1.
SPSS INSTRUCTION – CHAPTER 8
SPSS provides rather straightforward output for regression and correlation analysis. The
program’s graph, regression, and correlation functions can respectively produce
scatterplots, provide regression equation coefficients, and create correlation matrices.
Within the outputs for these functions, you can also find information, such as coefficients of
determination and significance values.
Preparing Regression and Correlation Analysis Data in SPSS
The first step in performing regression and correlation analyses in SPSS is, of course,
inputting data into the program. Each variable should receive its own column on SPSS’s
Data View screen. With this arrangement, each subject’s independent and dependent
variable scores should fall into the same row.
Example 8.25 – SPSS Data View Screen for Regression and Correlation Analysis
For a simple example, consider the five-subject sample introduced in Example 8.5 (selected
for this example due to the small sample size, which allows the entire data set to be shown
easily). Figure 8.19presents the data from this example as it would look in the SPSS Data
View screen .
FIGURE 8.19– SPSS REGRESSION AND CORRELATION ANALYSIS DATA ARRANGEMENT
Data for the independent variable appears on the left and data for the dependent variable appears on the
right. However, the variables do not need to appear in this order because, in forthcoming steps, SPSS asks the
user to identify the independent and the dependent variable by name. ▄
If your analysis involves more than two variables, you can simply include additional
columns. In the commands that you provide to SPSS about the analysis that you wish to
perform, you must specify which of these columns you wish to represent independent
variables, dependent variables, and intervening variables.
Creating Scatterplots in SPSS
2.
Basic scatterplots are most easily created through SPSS’s Graphs function. SPSS
instructions forChapter 2 and Chapter 3 explain how to use this function to create bar
graphs, pie charts, and frequency histograms. The process for creating scatterplots in SPSS
begins the same way.
1. From the pull-down menu under the Graphs option at the top of the data view or
variable view screen, select “Legacy Dialogues.” A listing of graphs and charts available
through this method should appear.
2. Select “Scatter/Dot.” A window entitled Scatter/Dot should appear. The Scatter/Dot
window contains various options for the graph. A two-variable situation requires a
Simple Scatter. A three-variable situation, such as that described in Section 8.3.1,
requires a 3-D Scatter. After selecting the name of the appropriate scatterplot, click
“Define.”
a. For a simple scatterplot, a new window, entitled Simple Scatterplot should appear.
FIGURE 8.20 – SPSS SIMPLE SCATTERPLOT WINDOW
The user creates two-variable scatterplot by identifying the independent (X) and dependent (Y)
variables from those listed on the left side of the window. To do so, highlight the name of each
variable and click on the arrow next to the box labeled with the appropriate axis name.
Identify the independent variable by moving its name from the box on the left to the
box labeled “X Axis.” Identify the dependent variable by moving its name from the
box on the left to the box labeled “Y Axis.”
b. For a 3-D scatterplot, a new window, entitled, 3-D Scatterplot should appear.
3.
FIGURE 8.21 – SPSS 3-D SCATTERPLOT WINDOW
The user creates three-variable scatterplot by identifying the two independent variables and the
dependent variable from those listed on the left side of the window. To do so, highlight the name of
each variable and click on the arrow next to the box labeled with the appropriate axis name.
Move the names of each of the two independent variables and the dependent
variable from the box on the left to a box on the right marked for one of the axis. The
assignment of the three variables to the X, Y, and Z axis on the graph depends upon
the user’s intentions and preference for the graph’s appearance.
3. Click OK.
Example 8.26 – Simple Scatterplot in SPSS
The steps for producing a simple scatterplot can be applied to the examples from Section
8.2.1. The following graph results from moving the name of the independent variable,
students, to the box labeled, “X Axis,” and moving the name of the dependent variable,
“hedgers,” to the box labeled “Y Axis.”
4.
FIGURE 8.22 – SPSS SIMPLE SCATTERPLOT OUTPUT
The scale for independent-variable scores lies along the X axis and the scale for dependent-variable scores
lies along the Y axis. Each point represents a particular independent and dependent variable score.
This particular scatterplot indicates that, as class size increases, teachers’ use of hedgers
tends to increase. Thus, it suggests a positively-sloped regression line. ▄
The basic SPSS scatterplot does not show the regression line. If you would like the graph to
include this line, you must use SPSS’s Chart Editor. To access the Chart Editor, you must
double click on the scatterplot.
