Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Presenting and Communicating Your Statistical Findings: Model Writeups » Writing Up Nonparametric Spearman rho Correlation

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • NCPEA

    This collection is included inLens: National Council of Professors of Educational Administration
    By: National Council of Professors of Educational Administration

    Click the "NCPEA" link to see all content they endorse.

Recently Viewed

This feature requires Javascript to be enabled.
 

Writing Up Nonparametric Spearman rho Correlation

Module by: John R. Slate, Ana Rojas-LeBouef. E-mail the authors

ncpealogo.gif

Note:

This module is published by NCPEA Press and is presented as an NCPEA/Connexions publication. Each chapter has been peer-reviewed, accepted, and endorsed by the National Council of Professors of Educational Administration (NCPEA) as a significant contribution to the scholarship and practice of education administration. Formatted and edited in Connexions by Theodore Creighton, Virginia Tech and Janet Tareilo, Stephen F. Austin State University.

Writing Up Your Nonparametric Spearman rho 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 Spearman rho 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

Relationships of Economically Disadvantaged and Minority Student Enrollment in Texas Middle Schools

Research Questions

The following research questions were addressed in this study:

  1. What is the relationship between the percent of economically disadvantaged students and the percent of minority students enrolled at Texas middle schools for the 2003-2004 school year?;
  2. What is the relationship between the percent of economically disadvantaged students and the percent of minority students enrolled at Texas middle schools for the 2004-2005 school year?; and
  3. What is the relationship between the percent of economically disadvantaged students and the percent of minority students enrolled at Texas middle schools for the 2005-2006 school year?

Results

Sample sizes, means, and standard deviations pertaining to the two variables of interest (i.e., percent of economically disadvantaged students and percent of minority students) for all three years are presented in Table 1. An examination of the scatterplots (not presented) suggested the presence of linearity for the two variables for each of the three years of data analyzed. The presence of linearity permitted the use of correlation coefficients. With respect to the distribution of scores underlying these measures, the standardized skewness coefficients (i.e., skewness divided by the standard error of skewness) and the standardized kurtosis coefficients (i.e., kurtosis divided by the standard error of kurtosis) revealed serious departures from normality for the two variables of interest for all three years of data analyzed. Specifically, for the percent of economically disadvantaged students, the standardized skewness coefficients were -202.38, -146.81, and -146.52, for each of the three years respectively. Similarly, the standardized kurtosis coefficients for the percent of economically disadvantaged students were -6.65, -6.48, and -10.86 for each of the three years respectively.

Concerning the standardized skewness coefficients for the percent of minority student enrollment, all three coefficients were outside of the limits of normality, -111.43, -162.24, and -130.92 for the 2003-2004, 2004-2005, and 2005-2006 school years respectively. The standardized kurtosis coefficients for minority student enrollment were -10.77, -10.92, and -6.74 for each of the three years respectively. Therefore, all six standardized skewness coefficients and all 6 standardized kurtosis coefficients were outside of the limits of normality, +/- 3, and were indicative of serious departures from normality (Onwuegbuzie & Daniel, 2002). Accordingly, a nonparametric procedure, the Spearman’s rank order correlation coefficient (i.e., Spearman's rho) was performed to address each research question previously delineated.

The Spearman’s rho revealed a statistically significant relationship between the percent of economically disadvantaged students and the percent of minority students enrolled in Texas middle schools during the 2003-2004 school year (rs[1528] = .76, p < .001). The effect size of this relationship was large (Cohen, 1988). Squaring the correlation coefficients indicated that 58.4% of the variance in the percent of economically disadvantaged students was explained by the presence of minority students. Similarly, 58.4% of the variance in the percent of minority student enrollment was accounted for by the presence of economically disadvantaged students.

For the 2004-2005 school year, the Spearman’s rho revealed a statistically significant relationship between the percent of economically disadvantaged students and the percent of minority students enrolled in Texas middle schools, (rs[1554] = .76, p < .001). The effect size of this relationship was large (Cohen, 1988). Squaring the correlation coefficients indicated that 58.2% of the variance in the percent of economically disadvantaged students was explained by the presence of minority students. Similarly, 58.2% of the variance in the percent of minority student enrollment was accounted for by the percent of economically disadvantaged students.

The Spearman’s rho revealed a statistically significant relationship between the percent of economically disadvantaged students and the percent of minority students enrolled in Texas middle schools during the 2005-2006 school year (rs[1563] = .78, p < .001). The effect size of this relationship was large (Cohen, 1988). Squaring the correlation coefficients indicated that 60.2% of the variance in the percent of economically disadvantaged students was explained by the presence of minority students. Similarly, 60.2% of the variance in the percent of minority student enrollment was explained by the presence of economically disadvantaged students.

In summary, results across the three years of data were consistent. Effect sizes for all three years were large (Cohen, 1988). Moreover, the percent of variance explained by each variable was consistent, ranging from 58.4% to 60.2%. Thus, findings revealed herein were supportive of a consistent relationship between the percent of economically disadvantaged students and the percent of minority students enrolled in Texas middle schools.

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.

Note:

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.
Table 1: Sample Sizes, Means, and Standard Deviations for Percentages of Economically Disadvantaged Students and Minority Student Enrollment for the 2003-2004, 2004-2005, and 2005-2006 School Years
Year and Variable n M SD
2003-2004 School Year      
Economically Disadvantaged 1,528 51.46 26.28
Minority Students 1,528 54.54 31.33
2004-2005 School Year      
Economically Disadvantaged 1,554 54.66 25.60
Minority Students 1,554 56.95 31.03
2005-2006 School Year      
Economically Disadvantaged 1,563 54.70 25.36
Minority Students 1,563 57.88 30.73

Note:

Figures 1, 2, 3, 4, 5, and 6 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 Table 1 above the Output from SPSS is compliant with APA format.

SPSS Statistical Output

Figure 1. Statistics for the 2003-2004 school year

figure4.1.png

Figure 2. Correlations/Spearman rho for the 2003-2004 school year

figure4.2.png

Figure 3. Statistics for the 2004-2005 school year

figure4.3.png

Figure 4. Correlations/Spearman rho for the 2004-2005 school year

figure4.4.png

Figure 5. Statistics for the 2005-2006 school year

figure4.5.png

Figure 6. Correlations/Spearman rho for the 2005-2006 school year

figure4.6.png

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks