Criterion• Y
Xiv
Ydv
Correlation(Pearson Product Moment or r)
•Are two variables related?•Car speed & likelihood of getting a ticket•Skinfolds & percent body fat
•What happens to one variable when the other one changes?
•Linear relationship between two variables•1 measure of 2 separate variables or 2 measures of 1 variable•Provides support for a test’s validity and reliability
Attributes of rmagnitude & direction
Negative Positive
-1.0 1.000-.70 0.700-.30 0.30
Perfect PerfectHigh HighLow LowZero
Scatterplot of correlation between pull-ups and chin-ups
(direct relationship/+)
0
2
4
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10
12
14
16
0 2 4 6 8 10 12 14
Pull-ups (#completed)
Ch
in-u
ps
(#co
mp
lete
d)
Scatterplot of correlation betweenbody weight and pull-ups
(indirect/inverse relationship/-)
0
2
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120 130 140 150 160 170 180
Weight (lb)
Pu
ll-u
ps
(#co
mp
lete
d)
Scatterplot of zero correlation (r = 0) Figure 4.4
0
2
4
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0 2 4 6 8 10
X
Y
Correlation Formula(page 60)
r n XY – X Y
n X 2 – X 2
n Y 2 – Y 2
Correlation issues
• Correlation ≠ causation
• -1.00 < r < +1.00
• Coefficient of Determination (r2) (shared variance)• r=.70 r2=.49 49% variance in Y accounted for by X
Xiv
Ydv
• Negative correlation possibly due to:• Opposite scoring scales• True negative relationship
• Linear or Curvilinear (≠ no relationship; fig 4.6)
• Range Restriction (fig 4.7; ↓ r)
• Prediction (relationship allows prediction to some degree)
• Error of Prediction (for r ≠ 1.0)
• Standard Error of Estimate (prediction error)
Limitations of r
Figure 4.6Curvilinear relationship
Example of variable?
Figure 4.7Range restriction
Limitations of r
Correlation & Prediction IREVIEW
• Bivariate nature of correlations• X (iv) & Y (dv)• +/- relationships• Range of r?
• Coefficient of Determination (r2) (shared variance)
• Coefficient of variation (S/M): 2 data sets• Low V (.1-.2=homo): M accounts for most variability in scores
• Curvilinear relationship? Fitness/PA
• Correlation/Causation?
Uses of Correlation
• Quantify RELIABILITY of a test/measure
• Quantify VALIDITY of a test/measure
• Understand nature/magnitude of bivariate relationship
• Provide evidence to suggest possible causality
Misuses of Correlation
• Implying cause/effect relationship
• Over-emphasize strength of relationship due to “significant” r
Correlation and prediction
Skinfolds
% Fat
Sample Correlations
Excel document
Standard Error of Estimate(SEE)
Average error in the process of predicting Y from XStandard Deviation of error
21 rSySe As r ↑, error ↓As r ↓, error ↑
Is ↑r good? Why/Not?Is ↑ error good? Why/Not?
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