SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients
Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of thes...
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| Published in | Behavior research methods Vol. 45; no. 3; pp. 880 - 895 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.09.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 − α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding. |
|---|---|
| AbstractList | Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 − α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding. Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 - α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding. [PUBLICATION ABSTRACT] Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 (1 - alpha )% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding. Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described in various books and articles. To our knowledge, however, no single resource describes all of the most common tests. Furthermore, many of these tests have not yet been implemented in popular statistical software packages such as SPSS and SAS. In this article, we describe all of the most common tests and provide SPSS and SAS programs to perform them. When they are applicable, our code also computes 100 × (1 - α)% confidence intervals corresponding to the tests. For testing hypotheses about independent regression coefficients, we demonstrate one method that uses summary data and another that uses raw data (i.e., Potthoff analysis). When the raw data are available, the latter method is preferred, because use of summary data entails some loss of precision due to rounding. |
| Author | Wuensch, Karl L. Weaver, Bruce |
| Author_xml | – sequence: 1 givenname: Bruce surname: Weaver fullname: Weaver, Bruce email: bweaver@lakeheadu.ca organization: Human Sciences Division, Northern Ontario School of Medicine, Centre for Research on Safe Driving, Lakehead University – sequence: 2 givenname: Karl L. surname: Wuensch fullname: Wuensch, Karl L. organization: Department of Psychology, East Carolina University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23344734$$D View this record in MEDLINE/PubMed |
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| References | WilliamsEJThe comparison of regression variablesJournal of the Royal Statistical Society (Series B)195921396399 KennyDAStatistics for the social and behavioral sciences1987Boston, MALittle, Brown and Company FisherRAOn the probable error of a coefficient of correlation deduced from a small sampleMetron19211332 Gould, W. (2009, July). Why does test sometimes produce chi-squared and other times F statistics? how are the chi-squared and F distributions related? [Support FAQ] Retrieved from http://www.stata.com/support/faqs/statistics/chi-squared-and-f-distributions Potthoff, R. F. (1966). Statistical aspects of the problem of biases in psychological tests. (Institute of Statistics Mimeo Series No. 479). Chapel Hill: University of North Carolina, Department of Statistics. URL: http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS_1966_479.pdf FleissJLThe statistical basis of meta-analysisStatistical Methods in Medical Research19932121145826125410.1177/096228029300200202 CochranWGThe comparison of percentages in matched samplesBiometrika19503725626614801052 CochranWGThe combination of estimates from different experimentsBiometrics19541010112910.2307/3001666 RaghunathanTERosenthalRRubinDBComparing correlated but nonoverlapping correlationsPsychological Methods1996117818310.1037/1082-989X.1.2.178 SteigerJHTests for comparing elements of a correlation matrixPsychological Bulletin19808724525110.1037/0033-2909.87.2.245 HotellingHThe generalization of Student’s ratioAnnals of Mathematical Statistics1931236037810.1214/aoms/1177732979 BeasleyWHDeSheaLToothakerLEMendozaJLBardDERodgersJLBootstrapping to test for nonzero population correlation coefficients using univariate samplingPsychological Methods2007124144331817935210.1037/1082-989X.12.4.414 ZouGYToward using confidence intervals to compare correlationsPsychological Methods2007123994131817935110.1037/1082-989X.12.4.399 Afifi, A. A., Clark, V., & May, S. (2003). Computer-aided multivariate analysis (4th Ed.). London, UK: Chapman & Hall/CRC. (ISBN-10: 1584883081; ISBN-13: 978-1584883081). HowellDCStatistical methods for psychology20138Belmont, CACengage Wadsworth PearsonKFilonLGNMathematical contributions to the theory of evolution. IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlationTransactions of the Royal Society London (Series A)189819122931110.1098/rsta.1898.0007 Behav Res Methods. 