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**Using SPSS for Windows (Version 25.0)**

This document contains instructions on using
SPSS to perform various statistical analyses.
The list of section and subsection titles is as follows:

I. Data Entry and Manipulation

IMPORTANT
NOTES

(1)
Defining Variables

(2)
Creating New Variables with Transformation of Existing Variables

(3)
Creating New Variables with Recoding of Existing Variables

II. Data Diagnostics, Graphical Displays, and
Descriptive Statistics

IMPORTANT
NOTES

(1)
Checking Data Ranges, Summary Statistics, and Missing Values

(2)
Checking for Skewness and Non-Normality

(3)
Creating Graphical Displays and Obtaining Descriptive Statistics

III. Statistical Analysis Involving One
Variable

(1)
Performing a One sample *t* Test about
a Mean m

(2)
Performing a Chi-square Goodness-of-Fit Test with Hypothesized Proportions

IV. Statistical Analysis Involving Two
Variables

(1)
Generating a Correlation Matrix with *p*-values

(2)
Performing a Paired Sample *t* Test
about a Mean Difference m* _{d}* (i.e., a difference between means from dependent
samples) or a Wilcoxon Signed Rank Test

(3)
Performing a Two Sample *t* Test about
a Difference Between Means m_{1} and m_{2} or a
Mann-Whitney Rank Sum Test

(4)
Performing a One-Way ANOVA (Analysis of Variance) to Test for at Least One
Difference Among Multiple Means m_{1 }, m_{2 },
…, m* _{k}* or a
Kruskal-Wallis Rank Sum Test

(5)
Performing a Chi-square Test Concerning Independence

(6)
Performing a Simple Linear Regression with Checks of Linearity,
Homoscedasticity, and Normality Assumptions

V. Statistical Analysis Involving Multiple
(Two or More) Variables

(1)
Performing a Quadratic Regression with Checks of Model, Homoscedasticity, and
Normality Assumptions

(2)
Performing a Multiple Linear Regression with Checks for Multicollinearity and
of Linearity, Homoscedasticity, and Normality Assumptions

(3)
Performing a Stepwise Linear Regression to Build a Model

(4)
Performing a Stepwise Binary Logistic Regression to Build a Model

(5)
Performing a Two-Way ANOVA (Analysis of Variance) with Checks of Equal Variance
and Normality Assumptions

(6)
Performing a One-Way ANCOVA (Analysis of Covariance) with Checks of Equal
Variance and Normality Assumptions

(7)
Performing a Two-Way ANCOVA (Analysis of Covariance) with Checks of Equal
Variance and Normality Assumptions

(8)
Performing a Repeated Measures Within-Subjects ANOVA with Checks of Sphericity
and Normality Assumptions

(9)
Performing a Repeated Measures Mixed Between-Within-Subjects ANOVA with Checks
of Sphericity, Equal Variance and Covariance, and Normality Assumptions

**I.
Data Entry and Manipulation**

__IMPORTANT NOTES__**:**

Data can be entered in SPSS either before or after
variables are defined; cells with missing values will display a period
point. The default in SPSS is to use all
cases. In order to use only selected
cases in the data file, first select the **Data > Select Cases**
options to display the **Select Cases** dialog box; then click on the **If** button to display the **Select
Cases: If** dialog box. After the
desired condition is entered, click on the **Continue**
button, and then click on the **OK**
button, after which only the desired cases should not be marked as being
excluded from data analysis; also, a variable named *filter_$* will be added to the data.

In many of the SPSS dialog boxes (generally from clicking
an **Options** button), there will be
two choices for handling missing data.
The **Exclude cases pairwise**
choice will have SPSS perform each specific procedure using all cases with no
missing data for the variables involved in the given procedure, which implies
that with missing data the sample size may not be same for each procedure
performed. The **Exclude cases listwise** choice will have SPSS perform each specific
procedure using only those cases with no missing data for the variables
involved in every procedure that is to be performed, which implies that with
missing data the sample size will be same for each procedure performed. (Of course when there is no missing data, it
makes no difference which of these two choices is made.)