The Chart Editor refers to the least-squares regression line as a fit line. The pull-down
menu for the Elements function in the Chart Editor contains a “Fit Line at Total” option.
(Often, the lowest menu bar in the Chart Editor also contains a shortcut icon for this
process.) Selecting this option begins the process for overlaying the regression line onto
the existing scatterplot.
1. From the “Elements” pull-down menu in the Chart Editor, select “Fit Line at Total.”
2. A new window entitled Properties should appear.
5.
FIGURE 8.23 – SPSS CHART EDITOR PROPERTIES WINDOW
The choice of a fit method determines the line or curve that SPSS superimposes on the scatterplot. Simple
analyses may require only a horizontal line to visually indicate the mean of all Y values. A linear fit
produces a least-squares regression line. Loess, quadratic, and cubic fits refer to curvilinear relationships.
Select the appropriate Fit Method from the options provided. Most analyses require a
linear fit. However, if you wish to investigate a possible curvilinear relationship, you
may wish to request a cubic, quadratic, or loess fit.
3. Click CLOSE.
Example 8.27 – Regression Line in SPSS
Figure 8.23 shows the scatterplot in Figure 8.22 with an added regression line, obtained by
requesting a linear fit within the Chart Editor window. As expected, the line has a positive
slope.
6.
FIGURE 8.24 – SPSS SIMPLE SCATTERPLOT WITH REGRESSION LINE OUTPUT
The regression line indicates the general linear trend of points. This particular line is the one that SPSS
identifies as producing the smallest sum of squared residuals for all points on the scatterplot.
In this case, the points may fit a curvilinear path, particularly a cubic curve, slightly better
than they fit a linear path. Requesting a cubic fit in the Chart Editor window produces
Figure 8.26.
7.
FIGURE 8.26 – SPSS SIMPLE SCATTERPLOT WITH CUBIC CURVE OUTPUT
The curve that appears in Figure 8.26 indicates the general cubic trend of points. This particular cubic curve
is the one SPSS identifies as producing the smallest sum of squared residuals for all points on the scatterplot.
This curve does, in fact, seem to fit the data better than Figure 8.25’s line does. The
researcher may, therefore, which to characterize the relationship between the number of
students in a class and the number of hedgers used per hour by the teacher as curvilinear.
▄
Example 8.28 – 3-D Scatterplot in SPSS
A three-dimensional scatterplot can represent the two variables from Example 8.26 and
Example 8.27 along with the questions/hour variable used to demonstrate calculation of
the multiple correlation coefficient in Example 8.13 In Example 8.13, x corresponds to the
number of students in a particular class, y corresponds to the number of hedgers used per
hour by the teacher, and z corresponds to the number of student questions per hour.
Assigning these three variables to the appropriate axes in the 3-D Scatterplot window
produces the following scatterplot.
FIGURE 8.25 – SPSS 3-D SCATTERPLOT OUTPUT
Scales for the two independent variables appear along the X axis and the Y axis. The scale for the dependent
variable appears along the Z axis. The researcher, however, can assign the variables to the axes that suit his or
her purposes. Each point represents a particular subject’s scores for the two independent variables and the
dependent variable.
8.
The points on this scatterplot seem to float in space. Actually, though, each point is situated
at the intersection of the planes representing the enrollment for a particular class, the
number of hedgers used per hour by the teacher of that class and the number of questions
asked per hour by students in the class. ▄
You should know that methods of creating a scatterplot in SPSS other than “Legacy
Dialogues” option exist. The “Chart Builder” function within the “Graph” menu, for
instance, also leads you through steps that produce a scatterplot. With the Chart Builder,
you gain some more control over the appearance and components of the scatterplot than
you have when using Legacy Dialogues. However, when comparing the two methods, the
process needed to use the Chart Builder is a bit more complicated.
If you need to create a scatterplot that uses data points other than raw values you may wish
to use a different approach. SPSS’s regression analysis function allows you to create such
scatterplots. By clicking on the window’s “plots” button, you can access a new, entitled,
Linear Regression: Plots, which allows you to specify scales based upon standardized
values, residuals, and predicted values. This function generally has the most value for
somewhat advanced analyses.
Regression Analysis in SPSS
With the exception of the scatterplot, itself, you can obtain all pairwise regression and
correlation values by using SPSS’s “Regression” function. Output from the following steps
includes regression equation coefficients, r, and r2.
