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Writing up your parametric pearson correlation

    About the Authors

  • John R. Slate is a Professor at Sam Houston State University where he teaches Basic and Advanced Statistics courses, as well as professional writing, to doctoral students in Educational Leadership and Counseling. His research interests lie in the use of educational databases, both state and national, to reform school practices. To date, he has chaired and/or served over 100 doctoral student dissertation committees. Recently, Dr. Slate created a website, Writing and Statistical Help to assist students and faculty with both statistical assistance and in editing/writing their dissertations/theses and manuscripts.
  • Ana Rojas-LeBouef is a Literacy Specialist at the Reading Center at Sam Houston State University where she teaches developmental reading courses. She recently completed her doctoral degree in Reading, where she conducted a 16-year analysis of Texas statewide data regarding the achievement gap. Her research interests lie in examining the inequities in achievement among ethnic groups. Dr. Rojas-LeBouef also assists students and faculty in their writing and statistical needs on the Writing and Statistical website, Writing and Statistical Help

The following is an example of how to write up (in manuscript text) your Pearson Correlation statistics. This module is used with a larger Collection (Book) authored by John R. Slate and Ana Rojas-LeBouef from Sam Houston State University and available at: Calculating Basic Statistical Procedures in SPSS: A Self-Help and Practical Guide to Preparing Theses, Dissertations, and Manuscripts

College-Readiness Rates in Reading and Math: Are They Related?

Research question

The following research question was addressed in this investigation: What is the relationship between Texas high school students’ college-readiness rates in reading and in math for the 2007-2008 school year?

Results

Prior to conducting correlational procedures, the scatterplot (present in the Appendix) was examined and was clearly suggestive of a bivariate linear relationship between the two variables. No departure from a linear relationship was evident, thereby justifying the use of a correlation coefficient. Regarding the underlying distribution of scores for college-readiness rates in reading and in math, the standardized skewness coefficients (i.e., the skewness value divided by the standard error of skewness) and the standardized kurtosis coefficients (i.e., the kurtosis value divided by the standard error of kurtosis) were calculated and yielded values that were well within the range of normality (i.e., +/- 3, Onwuegbuzie&Daniel, 2002). Readers are directed to Table 1 for the values of these standardized coefficients. Because all four coefficients were reflective of normally distributed data, a parametric correlation procedure, specifically the Pearson's product-moment correlation coefficient, was calculated.

To determine whether a statistically significant relationship was present between Texas students’ college-readiness rates in reading and math, a Pearson r was calculated. For the 2007-2008 school year, the finding was statistically significant, r (1371) = .69, p <.001, indicating the presence of a strong statistically significant positive relationship between college-readiness rates in reading and in math. Using Cohen’s (1988) values, this r value was reflective of a large relationship. Squaring this r value indicated that college-readiness rates in reading and in math overlapped 47.61%.

References

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) . Hillsdale, NJ: Lawrence Erlbaum.
  • Onwuegbuzie, A. J.,&Daniel, L. G. (2002). Uses and misuses of the correlation coefficient. Research in the Schools, 9 (1) , 73-90.
To be compliant with APA 6th edition, students and faculty are to be aware that Table titles are placed "above" the table entry. Titles here are placed below the tables because of special formatting templates and for conciseness of visual presentation.
Standardized Skewness Coefficients and Standardized Kurtosis Coefficients for College-Readiness Rates in Reading and in Math for All Texas High School Students
Variable Standardized Skewness Coefficient Standardized Kurtosis Coefficient
Reading Readiness Rates -1.63 -1.61
Math Readiness Rates -1.39 0.18
Descriptive Statistics for College-Readiness Rates in Reading and in Math for All Texas High School Students
Variable n M SD
Reading Readiness Rates 1377 53.91 16.09
Math Readiness Rates 1376 54.08 16.26

Spss statistical output

Figures 1, 2, and 3 below came directly from SPSS output. As such, they are not compliant with APA 6th edition and should not be used in theses, dissertations, or manuscripts. Only Tables 1 and 2above the Output from SPSS is compliant with APA format.

Figure 1. scatterplot of reading readiness rates with math readiness rates. linearity is clearly present

Figure 2

Figure 3

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Source:  OpenStax, Presenting and communicating your statistical findings: model writeups. OpenStax CNX. Apr 27, 2011 Download for free at http://cnx.org/content/col11299/1.3
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