** (1) Defining Variables**

** Step
1**: After entering SPSS, you
should see at the bottom of the screen a tab for

** Step
2**: For variables which are not to
be treated as categorical, no more information is required, although options
for columns such as

** Step
3**: In the

** Step
4**: To leave the dialog box, click
on the

** (2) Creating New Variables by
Transformation of Existing Variables**

** Step
1**: Select the

** Step
2**: In the

** Step
3**: In the

** Step
4**: Click on the

** (3) Creating New Variables by Recoding
Existing Variables**

** Step
1**: Select the

** Step
2**: From the list of variables on
the left, select the existing variable to be recoded into a new variable, and
click on the arrow pointing toward the

** Step
3**: In the

** Step
4**: Click the

** Step
5**: In the

** Step
6**: After all the recoding
information has been entered, click on the

**II.
Data Diagnostics, Graphical Displays, and Descriptive Statistics**

__IMPORTANT NOTES__**:**

After all data has been entered in SPSS, it can be
desirable to check for data entry errors that might have been made and to
assess how much missing data there is; this can be accomplished by checking
data ranges and missing values as described below. Also, it is can be desirable to evaluate the
degree to which the data satisfy certain assumptions required for statistical
analysis; some features in SPSS described below illustrate how to do this. Finally, it can be desirable to create
graphical displays and obtain descriptive statistics; using the appropriate
procedures in SPSS is addressed below.

** (1) Checking Data Ranges, Summary
Statistics, and Missing Values**

** Step
1**: Identify the qualitative
(i.e., categorical) variable(s) in the SPSS data file to be checked for data
entry errors and missing data.

** Step
2**: Select the

** Step
3**: The

** Step
4**: Click on the

** Step
5**: Identify the quantitative
variable(s) in the SPSS data file to be checked for data entry errors and
missing data.

** Step
6**: Select the

** Step
7**: To obtain descriptive
statistics, click on the

** Step
8**: Click on the

** (2) Checking for Skewness and
Non-Normality**

** Step
1**: In the SPSS data file,
identify one or more quantitative variables to be checked for normality or
skewness, and identify, if there are any, one or more qualitative (i.e.,
categorical) variables for defining groups.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the quantitative variable, or variables, for which skewness
and non‑normality are to be investigated, and click on the arrow pointing
toward the

** Step
4**: In the

** Step
5**: Click on the

** Step
6**: Click on the

** (3) Creating Graphical Displays and
Obtaining Descriptive Statistics**

__Creating
a Bar Chart__

** Step
1**: In the SPSS data file,
identify the qualitative (i.e., categorical) variable for which a bar chart is
to be created.

** Step
2**: Select the

** Step
3**: Make certain the

** Step
4**: Click on the

** Step
5**: From the list of variables on
the left, select the desired qualitative (i.e., categorical) variable, and
click on the arrow pointing toward the

** Step
6**: Click on the

** Step
7**: If it is desirable to make
changes to the bar chart, double click on the graph to enter the

** Step
8**: After making desired changes,
exit from the Chart Editor, after which you should see that the SPSS output has
been updated.

__Creating
a Pie Chart__

** Step
1**: In the SPSS data file,
identify the qualitative (i.e., categorical) variable for which a pie chart is
to be created.

** Step
2**: Select the

** Step
3**: Make certain the

** Step
4**: Click on the

** Step
5**: From the list of variables on
the left, select the desired qualitative (i.e., categorical) variable, and
click on the arrow pointing toward the

** Step
6**: Click on the

** Step
7**: Double click on the graph to
enter the

** Step
8**: Select the

** Step
9**: Move

** Step
10**: Close the

__Creating
a Stacked Bar Chart__

** Step
1**: In the SPSS data file,
identify the two qualitative (i.e., categorical) variables for which a stacked
bar chart is to be created.

** Step
2**: Select the

** Step
3**: Select the

** Step
4**: Click on the

** Step
5**: From the list of variables on
the left, select the qualitative variable name that will be used to define the
bars, and click on the arrow pointing toward the

** Step
6**: Select the

** Step
7**: In order to have relative
frequency (percentages) scaled on the vertical axis with the bars all scaled to
the same height, which are generally preferable, double click on the graph to
enter the

** Step
8**: Select the

** Step
9**: Exit from the chart editor,
after which you should see that the SPSS output has been updated; the stacked
bar chart displayed is one of two possible stacked bar charts.

