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CORRELATION

A graduate-level illustrated introduction to and tutorial for Pearson correlation, Spearman's rank correlation (rho), Kendall's rank correlation (tau-b). polyserial correlation, biserial correlation, polychoric correlation, tetrachoric correlation, phi, point-biserial correlation, rank-biserial correlation (Somers' D), and more.

Why we think it's important: Factor analysis, structural equation modeling, and other procedures accept correlation matrix input. No existing software package automatically creates matrices using forms of correlation designed for all types of variable pairings. Using the appropriate types of correlation can make a difference in substantive conclusions.

New in the 2013 edition:

• New and completely reworked sections on Pearson's, Spearman's, Kendall's, polyserial, polychoric, point biserial, rank biserial and phi correlations.
• Covers creation of appropriate correlation matrices for input to factor, structural equation modeling, and other procedures.
• Covers SAS 9.3's new polyserial and polychoric correlation options.
• Covers SPSS, SAS, and Stata for all types of correlation.
• Shows how to reconcile output among statistical packages.
• Two dozen new illustrations.

The full content is now available from Statistical Associates Publishers. Click here.

```CORRELATION
Overview	6
Key Concepts and Terms	8
Deviation	8
Covariance	8
Standardization	8
Use of correlation matrices	8
Data example	9
Pearson correlation (for interval data)	11
Overview	11
Coefficient of determination, r2	11
Attenuation of correlation	12
SPSS	17
Input example	17
The apples.sav example	19
SAS	21
Input example	21
The apples.sas7bdat example	24
Stata	25
Spearman's  rho (for ordinal data)	27
Overview	27
SPSS	27
SAS	28
Stata	29
Kendall's tau-b (for ordinal data)	30
Overview	30
SPSS	31
SAS	31
Stata	32
Polyserial correlation (for a continuous with an ordinal or binary variable)	33
Overview	33
SPSS	34
SAS	34
Stata	35
Polychoric correlation (for ordinal and binary variables)	35
Overview	35
SPSS	36
SAS	36
Stata	37
Other software for polychoric correlation	41
Phi (for two binary variables)	41
Overview	41
SPSS	41
SAS	42
Stata	42
Other types of correlation	42
Point-biserial correlation	42
Converting point-biserial to biserial correlation	43
Rank-biserial correlation (Somers' D)	43
SPSS	43
SAS	44
Stata	45
Correlation ratio, eta	47
Coefficient of intraclass correlation (ICC)	47
Assumptions	47
Data level	47
Linear relationships	48
Homoscedasticity	48
No outliers	48
Minimal measurement error	48
Unrestricted variance	49
Similar underlying distributions	49
Common underlying normal distributions	49
Normally distributed error terms	50
Do I want one-tailed or two-tailed significance?	50
How many correlations will there be among k variables?	50
What rules exist for determining the appropriate significance level for testing correlation coefficients?	50
How do I convert correlations into z scores?	51
Z-Score Conversions of Pearson's r	51
How is the significance of a Pearson correlation coefficient computed?	53
Significance of r	53
Significance of the difference between two correlations from two independent samples	53
Significance of the difference between two dependent correlations from the same sample	54
How do I set confidence limits on my correlation coefficients?	54
I have ordinal variables and thus used Spearman's rho. How do I use these ordinal correlations in SPSS for partial correlation, regression, and other procedures?	55
Are polyserial and biserial correlations simply Spearman's rho applied to appropriate variables?	55
What is the relation of correlation to ANOVA?	55
What is the relation of correlation to validity?	56
What is the SPSS syntax for correlation?	56
Bibliography	57
Acknowledgment	59
Pagecount: 61
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