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Writing Up Descriptive Statistics

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 Descriptive Statistics

Author 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 on 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 descriptive 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

  • Intelligence Test Scores of Students with Disabilities

Research Questions

The following research questions were addressed in this study: (a) Of the five groups of elementary school students in this study, which group had the most participants, which group had the second most participants, and which group had the fewest participants? How many participants comprised the total sample for this study?; (b) How did these students perform on the three scores of: Full Scale IQ, the Verbal IQ, the Performance IQ?; (c) To what extent were students’ scores normally distributed on the Full Scale IQ, the Verbal IQ, and the Performance IQ?; (d) How well or how poorly did the boys score on the Full Scale IQ, the Verbal IQ, and on the Performance IQ?; (e) How well or how poorly did the boys score on the Full Scale IQ, the Verbal IQ, and on the Performance IQ?; and (f) Without using the words statistically or significantly, compare girls’ scores with the boys’ scores.

Results

In this research investigation, the total number of participants was 1,789 students. Of the five groups of students whose scores were analyzed in this study, the largest group consisted of 702 students with listening disorders, with the second largest group being 605 students with a label of Other Health Impaired. The fewest participants were in the group of students with a label of Muscular Dystrophy (n = 275). For these five groups of students, students with muscular dystrophy obtained the highest scores on the Performance IQ (M = 92.66) and the lowest scores on the Full Scale IQ (M = 70.12). Readers are referred to Table 1 for the descriptive statistics concerning the IQ test scores.

Regarding the normality of the three IQ scores analyzed in this study, 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) were all within the range of +/- 3 (Onwuegbuzie & Daniel, 2002). With all standardized coefficients being within the +/- 3 range, students’ performance on the three IQ measures were determined to be normally distributed. Readers are referred to Table 2 for the standardized coefficients concerning normality of the IQ test scores.

Finally for the last three research questions, the scores of girls and boys were compared. Both girls and boys performed below the average score on the IQ measure (M = 100). Girls scored higher than boys on the Verbal IQ, the Performance IQ, and on the Full Scale IQ. The difference between girls and boys was greatest on the Verbal IQ, where boys outperformed girls by 13 points, and lowest on the Performance IQ, where girls only outperformed boys by 2 points. Readers are referred to Table 3 for the descriptive statistics for the three IQ measures by gender.

References

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 Student IQ Scores
Cognitive Measure M SD
Full Scale IQ 77.73 13.54
Verbal IQ 77.97 13.66
Performance IQ 81.14 14.01
Table 2: Standardized Skewness Coefficients and Standardized Kurtosis Coefficients for Students’ IQ Scores
Cognitive Measure Standardized Skewness Coefficient Standardized Kurtosis Coefficient
Full Scale IQ -1.28 0.89
Verbal IQ 2.03 0.76
Performance IQ -0.99 0.55
Table 3: Descriptive Statistics for Cognitive Scores by Gender
Descriptive Statistics for Cognitive Scores by Gender
  Boys Girls
Cognitive Measure M SD M SD
Full Scale IQ 69.52 15.21 85.88 3.34
Verbal IQ 90.12 18.91 76.99 23.03
Performance IQ 87.99 23.65 89.12 44.31

Output from SPSS

Note:

Tables 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 Tables 1, 2, and 3 above the Output from SPSS are compliant with APA format.
Table 4: Disability Group Membership
Frequency Percent Valid Percent Cumulative Percent
Valid Students with Listening Disorders 702 42.5 42.5 42.5
Students with Muscular Dystrophy 275 23.3 23.3 65.7
Students Labeled as Other Health Impaired 605 34.3 34.3 100.0
Total 1789 100.0 100.0
Table 5: Statistics
  Wechsler Full Scale IQ 3 Verbal IQ Performance IQ (Wechsler Performance Intelligence 3)
n 1789 1789 1789
Missing 0 0 2
Mean 70.12 77.97 92.66
Std. Deviation 13.541 13.661 14.005
Skewness -.279 .028 -.177
Std. Error of Skewness .071 .071 .071
Kurtosis .212 .142 .072
Std. Error of Kurtosis .142 .142 .142
Table 6: Statistics
Gender Wechsler Full Scale IQ 3 Verbal IQ (Wechsler Verbal Intelligence 3) Performance IQ (Wechsler Performance Intelligence 3)  
Boys n 522 522 567  
Missing 0 0 2  
Mean 79.52 80.12 82.17  
Std. Deviation 13.512 13.908 13.653  
Skewness -.253 .033 -.217  
Std. Error of Skewness .101 .101 .101  
Kurtosis .374 .291 .255  
Std. Error of Kurtosis .201 .201 .201  
Girls n 734 734 732
Missing 0 0 0  
Mean 75.88 75.75 80.07  
Std. Deviation 13.339 13.031 14.307  
Skewness -.327 -.046 -.120  
Std. Error of Skewness .101 .101 .101  
Kurtosis .037 -.084 -.069  
Std. Error of Kurtosis .201 .201 .201  

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