** Step
10**: To create the other stacked
bar chart, repeat all previous steps with the variable names switched in Step
5.

__Creating
a Histogram__

** Step
1**: In the SPSS data file,
identify the quantitative variable for which a histogram is to be created.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired quantitative variable, and click on the arrow
pointing toward the

** Step
4**: Click on the

** Step
5**: If it is desirable to make
changes to the histogram, double click on the graph to enter the

** Step
6**: After making desired changes,
exit from the Chart Editor, after which you should see that the SPSS output has
been updated.

__Creating
One Box Plot or Multiple Box Plots for Commensurate Variables__

** Step
1**: In the SPSS data file,
identify either the quantitative variable for which a box plot is to be
created, or the multiple commensurate quantitative variables for which box
plots are to be created.

** Step
2**: Select the

** Step
3**: Make certain the

** Step
4**: Click on the

** Step
5**: From the list of variables on
the left, select the desired quantitative variable(s), and click on the arrow
pointing toward the

** Step
6**: Click on the

** Step
7**: In order to get the numerical
scale displayed on the horizontal axis, which is what is more common, double
click on the graph to enter the

** Step
8**: Select the

** Step
9**: Exit from the Chart Editor,
after which you should see that the SPSS output has been updated.

__Creating Box Plots for Two or More Groups__

** Step
1**: In the SPSS data file,
identify the quantitative variable for which box plots are to be created, and
identify the qualitative (i.e., categorical) variable which defines the groups.

** Step
2**: Select the

** Step
3**: Make certain the

** Step
4**: Click on the

** Step
5**: From the list of variables on
the left, select the desired quantitative variable, and click on the arrow
pointing toward the

** Step
6**: From the list of variables on
the left, select the qualitative (i.e., categorical) variable which defines the
groups, and click on the arrow pointing toward the

** Step
7**: Click on the

** Step
8**: In order to get the numerical
scale displayed on the horizontal axis, which is what is more common, double
click on the graph to enter the

** Step
9**: Select the

** Step
10**: Exit from the Chart Editor,
after which you should see that the SPSS output has been updated.

__Creating
a Scatter Plot__

** Step
1**: In the SPSS data file,
identify the two quantitative variables for which a scatter plot is to be
created; if appropriate, one of the two variables can be designated as the
dependent (or response) variable and the other as the independent (or
predictor) variable.

** Step
2**: Select the

** Step
3**: Make certain that the

** Step
4**: From the list of variables on
the left, select the variable designated as the dependent variable or, if no
such designation was made, select either one of the quantitative variables, and
click on the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: If it is desirable to include
a graph of the least squares line on the scatter plot, double click on the
graph to enter the

** Step
7**: Select the

** Step
8**: You should notice that a label
displaying the equation of the least squares line appears in the middle of the
scatter plot; to delete this label, uncheck the

** Step
9**: Close the

__Creating
a Frequency Table__

** Step
1**: In the SPSS data file,
identify the variable, or variables, for which a frequency table is to be
created; the variable(s) can be either qualitative (in which case the table
will display a list of codes used to represent categories) or quantitative (in
which case the table will display a list of all values of the variable in the
data set).

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the variable, or variables, for which numerical summaries are
to be obtained, and click on the arrow pointing toward the

** Step
4**: Make certain the

__Obtaining
Numerical Summaries__

__First Method__

** Step
1**: In the SPSS data file,
identify one or more quantitative variables for which numerical summaries are
to be obtained, and identify, if there are any, one or more qualitative (i.e.,
categorical) variables for defining groups.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the quantitative variable, or variables, for which numerical
summaries are to be obtained, and click on the arrow pointing toward the

** Step
4**: In the

** Step
5**: Click on the

** Step
6**: Click on the

__Second Method__

** Step
1**: In the SPSS data file,
identify one or more quantitative variables for which numerical summaries are
to be obtained, and identify, if there are any, one or more qualitative (i.e.,
categorical) variables for defining groups.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the quantitative variable, or variables, for which numerical
summaries are to be obtained, and click on the arrow pointing toward the