1. Select “Regression” from SPSS’s Analyze pull-down menu and then, assuming a linear
regression is desired, select the “Linear” option.
2. A window entitled Linear Regression should appear. A box in the upper left of the
window contains the names of all variables.
9.
FIGURE 8.26 – SPSS LINEAR REGRESSION WINDOW
The user obtains regression values by identifying the independent variable(s) and the dependent variable
from those listed on the left side of the window. To do so, highlight the name of the variable and click on
the arrow next to the appropriate box.
Move the names of the independent and dependent variables to the properly-labeled
boxes on the right. If the user moves the name of only one variable the box labeled
“independent variable(s)”, SPSS performs a bivariate regression analysis. If the names
of more than one variable are moved to the “independent variable(s) box, SPSS
performs a multiple regression analysis.
3. Click OK
Four output tables result. The first of these tables simply identifies the variables used for
the analysis. The other three tables provide the information that you need to assess the
relationship between the independent and dependent variables. You can find the
correlation coefficient and the coefficient of determination in the Model Summary table and
coefficients for the regression equation in the Coefficients table’s column “B.” SPSS refers
to the y-intercept as the constant and lists each slope next to its corresponding variable’s
name.
The other table included in SPSS output provides ANOVA results. As explained in Section
8.6, some statisticians supplement regression and correlation analysis with an ANOVA.
Although a regression and correlation analysis addresses the trend in changes between
independent and dependent variable scores, it does not measure the sizes of differences
between scores on either factor. So, even if a trend exists, differences in dependent-variable
scores associated with changes in independent-variable scores may be so miniscule that
the trend becomes negligible. Those concerned about this issue may use an ANOVA
10.
determine whether significant differences exist between dependent-variable scores. When
conducting an ANOVA in this circumstance, SPSS regards the independent variable as a
categorical measure. Each independent-variable score, thus, defines a separate category,
often resulting in categories that contain only one subject. Then, the ANOVA compares the
dependent-variable score that corresponds to each independent-variable category. You can
interpret the results of this test just as you would interpret the results of any ANOVA.
(Please see Chapter 7 for information about ANOVAs.)
Example 8.29 – SPSS Regression Output
To further understand how to locate and interpret relevant regression and correlation
coefficients, consider the four output tables as they apply to the bivariate situation used for
Example 8.26 and Example 8.27.
Variables Entered/Removedb
Variables
Entered
Model
1
Variables
Removed
Method
studentsa
. Enter
a. All requested variables entered.
b. Dependent Variable: hedgers
Model Summary
Adjusted R
Model
1
R
Std. Error of the
Square
Estimate
R Square
.703a
.494
.481
2.59045
a. Predictors: (Constant), students
ANOVAb
Sum of
Model
1
Squares
df
Mean Square
Regression
249.405
1
249.405
Residual
254.995
38
6.710
Total
504.400
39
a. Predictors: (Constant), students
b. Dependent Variable: hedgers
F
37.167
Sig.
.000a
11.
Coefficientsa
Unstandardized
Coefficients
Model
1
Standardized
Coefficients
B
(Constant)
Std. Error
1.017
.017
T
.799
.101
Beta
Students
Sig.
1.272
.703
.211
6.096
.000
a. Dependent Variable: hedgers
TABLE 8.9, TABLE 8.10, TABLE 8.11, AND TABLE 8.12 – SPSS LINEAR REGRESSION OUTPUT
SPSS output for the linear regression command includes four tables. Table 8.9, entitled “Variables
Entered/Removed,” indicates the independent variables and footnotes the name of the dependent variable.
Table 8.10, Table 11, and Table 8.12 provide information about the changes in variable scores. The
correlation coefficient (r) and the coefficient of determination (r2) found in the Model Summary, indicate the
strength of the linear trend between the variables. The significance value in the ANOVA table, when compared
to a predetermined α, indicates whether changes in dependent- variable scores that accompany changes in
independent variable scores are significant. Finally, the Coefficients table provides the y-intercept and the
slope for the regression equation.
