© Charles T. Diebold, Ph.D., 72313, 101813, 102014. All .docx

© Charles T. Diebold, Ph.D., 7/23/13, 10/18/13, 10/20/14. All
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Odds Ratio Tutorial:
RSCH-8250 Advanced Quantitative Reasoning
Charles T. Diebold, Ph.D.
July 23, 2013 (revised October 20, 2014)
How to cite this document:
Diebold, C. T. (2014, October 20). Odds ratio tutorial: RSCH-
8250 advanced quantitative reasoning. Available
from [email protected]
Table of Contents

Assignment and Tutorial Introduction
...............................................................................................
..................... 2
Section 1: SPSS Specification of the Assignment
...............................................................................................
... 2
Descriptive Statistics
...............................................................................................
............................................ 3
Binary Logistic Regression
...............................................................................................
.................................. 4
Section 2: Annotated Example SPSS Output, Write Up Guide,
and Sample APA Tables .................................... 6
...............................................................................................
............................................ 6
...............................................................................................
.................................. 7
Relationship between B and Exp(B)
...............................................................................................
................ 9
Odds Ratios Greater than 1.0
...............................................................................................
........................... 9

Common Error: Interpreting Odds Ratio as Risk Ratio (i.e., as
Probability) ............................................... 10
Results Write Up Guide
...............................................................................................
................................. 11
Example APA Table
...............................................................................................
...................................... 12
Odds Ratio Tutorial:
RSCH-8250 Advanced Quantitative Reasoning
Assignment and Tutorial Introduction
This tutorial is intended to assist RSCH-8250 students in
completing the Week 8 application assignment. I
recommend that you use this tutorial as your first line of
instruction; then, if you have time, view Dr.
Morrow’s video or capitalize on other resources noted in the
classroom.

3
rd
edition of Field textbook:
Chapter 8 in the Field textbook, Smart Alex's Task #2 on p. 314
(as modified below).
4
th
edition of Field textbook:
Chapter 19 in the Field textbook, Smart Alex's Task #5 on p.
812 (as modified below).
The exercise uses the Burnout.sav SPSS datafile. The objective
of the exercise is to conduct a 2-predictor binary
logistic regression focused on reporting and interpreting the
odds ratios (other key aspects of logistic regression
will be addressed in the Week 9 application).
DV: Burnout, 0 = not burnt out, 1 = burnt out
IV1: Cope, which is a metric measure of coping ability
IV2: Teaching, which is a metric measure of stress from
teaching

The tutorial contains two sections. Section 1 provides step-by-
step graphic user interface (GUI) screencaptures
for specifying the assignment in SPSS. If you follow the steps
you will produce correct SPSS output. Section 2
presents and interprets output for a different set of variables,
and includes a results write up guide, and sample
APA style table (the variables and data in Section 2 are “made
up” and do not reflect real research).
Section 1: SPSS Specification of the Assignment
Open the Burnout.sav datafile, the Variable View screencapture
is shown below. There are six variables in the
datafile, but we are only interested in the three variables
described above.
s.

The Frequencies dialogue box appears (below left). Select the
“burnout” variable, which is the dichotomous
dependent variable, and move into the Variable(s) box (below
right).
Click the OK button which will produce frequencies output with
count and percentage of those who were and
were not burnt out.
For the predictors, which are metric variables, we need some
basic descriptive statistics.
Go
as shown on preceding page, but selecting
Descriptives instead of Frequencies.
The Descriptives dialogue box appears (below left). Select the
two predictors—cope and teaching—and move
into the Variable(s) box (below right).

Click OK, which will produce output with minimum, maximum,
mean, and standard deviation for both
variables.
In the Logistic Regression
dialogue box, highlight and move
burnout to the Dependent box
(this is what we are trying to
predict), then highlight and move
both the cope variable and the
teaching variable to the
Covariates box, as shown at left.

Click the “Options” button.
In the Options dialogue click “CI
for exp(B)” and “Include constant
in model”.
When complete, it should look as
shown at left.
Click the Continue button, which
will return you to the main
dialogue. Clicking the OK in the
main dialogue will produce
output needed for this particular
assignment.