** Step
4**: Click on the

** Step
5**: After selecting any additional
options desired from the list in the

** Step
6**: Click on the

__Third Method__

** Step
1**: In the SPSS data file,
identify one or more quantitative variables for which numerical summaries are
to be obtained.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the quantitative variable, or variables, for which numerical
summaries are to be obtained, and click on the arrow pointing toward the

** Step
4**: Click on the

** Step
5**: After checking any additional
options desired, click on the

** Step
6**: Click on the

**III. Statistical
Analysis Involving One Variable**

** (1) Performing a One sample t Test about a Mean **

** Step
1**: Identify the (quantitative)
variable in the SPSS data file on which the test is to be performed, decide on
the hypothesized value for the mean m, and select a (two‑sided) significance level a. (More than
one (quantitative) variable may be selected on which the test is to be
performed simultaneously, but only one hypothesized value for the mean is
permitted.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative) variable (and more than one
selection is permitted), and click on the arrow pointing toward the

** Step
4**: Type the hypothesized value
for the mean m in the

** Step
5**: Click on the

** Step
6**: Click on the

One possible appropriate graphical display
for the quantitative variable used in a one‑sample *t* test is a box plot, which can be obtained by following the steps
labeled “__Creating One Box Plot or Multiple Box Plots for Commensurate
Variables__” in Section II(3) of this document.

** (2) Performing a Chi-square
Goodness-of-Fit Test with Hypothesized Proportions**

** Step
1**: If the individual cases making
up the raw data have already been entered into an SPSS data file, identify the
(qualitative) variable on which the test is to be performed, and skip to Step
7; if the data is to be entered into SPSS with raw frequencies (i.e., counts),
then follow the instructions beginning in Step 2.

** Step
2**: Go to the

** Step
3**: Define codes for this
(qualitative) variable so that

** Step
4**: In the second row, enter the
variable name

** Step
5**: Go to the

** Step
6**: In the column for the variable

** Step
7**: If each line of the data file
represents one case (i.e., the data

** Step
8**: In the

** Step
9**: Which option should be
selected in the

** Step
10**: Click on the

One possible appropriate graphical display
for the qualitative variable used in a chi‑square goodness‑of‑fit
test is a bar chart, which can be obtained by following the steps labeled “__Creating
a Bar Chart__” in Section II(3) of this document;
another possible graphical display is a pie chart, which can be obtained by
following the steps labeled “__Creating a Pie Chart__” in Section II(3) of
this document.

**IV. Statistical
Analysis Involving Two Variables**

** (1) Generating a Correlation Matrix with
p-values**

** Step
1**: Identify the (quantitative or
qualitative‑ordinal) variables in the SPSS data file for which
correlations between pairs of variables are to be calculated.

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative) variables, and click on the arrow
pointing toward the

** Step
4**: In the

** Step
5**: In the

** Step
6**: Click on the

One possible appropriate graphical display
for the variables whose correlation is of interest a scatter plot, which can be
obtained by following the steps labeled “__Creating a Scatter Plot__” in
Section II(3) of this document.

** (2) Performing a Paired Sample t Test about a Mean Difference **

** Step
1**: Identify in the SPSS data file
the pair of (quantitative) variables for which the mean difference is being
tested, and select a (two‑sided) significance level a. (More than
one pair of (quantitative) variables may be selected on which to test the mean
difference simultaneously.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select one of the desired (quantitative) variables, and click on the
arrow pointing toward the

** Step
4**: Click on the

** Step
5**: Click on the

A nonparametric test which can be considered
an alternative to the paired‑sample *t*
test (when appropriate assumptions might not be satisfied) is the Wilcoxon
signed rank test to compare the median of a distribution of a quantitative or
qualitative‑ordinal variable to zero (0), which can be performed as
follows:

** Step
1**: Identify in the SPSS data file
the pair of (quantitative) variables for which the mean difference is being
tested, and select a (two‑sided) significance level a. (More than
one pair of (quantitative) variables may be selected on which to test the mean
difference simultaneously.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select one of the desired (quantitative or qualitative‑ordinal)
variables, and click on the arrow pointing toward the

** Step
4**: Click on the

The following two appropriate graphical
displays for the data used in a paired‑sample *t* test or a Wilcoxon signed rank test are possible:

(1)
one box plot of the differences between the two variables; the differences can
be obtained by following the steps labeled “__Creating New Variables by
Transformation of Existing Variables__” in Section I(2) of this document, and
noting that the formula to be entered in Step 3 should be one of the two
variables minus the other (and the minus sign button from the keypad displayed
in the middle of the dialog box can be used); the box plot of the new variable
of differences can then be obtained by following the steps labeled “__Creating
One Box Plot or Multiple Box Plots for Commensurate Variables__” in Section
II(3) of this document.

