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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 2: Bivariate Relationships
Lesson 1: Reviewing the Homework
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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University of North Texas Dr. J. Kyle Roberts © 2004
Kyle’s “Mock” Data
JohnMeredithKyleAddie
X1234
Y1112
1 2 3 4
X
1 2 3 4
Y
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University of North Texas Dr. J. Kyle Roberts © 2004
Deciphering the HomeworkX Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25SD 1.29 0.50Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
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University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25SD 1.29 0.50Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
Deciphering the Mean
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University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
Deciphering the Standard Deviation
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University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
Deciphering the Skewness
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X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69 -1.69 -1.69 -1.69 -1.69 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
Deciphering the Kurtosis
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University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69 -1.69 -1.69 -1.69 -1.69 -1.69COVX ???
N/A0.50
rx ???N/A
0.78
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69 -1.69 -1.69 -1.69 -1.69 -1.69COVX ???
N/A0.50 0.50 0.50 1.00 -0.25 1.00
rx ???N/A
0.78
Deciphering the Covariance
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University of North Texas Dr. J. Kyle Roberts © 2004
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69 -1.69 -1.69 -1.69 -1.69 -1.69COVX ???
N/A0.50 0.50 0.50 1.00 -0.25 1.00
rx ???N/A
0.78
X Y Y + 3 Y – 1 Y * 2 Y * -.5 (Y+1)*2
Mean 2.50 1.25 4.25 0.25 2.50 -.625 4.5SD 1.29 0.50 0.50 0.50 1.00 0.25 1.00Skewness 0 0.75 0.75 0.75 0.75 -0.75 0.75Kurtosis -2.08 -1.69 -1.69 -1.69 -1.69 -1.69 -1.69COVX ???
N/A0.50 0.50 0.50 1.00 -0.25 1.00
rx ???N/A
0.78 0.78 0.78 0.78 -0.78 0.78
Deciphering the Pearson r
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University of North Texas Dr. J. Kyle Roberts © 2004
Additive Constants
MeanSDSkewnessKurtosisCovariancePearson r
Changes by the value of the additive constantDoes not changeDoes not changeDoes not changeDoes not changeDoes not change
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University of North Texas Dr. J. Kyle Roberts © 2004
Multiplicative Constants
MeanSD
Skewness
KurtosisCovariancePearson r
Changes by the value of the multiplicative constantChanges by the value of the multiplicative constant,but cannot be negativeValue won’t change, but will flip signs with a negative MCDoes not changeChanges by the value of the multiplicative constantValue won’t change, but will flip signs with a negative MC
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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 2: Bivariate Relationships
Lesson 1: Reviewing the Homework
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
