Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Calculating Basic Statistical Procedures in SPSS: A Self-Help and Practical Guide to Preparing Theses, Dissertations, and Manuscripts » Conducting a Nonparametric Independent Samples t-test

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 display tagshide tags

    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.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Conducting a Nonparametric Independent Samples t-test

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

Summary: Conducting a Nonparametric Independent Samples t-test is Chapter 6 of Calculating Basic Statistical Procedures in SPSS: A Self-Help and Practical Guide to Preparing Theses, Dissertations, and Manuscripts, authored by John R. Slate and Ana Rojas-LeBouef from Sam Houston State University. 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 Sciences-PC (SPSS-PC) versions 15-19. 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 SPSS-PC in conducting basic statistical analyses.

ncpealogo.gif

Note:

This 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 and Brad Bizzell, Virginia Tech, Janet Tareilo, Stephen F. Austin State University, and Thomas Kersten, Roosevelt University.

This chapter is part of a larger Collection (Book) and is available at: Calculating Basic Statistical Procedures in SPSS: A Self-Help and Practical Guide to Preparing Theses, Dissertations, and Manuscripts

Note:

Slate and LeBouef have written a "companion book" which is available at: Preparing and Presenting Your Statistical Findings: Model Write Ups

Authors Information

  • 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 website Writing and Statistical Help.

Editors Information

  • Theodore B. Creighton, is a Professor at Virginia Tech and the Publications Director for NCPEA Publications, the Founding Editor of Education Leadership Review, and the Senior Editor of the NCPEA Connexions Project.
  • Brad E. Bizzell, is a recent graduate of the Virginia Tech Doctoral Program in Educational Leadership and Policy Studies, and is a School Improvement Coordinator for the Virginia Tech Training and Technical Assistance Center. In addition, Dr. Bizzell serves as an Assistant Editor of the NCPEA Connexions Project in charge of technical formatting and design.
  • Janet Tareilo, is a Professor at Stephen F. Austin State University and serves as the Assistant Director of NCPEA Publications. Dr. Tareilo also serves as an Assistant Editor of the NCPEA Connexions Project and as a editor and reviewer for several national and international journals in educational leadership.
  • Thomas Kersten is a Professor at Roosevelt University in Chicago. Dr. Kersten is widely published and an experienced editor and is the author of Taking the Mystery Out of Illinois School Finance, a Connexions Print on Demand publication. He is also serving as Editor in Residence for this book by Slate and LeBouef.

Conducting a Nonparametric Independent Samples t-test

In this set of steps, readers will calculate either a parametric or a nonparametric statistical analysis, depending on whether the data for the dependent variable 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 difference, 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. According, 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/

For this nonparametric independent samples t-test to be appropriately used, at least half of the standardized skewness coefficients and the standardized kurtosis coefficients must be outside the normal range (+/-3, Onwuegbuzie & Daniel, 2002). Research questions for which nonparametric independent samples t-tests are appropriate involve asking for differences in a dependent variable by group membership (i.e., only two groups are present for t-tests). The research question, “What is the difference between boys and girls in their science performance among middle school students?” could be answered through use of a nonparametric independent samples t-test.

Step One:

  • Calculate Frequencies on the Split Groups
  • √ Data
  • * Split File

figure6.1.PNG

Your screen will show that all cases are going to be analyzed and a “do not create groups”. You will need to click the compare groups and move the independent variable over to the “Group Based on”.

figure6.2.PNG

After you do this, your screen should resemble the following:

figure6.3.PNG

  • Then click OK
  • √ Analyze
  • * Descriptive Statistics
  • * Frequencies

figure6.4.PNG

  • √ Move over the dependent (outcome) variable

figure6.5.PNG

  • √ Statistics
  • * Mean
  • * Standard Deviation
  • * 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
  • http://www.statsoft.com/textbook/basic-statistics/#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 and divide it by the Std. error of skewness. 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:
  • 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 and divide it by the Std. error of kurtosis. 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.
  • http://www.statistics.com/index.php?page=glossary&term_id=326
  • http://www.statsoft.com/textbook/basic-statistics/#Descriptive%20statisticsb
  • * Continue
  • * OK

figure6.6.PNG

  • √ Charts (these are calculated only if you wish to have visual depictions of skewness and of kurtosis-they are not required)
  • * Histogram~ with normal curve (not required, optional)
  • √ Continue
  • √ OK

figure6.7.PNG

  • Note: Before you continue to another application you must complete the following:
  • √ Data
  • √ Split Files
  • √ Analyze all cases, do not create groups
  • √ OK

figure6.8.PNG

Step Two:

Check for Skewness and Kurtosis values falling within/without the parameters of normality (-3 to +3). Note that each variable has its own skewness value and its own kurtosis value. Thus, a total of three standardized skewness coefficients and three standardized kurtosis coefficients can be calculated from information in the table below.

Table 1: Skewness and Kurtosis Coefficients
    CH005TC09R CL005TC09R CW005TC09R
N
Valid 3125 1805 1877
Missing 5197 6517 6445
Skewness -1.129 -.479 -2.197
Std. Error of Skewness .044 .058 .056
Kurtosis 1.818 -.412 6.991
Std. Error of Kurtosis .088 .115 .113
  • Standard Coefficients Calculator
  • Copy variable #1 and #2 into the skewness and kurtosis calculator

figure6.9.PNG

Step Three

  • Calculate Nonparametric Independent Samples t-test on Data
  • √ Analyze
  • √ Nonparametric Tests
  • √ 2 Independent Samples
  • √ Test Variable would be your Dependent Variable (e.g., test scores)
  • √ Grouping Variable would be your dichotomous Independent Variable

figure6.10.1.PNG

  • √ Define Groups
  • √ Group One is No. 1 and Group Two is No. 2 (or whatever numbers you used to identify each group)
  • Note: Click on view than value labels to find the code for each group.
  • √ Continue
  • √ OK

figure6.11.1.PNG

Step Four:

  • Check for Statistical Significance
Table 2: Test Statisticsa
  Performance IQ(Wechsler Performance Intelligence 3)
Mann-Whitney U 6765.500
Wilcoxon W 44166.500
Z -20.752
Asymp. Sig. (2-tailed) .000
  • a. Grouping Variable:Disability Group Membership
  • Numerical sentence is written as: U = 6765.50, p < .001

Step Five:

figure6.12.png

Write Up Your Statistics

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 Rojas-LeBouef 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 nonparametric independent samples t-test statistics."

Click here to view: Writing Up Your Nonparametric Independent Samples t-test Statistics

References

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 | 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 ...

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