(2)
two box plots, one for each variable, which can be obtained by following the steps
labeled “__Creating One Box Plot or Multiple Box Plots for Commensurate
Variables__” in Section II(3) of this document.

** (3) Performing a Two Sample t Test about a Difference Between Means **

** Step
1**: Identify in the SPSS data file
both the (qualitative‑dichotomous) variable which defines the two groups
being compared and the (quantitative) variable for which the means are being
compared, and select a (two‑sided) significance level a. (More than
one (quantitative) variable may be selected on which to compare means
simultaneously, but only one grouping variable may be selected.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative) variable (and more than one
selection is permitted), and click on the arrow pointing toward the

** Step
4**: From the list of variables on
the left, select the desired (qualitative‑dichotomous) variable, and
click on the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: In the

** Step
7**: Click on the

** Step
8**: Click on the

A nonparametric test which can be considered
an alternative to the two‑sample *t*
test (when appropriate assumptions might not be satisfied) is the Mann‑Whitney
rank sum test to compare the distributions of a quantitative or qualitative‑ordinal
variable for two groups, which can be performed as follows:

** Step
1**: Identify in the SPSS data file
both the (qualitative‑dichotomous) variable which defines the two groups
being compared and the (quantitative or qualitative‑ordinal) variable for
which the distributions are being compared.
(More than one (quantitative or qualitative‑ordinal) variable may
be selected on which to compare distributions simultaneously, but only one
grouping variable may be selected.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative or qualitative‑ordinal)
variable (and more than one selection is permitted), and click on the arrow
pointing toward the

** Step
4**: From the list of variables on
the left, select the desired (qualitative‑dichotomous) variable, and
click on the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: In the

** Step
7**: Make certain that the

** Step
8**: Click on the

One possible appropriate graphical display
for the data used in a two‑sample *t*
test or a Mann‑Whitney rank sum test is two box plots, one for each
group, which can be obtained by following the steps labeled “__Creating Box
Plots for Two or More Groups__” in Section II(3) of this document.

** (4) Performing a One-Way ANOVA (Analysis
of Variance) to Test for at Least One Difference Among Multiple Means ****m**_{1 }**, ****m**_{2 }**, …, ****m**_{k}** or a
Kruskal-Wallis Rank Sum Test**

** Step
1**: Identify in the SPSS data file
both the (qualitative) variable which defines the groups being compared and the
(quantitative) variable for which the means are being compared, and select a
significance level a. (More than one (quantitative)
variable may be selected on which to compare means simultaneously, but only one
grouping variable may be selected.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative) variable (and more than one
selection is permitted), and click on the arrow pointing toward the

** Step
4**: From the list of variables on
the left, select the desired (qualitative) variable, and click on the arrow
pointing toward the

** Step
5**: Click on the

** Step
6**: Click on the

** Step
7**: Click on the

A nonparametric test which can be considered
an alternative to the one‑way ANOVA *f*
test (when appropriate assumptions might not be satisfied) is the Kruskal‑Wallis
rank sum test to compare the distributions of a quantitative or qualitative‑ordinal
variable for *k* groups, which can be
performed as follows:

** Step
1**: Identify in the SPSS data file
both the (qualitative‑dichotomous) variable which defines the two groups
being compared and the (quantitative or qualitative‑ordinal) variable for
which the distributions are being compared.
(More than one (quantitative or qualitative‑ordinal) variable may
be selected on which to compare distributions simultaneously, but only one
grouping variable may be selected.)