Section 2: Annotated Example SPSS Output, Write Up Guide,
and Sample APA Tables
The example output shown below uses variables different from
the Week 8 assignment. The purpose is to
explain key elements of the output, point out what to focus on,
and demonstrate how to interpret and report the
results in APA statistical style.
For the example, the variables are as follows:

DV: College, 0 = No, not planning to go to college, 1 = Yes,
planning to go to college
IV1: GPA, high school grade point average
IV2: PCT_Finance, the percent of college cost expecting to have
to finance with student loans
Reporting on the operationalization of each variable and the
observed values in the sample give the reader
insight into the variables being analyzed
As shown in the output (from the FREQUENCIES procedure in
SPSS), 116 (53.7%) of the 216 high school
seniors indicated they did not plan to go to college, and 100
(46.3%) said they were planning to go to college.
COLLEGE
Frequency Percent Valid Percent Cumulative
Percent
Valid
.00 No 116 53.7 53.7 53.7
1.00 Yes 100 46.3 46.3 100.0
Total 216 100.0 100.0

From the DESCRIPTIVES procedure output in SPSS, GPA
ranged from a minimum of 0 to a maximum of 4.0,
with a mean of 2.50 (SD = 0.91). The percent of college costs
that seniors estimated would have to be financed
by student loans ranged from 24.67% to 76.67%, with a mean of
52.85% (SD = 10.45).
N Minimum Maximum Mean Std. Deviation
GPA 216 .00 4.00 2.4954 .90988
PCT_Finance 216 24.67 76.67 52.8480 10.45221
Valid N (listwise) 216
Because the assignment this week is very limited in focus, most
of the logistic regression output can be ignored.
Below is a complete example of output as specified in Section 1

of this tutorial. You can ignore all but the very
last table in the output.
Case Processing Summary
Unweighted Cases
a
N Percent
Selected Cases
Included in Analysis 216 100.0
Missing Cases 0 .0
Total 216 100.0
Unselected Cases 0 .0
Total 216 100.0
a. If weight is in effect, see classification table for the total
number of cases.
Dependent Variable Encoding
Original Value Internal Value
.00 No 0
1.00 Yes 1

Block 0: Beginning Block
Classification Table
a,b
Observed Predicted
COLLEGE Percentage
Correct .00 No 1.00 Yes
Step 0
COLLEGE
.00 No 116 0 100.0
1.00 Yes 100 0 .0
Overall Percentage 53.7
a. Constant is included in the model.
b. The cut value is .500
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 0 Constant -.148 .136 1.183 1 .277 .862
Variables not in the Equation
Score df Sig.

Step 0
Variables
GPA 22.369 1 .000
PCT_Finance 24.161 1 .000
Overall Statistics 32.214 2 .000
Block 1: Method = Enter
Omnibus Tests of Model Coefficients
Chi-square df Sig.
Step 1
Step 34.600 2 .000
Block 34.600 2 .000
Model 34.600 2 .000
Model Summary
Step -2 Log likelihood Cox & Snell R

Square
Nagelkerke R
Square
1 263.653
a
.148 .198
a. Estimation terminated at iteration number 4 because
parameter
estimates changed by less than .001.
Classification Table
a
Observed Predicted
COLLEGE Percentage
Correct .00 No 1.00 Yes
Step 1
COLLEGE
.00 No 81 35 69.8
1.00 Yes 40 60 60.0
Overall Percentage 65.3
a. The cut value is .500

Below is the only part of the logistic output relevant for the
Week 8 assignment. It is copied on the next page
along with comments.
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B)
Lower Upper
Step 1
a
GPA .560 .190 8.676 1 .003 1.751 1.206 2.541
PCT_Finance -.052 .016 10.275 1 .001 .949 .919 .980
Constant 1.189 1.122 1.123 1 .289 3.285
a. Variable(s) entered on step 1: GPA, PCT_Finance.

