Using the Humble Crosstab

Jack WilliamsenOffice of Institutional EffectivenessSt. Norbert CollegeDe Pere, WisconsinUsing the Humble Crosstab to Partner with Parametrics1Sidebar: Some info about St. Norbert & the sample used in this presentationSt. 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. ButTerminating a quantitative analysis after computing summary statistics is like setting a book aside after reading the dust jacketYou know something, but there is more to learnuseful knowledge that could deepen understanding or lead to more precise real-world action. Crosstabs to the RescueCrosstabs 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 EXPLOREs 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 CorrelationThe 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: NotesAlthough 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 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.Sheet

2005-07 FreshmenGenderPercentiles for HSGPA5102550759095

H.S. GPAMen (N = 654)2.212.412.763.153.613.893.98Women (N = 879)2.562.743.133.533.854.004.05

Diff (M-F)-0.35-0.34-0.37-0.38-0.24-0.12-0.07

2005-07 FreshmenGenderPercentiles for SNC SEM1 GPA5102550759095

1st Sem GPAMen (N = 654)1.501.852.332.883.383.753.88Women (N = 879)1.822.142.673.173.603.884.00

Diff (M-F)-0.32-0.29-0.34-0.29-0.22-0.13-0.12Gender Differences in both HSGPA and SNC SEM1 GPA shrink for above-average Freshmen5102550759095

HSGPA0.350.340.370.380.240.120.07SEM1 GPA0.320.290.340.290.220.130.12

&"Arial,Bold"&16 2005-2007 Freshmen&12Gender Differences in HSGPA and SNC SEM1 GPA, by Percentile Rank

2005-07 Freshman Men: Percent Retained to Sophomore Year, by GPA GPA Quintile