** Step
2**: Select the

** Step
3**: From the list of variables on
the left, select the desired (quantitative or qualitative‑ordinal)
variable (and more than one selection is permitted), and click on the arrow
pointing toward the

** Step
4**: From the list of variables on
the left, select the desired (qualitative‑dichotomous) variable, and
click on the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: In the

** Step
7**: Make certain that the

** Step
8**: Click on the

One possible appropriate graphical display
for the data used in a one‑way ANOVA or a Kruskal‑Wallis rank sum
test is multiple box plots, one for each group, which can be obtained by
following the steps labeled “__Creating Box Plots for Two or More Groups__”
in Section II(3) of this document.

** (5) Performing a Chi-square Test
Concerning Independence**

** Step
1**: If the individual cases making
up the raw data have already been entered into an SPSS data file, identify the
two (qualitative) variables on which the test is to be performed, and skip to
Step 7; otherwise, enter the data into SPSS by following the instructions
beginning in Step 2.

** Step
2**: Go to the

** Step
3**: For each of the two
(qualitative) variables, define codes so that

** Step
4**: In the third row, enter the
variable name

** Step
5**: Go to the

** Step
6**: In the column for the variable

** Step
7**: If each line of the data file
represents one case (i.e., the data

** Step
8**: From the list of the variables
on the left, select one of the two (qualitative) variables on which the test is
to be performed, and click on the arrow button pointing toward the

** Step
9**: Click on the

** Step
10**: Click on the

** Step
11**: Click on the

One possible appropriate graphical display
for the data used in a chi‑square test concerning independence is a
stacked bar chart, which can be obtained by following the steps labeled “__Creating
a Stacked Bar Chart__” in Section II(3) of this document.

** (6) Performing a Simple Linear
Regression with Checks of Linearity, Homoscedasticity, and Normality
Assumptions**

** Step
1**: Identify in the SPSS data file
the (quantitative) dependent (response) variable and the (quantitative) independent
(explanatory or predictor) variable.

** Step
2**: Select the

** Step
3**: Make certain that the

** Step
4**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: Select the

** Step
7**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
8**: Click on the

** Step
9**: In the

** Step
10**: Click on the

** Step
11**: Click on the

** Step
12**: The scatter plot with
standardized predicted values on the horizontal axis and standardized residuals
on the vertical axis, requested in Step 8, will be displayed on the SPSS output
without a horizontal line at zero; since this line can be helpful in examining
this plot, the instructions in Step 5 to have the least squares line appear on
the scatter plot can be used to add this horizontal line at zero.

**V.
Statistical Analysis Involving Multiple (Two or More) Variables**

** (1) Performing a Quadratic Regression
with Checks of Model, Homoscedasticity, and Normality Assumptions**

** Step
1**: Identify in the SPSS data file
the (quantitative) dependent (response) variable and the (quantitative) independent
(explanatory or predictor) variable.

** Step
2**: Create a new variable in the
SPSS data file which is the square of independent (explanatory or predictor)
variable. (This can be done using the
instructions in subsection (2) of section I.)

** Step
3**: Select the

** Step
4**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: In the

** Step
7**: Click on the

** Step
8**: Click on the

** Step
9**: The scatter plot with
standardized predicted values on the horizontal axis and standardized residuals
on the vertical axis, requested in Step 5, will be displayed on the SPSS output
without a horizontal line at zero; since this line can be helpful in examining
this plot, add this horizontal line at zero by doing following: double click on
the graph to enter the

** (2) Performing a Multiple Linear
Regression with Checks for Multicollinearity and of Linearity,
Homoscedasticity, and Normality Assumptions**

** Step
1**: Identify in the SPSS data file
the (quantitative) dependent (response) variable, all quantitative independent
(explanatory or predictor) variables, and all qualitative independent
(explanatory or predictor) variables.

** Step
2**: Select the

** Step
3**: Make certain that the

** Step
4**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
5**: Click on the

** Step
6**: Repeat Steps #2 to #5 for each
of the quantitative independent (explanatory or predictor) variables.

** Step
7**: For each of the qualitative
independent (explanatory or predictor) variables, add the appropriate dummy
variable(s) to the data file. For a
qualitative variable with

** Step
8**: Select the

** Step
9**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
10**: Click on the

** Step
11**: In the

** Step
12**: Click on the

** Step
13**: Click on the

** Step
14**: The scatter plot with
standardized predicted values on the horizontal axis and standardized residuals
on the vertical axis, requested in Step #8, will be displayed on the SPSS
output without a horizontal line at zero; since this line can be helpful in
examining this plot, the instructions in Step #5 to have the least squares line
appear on the scatter plot can be used to add this horizontal line at zero.