B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B)
Lower Upper
Step 1
a
GPA .560 .190 8.676 1 .003 1.751 1.206 2.541
PCT_Finance -.052 .016 10.275 1 .001 .949 .919 .980
Constant 1.189 1.122 1.123 1 .289 3.285
a. Variable(s) entered on step 1: GPA, PCT_Finance.
Relationship between B and Exp(B)
The column labeled “Exp(B)” is the odds ratio. “Exp” is short
for exponentiation, and (B) refers to the values in
the column labeled “B”. That is, The values in the Exp(B) are
the exponentiation of the values in the B column.
To exponentiate a value is to raise “e” (≈ 2.7183) to the power
of that value.
For example, the B value for GPA is 0.560, so Exp(0.560) is e
0.560
or approximately 2.7183
0.560

. The calculation
can be done with a scientific calculator or in Excel by typing
the following into a cell: = EXP(0.56), which
returns the value 1.750673 that, rounded to 3 decimal places,
matches the 1.751 in the output.
Calculations can also be made from the odds ratio back to the B
value by taking the natural log (ln) of the odds
ratio. For example, the natural log of 0.949 = -0.05235, in Excel
type the formula: = ln(0.949).
Odds Ratios Greater than 1.0
The odds ratio, or Exp(B) value, relates to membership in the
level of the dichotomous dependent variable that
was coded 1 (the other being coded 0). An odds value of 1.0
means equal odds of being in either group. Odds
values greater than 1.0 reflect higher odds for being in the
group coded 1. For example, holding percent of
college costs to be financed constant, for a one point increase in
GPA (from 0 to 1) the odds of being in the
planning to go to college group is 1.751 that of being in the not
planning to go to college group. Said another
way, for a one point increase in GPA the odds of being in the

going to college group are 1.751-to-1; or, yet
another way, for a one point increase in GPA the odds of being
in the going to college group are 75.1% greater
than the odds of being in the not going to college group.
Odds Ratios Less than 1.0
A metric predictor with an odds ratio < 1.0 indicates a negative,
or inverse, relationship between scores on that
variable and membership in the group coded 1. For example, for
a one point increase in PCT_Finance from 0 to
1 (GPA held constant), the odds of being in the planning to go
to college group are 0.949 the odds of being in
the not going to college group; or, said another way, the odds
are 0.949-to-1 of being in the planning to go to
college group; or, yet another way, for a one point increase in
PCT_Finance (GPA held constant) the odds of
being in the planning to go to college group decrease by 5.1%
(i.e., the odds are multiplied by 0.949, which is
.051, or 5.1%, less than 1.0).
Nonlinear Nature of Logistic Regression
In multiple linear regression it was demonstrated that if a

variable, say IQ, had an unstandardized B coefficient
of 0.05 with respect to GPA, it was not only the case that for a
one point increase in IQ, GPA was expected to
increase by 0.05 points, it was also true that for a 10 point
increase in IQ, GPA was expected to increase 0.5
points (i.e., 10 x 0.05 = 0.5). That is, you could just multiply
the B coefficient by the number of increased points
on the predictor to obtain the expected increase in the criterion.
This does not work in logistic regression because logistic
regression is not linear. Figure 1 displays the
nonlinear nature of logistic regression. Along the X-axis are
increasing values of B, and the Y-axis is the
exponentiation of those B values. Larger B values have steeper
slopes than smaller B values.
Mathematically, a two point increase would result in an odds
ratio of e
2B
. For example, if GPA increases 2
points, the odds are not 2 x 1.751 = 3.502, but e

2(0.56)
= e
1.1
= 3.065.
Logistic is Nonlinear
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.41 0.45 0.49
0.53 0.58 0.62 0.66 0.71 0.75 0.80 0.85 0.90 0.94 0.99
O
d
d

s
R
a
ti
o
:
E
x
p
(B
)
B
Figure 1. Odds ratios do not increase linearly (in a straight line)
across B values, but get exponentially steeper
with increasing values of B.
Common Error: Interpreting Odds Ratio as Risk Ratio (i.e., as
Probability)
A common error, and one that Dr. Morrow makes in the video,
is to interpret the odds ratio as relative risk, that
is, as “times more likely’, such as for a one point increase in

