This chapter is part of a larger Collection (Book) and is available at: Calculating Basic Statistical Procedures in SPSS: A SelfHelp and Practical Guide to Preparing Theses, Dissertations, and Manuscripts
Inside Collection (Textbook): Calculating Basic Statistical Procedures in SPSS: A SelfHelp and Practical Guide to Preparing Theses, Dissertations, and Manuscripts
Summary: Calculating Correlations: Parametric and Non Parametric is Chapter 3 of Calculating Basic Statistical Procedures in SPSS: A SelfHelp and Practical Guide to Preparing Theses, Dissertations, and Manuscripts. This book is written to assist graduate students and faculty members, as well as undergraduate students, in their use of the Statistical Package of the Social SciencesPC (SPSSPC) versions 1519. Specifically, we have generated a set of steps and screenshots to depict each important step in conducting basic statistical analyses. We believe that this book supplements existing statistical texts in which readers are informed about the statistical underpinnings of basic statistical procedures and in which definitions of terms are provided. Accordingly, other than providing a few basic definitions, we assume that dissertation chairs/thesis directors, students, and/or faculty will obtain their own definition of terms. We hope you find this set of steps and screenshots to be helpful as you use SPSSPC in conducting basic statistical analyses.
This chapter is part of a larger Collection (Book) and is available at: Calculating Basic Statistical Procedures in SPSS: A SelfHelp and Practical Guide to Preparing Theses, Dissertations, and Manuscripts
In this set of steps, readers will calculate either a parametric or a nonparametric statistical analysis, depending on whether the data reflect a normal distribution. A parametric statistical procedure requires that its data be reflective of a normal curve whereas no such assumption is made in the use of a nonparametric procedure. Of the two types of statistical analyses, the parametric procedure is the more powerful one in ascertaining whether or not a statistically significant relationship, in this case, exists. As such, parametric procedures are preferred over nonparametric procedures. When data are not normally distributed, however, parametric analyses may provide misleading and inaccurate results. Accordingly, nonparametric analyses should be used in cases where data are not reflective of a normal curve. In this set of steps, readers are provided with information on how to make the determination of normally or nonnormally distributed data. For detailed information regarding the assumptions underlying parametric and nonparametric procedures, readers are referred to the Hyperstats Online Statistics Textbook at http://davidmlane.com/hyperstat/ or to the Electronic Statistics Textbook (2011) at http://www.statsoft.com/textbook/
Research questions for which correlations are appropriate involve asking for relationships between or among variables. The research question, “What is the relationship between study skills and grades for high school students?” could be answered through use of a correlation.
Check for Skewness and Kurtosis values falling within/without the parameters of normality (3 to +3)
* Skewness [Note. Skewness refers to the extent to which the data are normally distributed around the mean. Skewed data involve having either mostly high scores with a few low ones or having mostly low scores with a few high ones.] Readers are referred to the following sources for a more detailed definition of skewness: http://www.statistics.com/index.php?page=glossary&term_id=356 and http://www.statsoft.com/textbook/basicstatistics/#Descriptive%20statisticsb
To standardize the skewness value so that its value can be constant across datasets and across studies, the following calculation must be made: Take the skewness value from the SPSS output (in this case it is .177) and divide it by the Std. error of skewness (in this case it is .071). If the resulting calculation is within 3 to +3, then the skewness of the dataset is within the range of normality (Onwuegbuzie & Daniel, 2002). If the resulting calculation is outside of this +/3 range, the dataset is not normally distributed.
* Kurtosis [Note. Kurtosis also refers to the extent to which the data are normally distributed around the mean. This time, the data are piled up higher than normal around the mean or piled up higher than normal at the ends of the distribution.] Readers are referred to the following sources for a more detailed definition of kurtosis: http://www.statistics.com/index.php?page=glossary&term_id=326 and http://www.statsoft.com/textbook/basicstatistics/#Descriptive%20statisticsb
To standardize the kurtosis value so that its value can be constant across datasets and across studies, the following calculation must be made: Take the kurtosis value from the SPSS output (in this case it is .072) and divide it by the Std. error of kurtosis (in this case it is .142). If the resulting calculation is within 3 to +3, then the kurtosis of the dataset is within the range of normality (Onwuegbuzie & Daniel, 2002). If the resulting calculation is outside of this +/3 range, the dataset is not normally distributed.
Statistics  
Performance IQ (Wechsler Performance Intelligence 3)  
N 


Mean  81.14  
Std. Deviation  14.005  
Skewness  .177  
Std. Error of Skewness  .071  
Kurtosis  .072  
Std. Error of Kurtosis  .142 
Verbal IQ (Wechsler Verbal Intelligence 3)  Performance IQ (Wechsler Performance Intelligence 3)  
Verbal IQ (Wechsler Verbal Intelligence 3) 


Performance IQ (Wechsler Performance Intelligence 3) 


**. Correlation is significant at the 0.01 level (2tailed). 
Verbal IQ (Wechsler Verbal Intelligence 3)  Performance IQ (Wechsler Performance Intelligence 3)  
Verbal IQ (Wechsler Verbal Intelligence 3) 


Performance IQ (Wechsler Performance Intelligence 3) 


** Correlation is significant at the 0.01 level (2tailed). 
So, how do you "write up" your Research Questions and your Results? Schuler W. Huck (2000) in his seminal book entitled, Reading Statistics and Research, points to the importance of your audience understanding and making sense of your research in written form. Huck further states:
This book is designed to help people decipher what researchers are trying to communicate in the written or oral summaries of their investigations. Here, the goal is simply to distill meaning from the words, symbols, tables, and figures included in the research report. To be competent in this arena, one must not only be able to decipher what's presented but also to "fill in the holes"; this is the case because researchers typically assume that those receiving the research report are familiar with unmentioned details of the research process and statistical treatment of data.
Researchers and Professors John Slate and Ana RojasLeBouef understand this critical issue, so often neglected or not addressed by other authors and researchers. They point to the importance of doctoral students "writing up their statistics" in a way that others can understand your reporting and as importantly, interpret the meaning of your significant findings and implications for the preparation and practice of educational leadership. Slate and LeBouef provide you with a model for "writing up your Parametric and NonParametric Correlations statistics."
Click here to view: Writing Up Your Parametric Correlation Statistics
Click here to view: Writing Up Your Nonparamteric Correlation Statistics