** (3) Performing a Stepwise Linear Regression
to Build a Model**

** Step
1**: Identify in the SPSS data file
the (quantitative) dependent (response) variable, all potential quantitative
independent (explanatory or predictor) variables, and all potential qualitative
independent (explanatory or predictor) variables.

** Step
2**: For each of the qualitative
independent (explanatory or predictor) variables, add the appropriate dummy
variable(s) to the data file. For a
qualitative variable with

** Step
3**: Select the

** Step
4**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
5**: In the

** Step
6**: Click on the

** Step
7**: Click on the

** (4) Performing a Stepwise Binary
Logistic Regression to Build a Model**

??????????????*********** THIS SECTION (4) IS STILL UNDER
CONSTRUCTION **************???????????????????

** Step
1**: Identify in the SPSS data file
the ?????????????????????(quantitative) dependent (response) variable, all
potential quantitative independent (explanatory or predictor) variables, and
all potential qualitative independent (explanatory or predictor) variables.

** Step
2**: For each of the qualitative
independent (explanatory or predictor) variables, add the appropriate dummy
variable(s) to the data file. For a
qualitative variable with

** Step
3**: Select the

** Step
4**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
5**: In the

** Step
6**: Click on the

** Step
7**: Click on the

** (5) Performing a Two-Way ANOVA (Analysis
of Variance) with Checks of Equal Variance and Normality Assumptions**

** Step
1**: Identify in the SPSS data file
the quantitative (response) variable for which means are to be compared and the
two qualitative (independent) variables which defines the groups among which
the means are to be compared; then select a significance level a.

** Step
2**: In order to examine residuals
for non-normality, first add the appropriate dummy variables to the data file
for each of the two qualitative (independent) variables as follows (but if no
check for non-normality in residuals is desired, skip to Step 7.): If one of the qualitative variables is
defined by

** Step
3**: Select the

** Step
4**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
5**: Click on the

** Step
6**: Click on the

** Step
7**: Select the

** Step
8**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
9**: From the list of variables on
the left, select the two qualitative (independent) variables, and click on the
arrow pointing toward the

** Step
10**: Click on the

** Step
11**: Click on the

** Step
12**: Click on the

** Step
13**: Click on the

** Step
14**: Click on the

An appropriate graphical display for
significant interaction in a two‑way ANOVA is one of the plots created in
Step 13; however, if there is no significant interaction, then an appropriate
graphical display for significant main effects is multiple box plots, which can
be obtained by following the steps labeled “__Creating Box Plots for Two or
More Groups__” in Section II(3) of this document.

** (6) Performing a One-Way ANCOVA
(Analysis of Covariance) with Checks of Equal Variance and Normality
Assumptions**

** Step
1**: Identify in the SPSS data file
the quantitative (response) variable for which means are to be compared, the
qualitative independent variable which defines the groups among which the means
are to be compared, and each quantitative variable which is a covariate.

** Step
2**: In order to use one-way
ANCOVA, the assumption of no interaction between the qualitative independent
variable and each covariate must be satisfied; to check the validity of this
assumption, select the

** Step
3**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
4**: From the list of variables on
the left, select the qualitative independent variable, and click on the arrow
pointing toward the

** Step
5**: From the list of variables on
the left, select each of the covariate quantitative independent variables, and
click on the arrow pointing toward the

** Step
6**: Click on the

** Step
7**: From the list of variables in
the

** Step
8**: Repeat the previous step for
each quantitative variable which is a covariate.

** Step
9**: From the list of variables in
the

** Step
10**: Repeat the previous step for
the qualitative independent variable and each quantitative variable which is a
covariate.

** Step
11**: Verify that

** Step
12**: Click on the

** Step
13**: Click on the

** Step
14**: The validity of the
no-interaction assumption (in

** Step
15**: If the no-interaction
assumption and equal variance assumption are considered to be satisfied, then
select a significance level a for the one-way ANCOVA and proceed to the next step; if the
no-interaction assumption is not considered to be satisfied, then one-way
ANCOVA is NOT an appropriate statistical analysis and instead of proceeding to
the next step, perform a more complicated regression analysis which is an
appropriate statistical analysis.

