Using the Humble Crosstab

Report
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.

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