The correlation coefficient of .703, from Table 8.10, suggests that the number of students in
a class and number of hedgers used per hour by the teacher have a strong (although barely
so) linear relationship. For those who do not wish to square the correlation coefficient
themselves, this table also includes the coefficient of determination, which indicates that
differences in the number of student in the class can explain 49.4% of differences in
teachers’ use of hedgers. Further, the ANOVA produces a p-value of .000, which, obviously,
lies below all α values. So, one could conclude that the number of hedgers used by teachers
per hour changes significantly with respect to in the number of students in the class. The
regression equation helps to further describe this change. Using the regression equation of
y = 1.017 + .101x, obtained from value in Table 8.12, one can the dependent-variable score
for each independent-variable score. Each x value substituted into the equation and the y
value that results provides an ordered pair that falls on the regression line. This process
produces a best guess for the number of hedgers used based upon class size. ▄
If you input more than one variable name into the Linear Regression window’s
“Independent Variable(s)” box, output looks similar to that shown in Example 8.29. In this
case, however, the Model Summary provides the multiple correlation coefficient and the
coefficient of multiple determination. Also, the “B” column in the Coefficients table includes
a slope for each independent variable.
Correlation Matrices in SPSS
12.
You may not always want to obtain all of the information provided by SPSS’s regression
analysis. In some situations, correlation coefficients, alone, suffice. The Correlate function
can not only provide these values without unneeded regression output, but can also display
coefficients for more than one pair of variables at a time and can compute partial
correlation coefficients. Coefficients appear in a correlation matrix. The following steps
produce this output.
1. Select “Correlate” from SPSS’s Analyze pull-down menu. Then, indicate whether SPSS
should calculate bivariate (pairwise) or partial correlation coefficients.
2. a. For a bivariate analysis, a new window entitled Bivariate Correlations, should
appear.
FIGURE 8.27 – SPSS BIVARIATE CORRELATIONS WINDOW
SPSS calculates correlation coefficients between each pair of variables with names appearing in the
box labeled “Variables.” The user should move the name of each variable involved in the analysis
from the box on the left of the window by highlighting the name of the variable and clicking on the
arrow to the left of the “Variables” box.
Move the name of all variables that you would like to analyze from the list of
variables on the left of the window to the box labeled “Variables.” The “Variables”
box can contain as many variable names as needed. SPSS will calculate the pairwise
correlation coefficient between each pair of variables listed. For instance, if the
names of variables “x”, “y”, and “z” appear in the “Variable” box, SPSS calculates rXY,
rXZ, and rYZ.
b. For partial correlations, a new window entitled, Partial Correlations, should appear.
13.
FIGURE 8.28 – SPSS PARTIAL CORRELATIONS WINDOW
SPSS calculates correlation coefficients between each pair of variables with names appearing in the
box labeled “Variables,” while removing the effects of any variables with names appearing in the box
labeled “Controlling for.” The user should move the name of each variable involved in the analysis
from the box on the left of the window by highlighting the name of the variable and clicking on the
arrow to the left of the appropriate box.
The names of intervening variables should be moved from the list of variable son
the left of the window to the box labeled “Controlling for.” Move the name of the
variables involved in the correlation, itself, to the box labeled “Variables.”
The “Variables” box can contain as many variable names as needed. SPSS will
calculate the correlation coefficient between each pair of variables listed while
holding steady the influence of the variable(s) appearing in the “Controlling for” box.
3. Click OK.
SPSS assigns each variable for which you requested a correlation to a row and column of
the resulting correlation matrix. The coefficient for a particular linear relationship appears
at the intersection of each relevant row and column, as shown in Table 8.13, based upon an
analysis involving four variables, W, X, Y, and Z.
W
X
Y
Z
W
rWW
rXW
rYW
rZW
X
rWX
RXX
rYX
rZX
Y
rWY
rXY
rYY
rZY
Z
rWZ
rXZ
rYZ
rZZ
TABLE 8.13 - BASIC CORRELATION MATRIX
The interior portion of the table contains correlation coefficients for all pairs of variables. Values along the
diagonal, which represent associations between each variable and itself, equal +1.00. This diagonal also
serves as a line of symmetry because rWX = rXW, rWY =rYW, etc.
14.
SPSS’s correlation matrix contains correlation coefficients as well as significance values and
sample sizes for the data used to analyze each pair of variables.
In some cases, your analysis may focus entirely upon these pairwise correlation
coefficients. Often, though, obtain these values is just the first step in a multiple regression
or correlation analysis.
Example 8.30 – SPSS Correlation Matrix
One may wish to begin an investigation into the relationship between class size, the
number of hedgers used per hour by a teacher, and the number of questions asked per hour
by students by considering pairwise correlation coefficients. These values appear in Table
8.14.
