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Writing Up Parametric ANOVA

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

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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 and Brad Bizzell, Virginia Tech and Janet Tareilo, Stephen F. Austin State University.

Writing Up Your Parametric ANOVA

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 Parametric ANOVA test 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 in Reading: Differences by Accountability Rating

Research Question

The following research question was addressed in this study:

  • What is the difference in college-readiness reading rates between Texas high school campuses as a function of accountability rating?

Results

Prior to conducting an inferential statistical procedure, checks for normality of data were conducted. With respect to the distribution of scores underlying college-readiness rates in reading, 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 no serious departures from normality for the variable of interest. Readers are directed to the Appendix where the skewness and kurtosis values are present. By calculating the standardized coefficients, the reader can ascertain that all of the standardized coefficients were within the +/-3 range (Onwuegbuzie & Daniel, 2002). Because these standardized coefficients were indicative of normally distributed data, use of a parametric Analysis of Variance (ANOVA) procedure was justified.

Regarding the extent to which differences might be present in college-readiness rates in reading as a function of school accountability rating (i.e., Exemplary, Academically Recognized, Academically Acceptable, and Academically Unacceptable), an ANOVA was calculated. This ANOVA revealed a statistically significant difference, F(3, 1228) = 97.45, p < .001, n2 = .19. The effect size for this statistically significant difference was large (Cohen, 1988). Scheffe` post hoc procedures revealed that differences were present in college-readiness rates in reading between each pair of accountability ratings. As evidenced in Table 1, college-readiness rates in reading were highest at Exemplary high schools, followed by Academically Recognized high schools. As the accountability rating became poorer, college-readiness rates in reading were statistically significantly lower. Readers are directed to Table 1 for the descriptive statistics for college-readiness rates in reading by school accountability rating.

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: Descriptive Statistics for College-Readiness Rates in Reading by Accountability Rating
Variable n M SD
Exemplary 117 56.51 18.74
Academically Recognized 542 44.47 13.99
Academically Acceptable 501 36.26 12.34
Academically Unacceptable 72 29.13 13.03

Note:

Figures 1, 2, 3, and 4 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

figure9.1.png

Figure 2. Descriptive Statistics

figure9.2.png

Figure 3. Tests of Between Subjects Effects

figure9.3.png

Figure 4. Multiple Comparisons

figure9.4.png

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