2013 Sep;45(3):896-7 289_CR1 DC Howell (289_CR9) 2013 WG Cochran (289_CR3) 1950; 37 WG Cochran (289_CR4) 1954; 10 JH Steiger (289_CR14) 1980; 87 K Pearson (289_CR11) 1898; 191 WH Beasley (289_CR2) 2007; 12 JL Fleiss (289_CR6) 1993; 2 289_CR7 DA Kenny (289_CR10) 1987 289_CR12 EJ Williams (289_CR15) 1959; 21 TE Raghunathan (289_CR13) 1996; 1 H Hotelling (289_CR8) 1931; 2 RA Fisher (289_CR5) 1921; 1 GY Zou (289_CR16) 2007; 12 |
| References_xml | – volume: 37 start-page: 256 year: 1950 ident: 289_CR3 publication-title: Biometrika doi: 10.1093/biomet/37.3-4.256 contributor: fullname: WG Cochran – volume: 2 start-page: 121 year: 1993 ident: 289_CR6 publication-title: Statistical Methods in Medical Research doi: 10.1177/096228029300200202 contributor: fullname: JL Fleiss – ident: 289_CR7 – volume: 12 start-page: 399 year: 2007 ident: 289_CR16 publication-title: Psychological Methods doi: 10.1037/1082-989X.12.4.399 contributor: fullname: GY Zou – ident: 289_CR1 – volume: 191 start-page: 229 year: 1898 ident: 289_CR11 publication-title: Transactions of the Royal Society London (Series A) doi: 10.1098/rsta.1898.0007 contributor: fullname: K Pearson – volume: 2 start-page: 360 year: 1931 ident: 289_CR8 publication-title: Annals of Mathematical Statistics doi: 10.1214/aoms/1177732979 contributor: fullname: H Hotelling – volume-title: Statistical methods for psychology year: 2013 ident: 289_CR9 contributor: fullname: DC Howell – volume: 1 start-page: 178 year: 1996 ident: 289_CR13 publication-title: Psychological Methods doi: 10.1037/1082-989X.1.2.178 contributor: fullname: TE Raghunathan – volume: 21 start-page: 396 year: 1959 ident: 289_CR15 publication-title: Journal of the Royal Statistical Society (Series B) doi: 10.1111/j.2517-6161.1959.tb00346.x contributor: fullname: EJ Williams – ident: 289_CR12 – volume: 87 start-page: 245 year: 1980 ident: 289_CR14 publication-title: Psychological Bulletin doi: 10.1037/0033-2909.87.2.245 contributor: fullname: JH Steiger – volume-title: Statistics for the social and behavioral sciences year: 1987 ident: 289_CR10 contributor: fullname: DA Kenny – volume: 10 start-page: 101 year: 1954 ident: 289_CR4 publication-title: Biometrics doi: 10.2307/3001666 contributor: fullname: WG Cochran – volume: 1 start-page: 3 year: 1921 ident: 289_CR5 publication-title: Metron contributor: fullname: RA Fisher – volume: 12 start-page: 414 year: 2007 ident: 289_CR2 publication-title: Psychological Methods doi: 10.1037/1082-989X.12.4.414 contributor: fullname: WH Beasley |
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| Snippet | Several procedures that use summary data to test hypotheses about Pearson correlations and ordinary least squares regression coefficients have been described... |
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| SubjectTerms | Behavioral Science and Psychology Body Height Body Weight Cognitive Psychology Confidence Intervals Data Interpretation, Statistical Economic models Female Humans Least-Squares Analysis Male Models, Statistical Multivariate analysis Psychology Pulmonary Disease, Chronic Obstructive - diagnosis Regression Analysis Research Design Respiratory Function Tests Software Variables |
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| Title | SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients |
| URI | https://link.springer.com/article/10.3758/s13428-012-0289-7 https://www.ncbi.nlm.nih.gov/pubmed/23344734 https://www.proquest.com/docview/1469451007 https://search.proquest.com/docview/1426512703 https://search.proquest.com/docview/1512328494 https://search.proquest.com/docview/1534839013 |
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