Correlations
Students
students
Pearson Correlation
1.000
hedgers
Pearson Correlation
Sig. (2-tailed)
N
questions
Pearson Correlation
Sig. (2-tailed)
N
questions
.703**
.592**
.000
.000
40
40
40
.703**
1.000
.495**
Sig. (2-tailed)
N
Hedgers
.000
.001
40
40
40
.592**
.495**
1.000
.000
.001
40
40
40
TABLE 8.14 - SPSS PAIRWISE CORRELATION MATRIX
The correlation coefficient for each pair of variables appears at the intersection of one variable’s row and the
other variable’s column. Each variable correlates perfectly with itself, as evidenced by the coefficients of
+1.00 at the intersection of a particular variables’ row and column.
The number of students in a class correlates strongly with the number of hedgers used per
hour by the teacher of that class (rXY = +.703). A moderate correlation exists between the
number or students in a class and the number of questions asked per hour by students (rXZ
= +.592) as well as between the number of questions asked per hour by students and the
number of hedgers used per hour by the teacher (rYZ = +.495). The fact that all of these
correlation coefficients have positive values indicates that increases in one variable
correspond to increases in the other. ▄
15.
A table similar to Table 8.14 emerges from SPSS when you request partial correlation
coefficients. In this case, SPSS informs the user that it has held constant the impact of
intervening variables by including their names under a “control variable” heading in the
output.
Example 8.31 – SPSS Partial Correlation Matrix
Table 8.15 shows the SPPS results comparable to the calculations in Example 8.16. The
correlation matrix values describe the relationship between the number of questions asked
per hour by students and the number of hedgers used per hour by the teacher researcher
asks SPSS, independent of any influence of the percentage of factual information in course
material.
Correlations
Control Variables
factualinfo
students
students
1.000
.628
Significance (2-tailed)
.
.372
Df
0
2
Correlation
.628
1.000
Significance (2-tailed)
hedgers
Correlation
Hedgers
.372
.
2
0
Df
TABLE 8.15 - SPSS PARTIAL CORRELATION MATRIX
By listing “factualinfo” as a control variable on the left side of the table, SPSS reminds the user that it removed
any influence that the percentage of factual information in a course has upon the number of students in the
class and the number of hedgers used per hour by the teacher.
Because it plays the role of an intervening variable, “factual” is identified as a control
variable in Table 8.15 rather than appearing as part of the main correlation matrix. The
resulting partial correlation coefficient of +.628 also emerged from the calculations in
Example 8.16. This value indicates a moderate tendency for the number of hedgers used by
the teacher to increase as class enrollment increases when discounting the effects of the
intervening variable upon both of the other two variables. ▄
The “Linear Regression” box provides another method for obtaining partial correlations.
Although this method only displays one partial correlation coefficient at a time, it also
provides part correlation coefficients, which you cannot obtain in matrix form. If you need
16.
to include part correlation coefficients in your analysis, therefore, you may prefer following
procedure.
1. Select “Regression” from SPSS’s Analyze pull-down menu. Then, select the “Linear”
option.
2. A window entitled Linear Regression should appear. Follow the procedure described
earlier in this document for identifying the independent variable(s) and dependent
variable for the analysis. However, include the intervening variable(s) among those on
the independent variable list. Be sure to remember which of the variables is the true
independent variable and which are intervening variables.
3. Click on the button marked, “Statistics,” on the right of the Linear Regression window. A
new window, entitled, Linear Regression: Statistics should appear.
FIGURE 8.29 – LINEAR REGRESSION: STATISTICS WINDOW
The prompt for part and partial correlations can be found in this window. With this option selected, SPSS
calculates correlation coefficients between one independent variable and the dependent variable,
independent of all other independent variables identified in the Linear Regression window.
4. Mark the box labeled “Part and partial correlations,” located on the right side of the
window. Doing so tells SPSS to calculate the correlation between the dependent
variable and each independent variable while holding constant the effects of all other
independent variables.
5. Click “Continue” to return to the Linear Regression window.
6. Click OK.
The partial and part correlation coefficients appear in the output’s “Coefficients” table,
under the heading “Correlations.”
17.
Example 8.32 – SPSS Part and Partial Correlation Output
Table 8.16 includes the partial correlation coefficient first presented in Example 8.31 as
well as the comparable part correlation coefficient.
