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 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. 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. 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.” 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. Example 1: How to dissect a Correlation The correlation (0.62) between HSGPA and 1st sem 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. 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.” Example 1: Dissecting a Correlation with Quintiles Example 2: Mean GPA Differences Women consistently have higher mean GPAs than men 1st Year GPAs of 2007 SNC Freshmen 2007 Freshmen Women Men Difference (W – M) HSGPA 3.56 3.26 0.30 1 Sem GPA 3.07 2.71 0.36 3.15 2.80 0.35 st 2 nd Sem GPA GPAs of all 2007-08 enrolled SNC Students 2007 Enrolled Women Men Difference (W – M) HSGPA 3.48 3.18 0.30 SNC GPA 3.16 2.84 0.32 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. 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. Example 2: Mean GPA Differences by EXPLORE Ranks 2005-2007 Freshmen 2005-07 Freshmen Gender H.S. GPA Percentiles for HSGPA 5 10 25 50 75 90 95 Men (N = 654) Women (N = 879) 2.21 2.56 2.41 2.74 2.76 3.13 3.15 3.53 3.61 3.85 3.89 4.00 3.98 4.05 Diff (M-F) -0.35 -0.34 -0.37 -0.38 -0.24 -0.12 -0.07 2005-07 Freshmen Gender 1st Sem GPA Percentiles for SNC SEM1 GPA 5 10 25 50 75 90 95 Men (N = 654) Women (N = 879) 1.50 1.82 1.85 2.14 2.33 2.67 2.88 3.17 3.38 3.60 3.75 3.88 3.88 4.00 Diff (M-F) -0.32 -0.29 -0.34 -0.29 -0.22 -0.13 -0.12 The mean gender difference in GPA continually shrinks in the above-average ranks. 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 mean HSGPAs 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%). 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 preand 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? 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: 2005-07 Freshman Men: Percent Retained to Sophomore Year, by GPA GPA Quintile <=2.38 2.39-2.88 2.89-3.25 3.26-3.63 3.64+ Business All Others 79% 66% 94% 90% 94% 92% 96% 82% 100% 94% Diff (Bu-Others) 13% 4% 2% 14% 6% 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. 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! [email protected] 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.