GPA you are 1.751 times more likely to be in the
going to college group. Do not make this same error in your
results write up.
Relative risk (or times more likely), is a ratio of probabilities,
not a ratio of odds. A simple example will
demonstrate the difference. Suppose 6 out of every 10 males
who apply to medical school are accepted, and that
3 out of every 10 females who apply are accepted. So, it should
be clear that twice as many males (6) are
accepted than females (3); or, said another way: males are 2
times more likely to be accepted than females.
Let’s do some simple math:
The probability that a male is accepted = 6 ÷ 10 = .6. This also
means that the probability of a male not being
accepted = 4 ÷ 10 = .4; or, equivalently, 1 – probability of
acceptance = 1 - .6 = .4.
For females, the probability of acceptance = 3 ÷ 10 = .3, and the

probability of not being accepted = 7 ÷ 10 = .7;
or, equivalently, 1 – probability of acceptance = 1 - .3 = .7.
Odds =
Pr1
Pr
. That is, odds are the probability of occurrence divided by the
probability of nonoccurrence.
So, the odds for male acceptance = .6 ÷ .4 = 1.5. The odds for
female acceptance = .3 ÷ .7 = .4286.
The odds ratio of male acceptance to female acceptance = 1.5 ÷
.4286 = 3.5.
However, as was originally clear, the probability ratio of male
acceptance to female acceptance = .6 ÷ .3 = 2.0.
So, it is incorrect to interpret the odds ratio of 3.5 as meaning
that males were 3.5 times more likely than
females to be accepted. Male odds of acceptance (1.5) were 3.5
times that of female odds of acceptance (.4286),
but it should be clear now that is not the same thing as how
many times more likely males were than females to

be accepted.
Results Write Up Guide
The write up for Week 8 is very limited (about 3 brief
paragraphs will suffice). Begin the write up by describing
the context of the research and the variables. If known, state
how each variable was operationalized, for
example: “Overall GPA was measured on the traditional 4-point
scale from 0 (F) to 4 (A)”, or “Satisfaction was
measured on a 5-point likert-type scale from 1 (not at all
satisfied) to 5 (extremely satisfied).” Please pay
attention to APA style for reporting scale anchors (see p. 91 and
p. 105 in the 6
th
edition of the APA Manual).
Report descriptive statistics such as minimum, maximum, mean,
and standard deviation for each metric
variable. For nominal variables, report percentage for each level
of the variable, for example: “Of the total
sample (N = 150) there were 40 (26.7%) males and 110 (73.3%)
females.” Keep in mind that a sentence that
includes information in parentheticals must still be a sentence

(and make sense) if the parentheticals are
removed. For example: “Of the total sample there were 40 males
and 110 females.”
State the purpose of the analysis or provide the guiding research
question(s). If you use research questions, do
not craft them such that they can be answered with a yes or no.
Instead, craft them so that they will have a
quantitative answer. For example: “What is the strength and
direction of relationship between X and Y?” or
“What is the difference in group means on X between males and
females?” or “What are the odds ratios for
variable X1 and variable X2 in predicting Y while holding each
other constant?”
For Week 8 there are no required null and alternative
hypotheses because you are not required to examine and
interpret the statistical significance of the predictors (for rubric
purposes, stating a clear purpose or research
question will suffice).