Coefficients
Unstandardized
Model
1
Standardized
Coefficients
Coefficients
B
(Constant)
a
Std. Error
5.145
.152
.133
factualinfo
.000
.181
T
15.399
students
Beta
Correlations
Sig.
Zero-order
Partial
Part
.334
.770
.771
1.142
.372
.773
.628
.512
-.003
-.004
.997
-.580
-.003
-.002
a. Dependent Variable: hedgers
TABLE 8.16 – SPSS COEFFICIENTS TABLE WITH PARTIAL AND PART CORRELATIONS
Partial and part correlation coefficients appear on the far right of the table. The values in the row labeled,
“students” pertain to the relationship between the number of students in the course and the number of
hedgers used per hour by the teacher independent of the amount of factual information in the course. The
table also provides coefficients for the multiple regression equation that uses the number of students and the
percentage of factual information in a course to predict the number of hedgers used per hour by the teacher.
Not surprisingly, Table 8.16 and the correlation matrix in Example 8.32 both identify the
partial correlation as +.628. One would rely upon Table 8.16, however, to learn the part
correlation coefficient. This value, +.512, describes the linear relationship between the
number of student in a class and the number of hedgers used by the teacher, independent
of any effect that the amount of factual information in the class has upon the former. This
value lies below both the pairwise and the partial correlation coefficients, but still
characterizes the relationship as moderately strong. ▄
Phi Analysis in SPSS
The request for a phi coefficient in SPSS takes place within the Crosstabulations context. To
access this window and to instruct SPSS to include the phi-coefficient along with its
crosstabulation output, you should use the following steps.
1. Select “Descriptive Statistics” from SPSS’s Analyze pull-down menu.
2. A new menu, containing a “Crosstabs” option appears. Select this option.
3. A Crosstabs window should appear.
18.
FIGURE 8.30 – SPSS CROSSTABS WINDOW
The user should move the name of one variable from the box on the left of the window to the box labeled
“Row(s)” and the name of another variable from the box on the left to the box labeled “Colunm(s).”
Highlighting the name of the variable and clicking on the arrow to the left of the “Row(s)” or “Column(s)”
box moves the variable name to the appropriate place.
Move the name of one variable involved in the analysis from the list on the left of the
window to the “Row(s)” box. Move the name of the other variable involved in the
analysis from the list on the left of the window to the “Column(s)” box.
4. Click the “Statistics” button, located on the right of the window. A new window entitled
Crosstabs: Statistics should appear.
FIGURE 8.31 – SPSS CROSSTABS:STATISTICS WINDOW
19.
The user instructs SPSS to include in its crosstabulation output by selecting the “Phi and Cramer’s V”
option in the Crosstabs: Statitistics Window. The resulting value describes the trend in frequencies for
categories of the variables in the crosstabulation.
Click on the open box next to the “Phi and Cramer’s V” listing. Be sure that this box
contains a check mark.
5. Click the “Continue” button at the bottom of the page. You should return to the
Crosstabs window.
6. Click OK.
The output that results from these steps consists of a crosstabulation table (discussed in
Chatper 2) and a Symmetric Measures table. The second of these contains the phi
coefficient.
Example 8.33 – SPSS Crosstabulation Output Including Symmetric Measures
The output for a crosstabulation and phi analysis involving the student enrollment
categories and the hedger use categories introduced in Section 8.4 of the chapter appears
as follows.
Case Processing Summary
Cases
Valid
N
studcats * hedgecats
Missing
Percent
40
N
Total
Percent
100.0%
0
N
.0%
Percent
40
studcats * hedgecats Crosstabulation
Count
hedgecats
less than 5
Studcats
fewer than 30
Total
13
2
15
4
21
25
17
30 or more
Total
5 or more
23
40
Symmetric Measures
Value
Approx. Sig.
100.0%
20.
Nominal by Nominal
Phi
.692
.000
Cramer's V
.692
.000
N of Valid Cases
40
TABLE 8.17, TABLE 8.18, and TABLE 8.19 – SPSS CROSSTABULATION AND PHI COEFFICIENT OUTPUT
Table 8.6 and 8.7 are part of SPSS’s standard crosstabulation output. The value of that appears in the
Symmetric Measures table indicates the strength of the trend in frequencies of classes that fall into the two
enrollment and the two hedgers categories.
Table 8.19’s phi coefficient of +.692 indicates a moderate (close to strong) trend of larger
values in the upper left and lower right cells than in the other two cells of the Table 8.18’s
crosstabulation. ▄
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