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Using the Humble Crosstab to Partner with Parametrics

Using the Humble Crosstab to Partner with Parametrics. Jack Williamsen Office of Institutional Effectiveness St. Norbert College De Pere, Wisconsin. Sidebar : Some info about St. Norbert & the sample used in this presentation.

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Using the Humble Crosstab to Partner with Parametrics

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  1. Using the Humble Crosstab to Partner with Parametrics Jack Williamsen Office of Institutional Effectiveness St. Norbert College De Pere, Wisconsin

  2. Sidebar: Some info about St. Norbert & the sample used in this presentation • St. Norbert College (“SNC”) is a Catholic Liberal Arts College near Green Bay, WI with an undergraduate population of ~ 2000 students. • The two largest undergraduate majors are Business Administration and Education. • Data in this presentation come from a larger study of the role of gender in the educational experiences of SNC men and women conducted by the Office of Institutional Effectiveness.

  3. Do parametrics need a partner? • Parametric statistics (e.g., means, Pearson r) are central to many quantitative analyses of information. • They convey useful information in a compact “package.” But…… • Terminating a quantitative analysis after computing summary statistics is like setting a book aside after reading the dust jacket • You know something, but there is more to learn—useful knowledge that could deepen understanding or lead to more precise real-world action.

  4. Crosstabs to the Rescue • Crosstabs provide a convenient, useful method to explore the continuous distribution(s) of variables summarized by means and correlations. • Although parametric tools (such as the SD) offer insight into distributions…. • Crosstabs convey information in tables that are understandable by non-statisticians. • And they lend themselves to transformation into graphic visuals for the “numerically-challenged.”

  5. This presentation uses three examples: • Example 1: The correlation between HSGPA & 1st semester freshman GPA (= 0.62) is dissected using a dual quintile (HSGPA quintiles by 1st sem. Fr. GPA quintiles) table. • Example 2: Robust mean GPA differences (~0.30) between men and women students are analyzed using SPSS EXPLORE’s seven percentile categories. • Example 3: Unusually high retention of business majors (vs. all other majors) is explored across the ‘GPA spectrum’ using quintiles.

  6. Example 1: How to dissect a Correlation • The correlation (0.62) between HSGPA and 1stsem Fr. GPA is both typical and an indicator of a less-than-perfect ordering of case-by-case GPA pairs. • We can literally see the nature of this “imperfection” by: (1) identifying quintile break points for HSGPA and for Fr. GPA. (See Appendix for methods.) • Then (2) use Transform > “Recode [GPA] into another variable” [quintile] to create two categorical GPAs • Finally (3), cross-tab the two “quintiled” GPAs in SPSS, using “Row Percent” to fill in the resulting table.

  7. Example 1: Notes • Although quintiles are used in this example, any “slice & dice” set of categories can be used. • The table in the next slide is “data-dense.” • Readers may need some initial guidance (e.g., “Read table from rows, left to right”) and/or an illustration: • “The table shows, for example, that 54% of freshmen with HSGPA < = 2.84 have 1st semester GPAs <= 2.38.”

  8. Example 1: Dissecting a Correlation with Quintiles

  9. Example 2: Mean GPA Differences • Women consistently have higher mean GPAs than men

  10. Example 2: Exploring Mean Differences • It is an easily-made assumption that a mean difference is present equally “across the board.” • Example: “The mean GPA for women students is ~ 0.30 higher than the mean GPA for men” can easily become: “The GPA for women is ~0.30 higher than for men.” • The second statement encourages the assumption that the mean difference is present throughout the range of GPAs (i.e., “across the board”). Let’s see.

  11. Example 2: EXPLORE-ing a Mean Difference • I used the “Percentiles” table provided by SPSS EXPLORE to get percentile points across the “GPA spectrum” for men and women students. • The EXPLORE Percentiles table gives weighted mean GPAs for each of seven (5th, 10th, 25th, 50th, 75th, 90th, & 95th)percentile ranks. • I then used EXCEL to create a visually more attractive and useful crosstab table than the one provided in SPSS output. See the next slide.

  12. Example 2: Mean GPA Differences by EXPLORE Ranks • 2005-2007 Freshmen • The mean gender difference in GPA continually shrinks in the above-average ranks.

  13. Example 3: Investigating an Unusual Result. • Fact: HSGPA and 1st sem. GPA are positively correlated with retention to sophomore year (rpbis= ~0.24 & ~0.35, respectively). • Fact: Freshman males in business had lower meanHSGPAs than men in all other majors (3.17 vs. 3.36) and lower 1st semester GPAs (2.75 vs. 3.00) as well. • Fact: 2005-2007 freshman males in business retained to 2nd year at a higher rate than men in all other majors combined (89% vs. 80%).

  14. Example 3: Question • Linear correlations of HSGPA and 1st semester GPA with retention to sophomore year are modest in size but both GPAs are typically two of the strongest pre- and post-matriculation correlates of retention. • Based on GPAs, we would not expect 1st year men majoring in business to retain at a higher rate than men in other majors. But they clearly do (89% vs. 80%). • Question: Is this higher retention rate present across the GPA spectrum? What do you think?

  15. Example 3: Percent retained, by GPA Quintile—Business vs. all other majors • Male 2005-2007 Freshman Business majors, compared to men in all other majors, are retained to sophomore year in greater percentages at every GPA quintile:

  16. Conclusions • Crosstabs: a convenient and useful way to further explore continuous variables summarized with a single parametric statistic. • Crosstabs : (1)improve understanding of variables of interest and… • (2)suggest directions for further research and/or “real world” action.

  17. Questions?? • 1. ?? • Etc.? • This PowerPoint and the “Gender Matters” monograph can be accessed at : www.snc.edu/oie/ • Click on the “Public Access Documents and Resources” Quick Link on right side of page. • Thank You for Coming! • jack.williamsen@snc.edu

  18. Appendix: SPSS methods for creating categories from continuous variables • (Analyze > Frequencies > Statistics > Percentile Values) offers a number of user-selected options for generating categories, including percentiles. • (Transform > Visual Binning) is also versatile, and provides a visual representation of the distribution of the variable of interest. Make cuts any way you wish. • (Analyze > Descriptive Statistics >Explore > Statistics > Percentiles) provides a fixed set of percentile breaks. See Example 2 for an illustration.

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