For Week 8 there are no assumptions or other conditions for
which statistical tests need to be reported. Just
make a general summary statement about the issues Field lists
on p. 273 in the 3
rd
edition and pp. 768-769 in the
4
th
edition.
Report and interpret the odds ratios for each predictor.
Provide APA style tables appropriate to the analysis. Do not use
SPSS output, it is not in APA style. An
example APA table for Week 8 is shown in the next section
using the results from the example output in this
tutorial. Although one would typically not duplicate information
in text and tables, it is important to
demonstrate competence in both ways of reporting the results;
so, you cannot just provide tables, you must also
report the relevant statistical results within the textual write up.
Example APA Table

Table 1
Logistic Regression Predicting Planning to Go to College (N =
216)
Predictor B SEB p OR 95% CI
GPA .560 .190 .003 1.751 [1.206, 2.541]
% College Costs Financed -.052 .016 .001 0.949 [0.919, 0.980]
Note. CI = confidence interval for odds ratio (OR).
The Week 8 SPSS Assignment
4th edition of Field textbook:
Chapter 19 in the Field textbook, Smart Alex's Task #5 on p.
812 (as modified below).
The exercise uses the Burnout.sav SPSS datafile. The objective
of the exercise is to conduct a 2-predictor binary logistic
regression focused on reporting and interpreting the odds ratios
(other key aspects of logistic regression will be addressed in the
Week 9 application).
DV: Burnout, 0 = not burnt out, 1 = burnt out
IV1: Cope, which is a metric measure of coping ability
IV2: Teaching, which is a metric measure of stress from
teaching
The tutorial includes step-by-step SPSS screenshots to produce
the needed output, annotated example output (including
discussion of a common odds ratio interpretation error that even

Dr. Morrow commits in the video), write up guide, and sample
APA table (the APA table is a required element of the Week 8
assignment). If you follow the steps in the tutorial you will
produce correct SPSS output.
IMPORTANT: Results Write Up Guide
The write up for Week 8 is very limited (about 3 brief
paragraphs will suffice). Begin the write up by describing the
context of the research and the variables. If known, state how
each variable was operationalized, for example: “Overall GPA
was measured on the traditional 4-point scale from 0 (F) to 4
(A)”, or “Satisfaction was measured on a 5-point likert-type
scale from 1 (not at all satisfied) to 5 (extremely satisfied).”
Please pay attention to APA style for reporting scale anchors
(see p. 91 and p. 105 in the 6th edition of the APA Manual).
Report descriptive statistics such as minimum, maximum, mean,
and standard deviation for each metric variable. For nominal
variables, report percentage for each level of the variable, for
example: “Of the total sample (N = 150) there were 40 (26.7%)
males and 110 (73.3%) females.” Keep in mind that a sentence
that includes information in parentheticals must still be a
sentence (and make sense) if the parentheticals are removed.
For example: “Of the total sample there were 40 males and 110
females.”
State the purpose of the analysis or provide the guiding research
question(s). If you use research questions, do not craft them
such that they can be answered with a yes or no. Instead, craft
them so that they will have a quantitative answer. For example:
“What is the strength and direction of relationship between X
and Y?” or “What is the difference in group means on X
between males and females?” or “What are the odds ratios for
variable X1 and variable X2 in predicting Y while holding each
other constant?”
For Week 8 there are no required null and alternative
hypotheses because you are not required to examine and
interpret the statistical significance of the predictors (for rubric

purposes, stating a clear purpose or research question will
suffice).
For Week 8 there are no assumptions or other conditions for
which statistical tests need to be reported. Just make a general
summary statement about the issues Field lists on pp. 768-769
in the 4th edition.
Report and interpret the odds ratios for each predictor.
Provide APA style tables appropriate to the analysis. Do not use
SPSS output, it is not in APA style. An example APA table is
shown below. Although one would typically not duplicate
information in text and tables, it is important to demonstrate
competence in both ways of reporting the results; so, you cannot
just provide tables, you must also report the relevant statistical
results within the textual write up.
Week 8 Application Rubric
In a previous announcement I posted the generic rubric that will
be used for SPSS application assignments. Below is that rubric
with breakout of points for odds ratio. A complete and thorough
write up is required even if a statistical assumption is violated
or results are statistically nonsignificant.
Week 8: Odds Ratio
50-pt Weight
Graded Elements
4
purpose or research question
3
general statement about statistical assumptions
5
results: descriptives
20
results: odds ratio each predictor
5
APA style results write up

5
APA table(s)
8
spss syntax and output
50

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