** Step
16**: In order to examine residuals
for non-normality, first add the appropriate dummy variables to the data file
for the qualitative independent variable as follows (but if no check for
non-normality in residuals is desired, skip to Step 21.): If the qualitative variable is defined by

** Step
17**: Select the

** Step
18**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
19**: Click on the

** Step
20**: Click on the

** Step
21**: In order to verify the
linearity assumption for the dependent variable and each covariate (i.e., each
quantitative independent (explanatory or predictor) variable), select the

** Step
22**: Make certain that the

** Step
23**: From the list of variables on
the left, select the quantitative dependent (response) variable, and click on
the arrow pointing toward the

** Step
24**: Click on the

** Step
25**: Repeat Steps #21 to #24 for
each covariate. Each scatter plot can be
examined for significant departures from linearity.

** Step
26**: In order to do the one-way
ANCOVA, select the

** Step
27**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
28**: From the list of variables on
the left, select the qualitative independent variable, and click on the arrow
pointing toward the

** Step
29**: From the list of variables on
the left, select each of the covariates, and click on the arrow pointing toward
the

** Step
30**: Click on the

** Step
31**: Click on the

** Step
32**: Click on the

** Step
33**: Click on the

** Step
34**: Based on the statistically
significant differences among parallel regressions found, decide which of the

** Step
35**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
36**: Click on the

** (7) Performing a Two-Way ANCOVA
(Analysis of Covariance) with Checks of Equal Variance and Normality
Assumptions**

** Step
1**: Identify in the SPSS data file
the quantitative (response) variable for which means are to be compared, the
two qualitative independent variables which define the groups among which the
means are to be compared, and each quantitative variable which is a covariate.

** Step
2**: In order to use two-way
ANCOVA, the assumption of no interaction between each qualitative independent
variable and each covariate must be satisfied; to check the validity of this
assumption and also check the equal variance assumption, select the

** Step
3**: From the list of variables on the
left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
4**: From the list of variables on
the left, select each of the two qualitative independent variables, and click
on the arrow pointing toward the

** Step
5**: From the list of variables on
the left, select each of the covariate quantitative independent variables, and
click on the arrow pointing toward the

** Step
6**: Click on the

** Step
7**: From the list of variables in
the

** Step
8**: From the list of variables in
the

** Step
9**: Verify that

** Step
10**: Click on the

** Step
11**: Click on the

** Step
12**: The validity of the
no-interaction assumption (in

** Step
13**: If the no-interaction assumption
and equal variance assumption are considered to be satisfied, then select a
significance level a for the one-way ANCOVA and proceed to the next step; if the
no-interaction assumption is not considered to be satisfied, then one-way ANCOVA
is NOT an appropriate statistical analysis and instead of proceeding to the
next step, perform a more complicated regression analysis which is an
appropriate statistical analysis.

** Step
14**: In order to examine residuals
for non-normality, first add the appropriate dummy variables to the data file
for each of the two qualitative (independent) variables as follows (but if no
check for non-normality in residuals is desired, skip to Step 19.): If one of the qualitative variables is
defined by

** Step
15**: Select the

** Step
16**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
17**: Click on the

** Step
18**: Click on the

** Step
19**: In order to verify the
linearity assumption for the dependent variable and each covariate (i.e., each
quantitative independent (explanatory or predictor) variable), select the

** Step
20**: Make certain that the

** Step
21**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
22**: Click on the

** Step
23**: Repeat Steps #19 to #22 for each
covariate. Each scatter plot can be
examined for significant departures from linearity.

** Step
24**: In order to do the two-way
ANCOVA, select the

** Step
25**: From the list of variables on
the left, select the quantitative (response) variable, and click on the arrow
pointing toward the

** Step
26**: From the list of variables on
the left, select each of the two qualitative independent variables, and click
on the arrow pointing toward the

** Step
27**: From the list of variables on
the left, select each of the covariates, and click on the arrow pointing toward
the

** Step
28**: Click on the

** Step
29**: Click on the

** Step
30**: Click on the

** Step
31**: Click on the

** Step
32**: Click on the

** Step
33**: Based on the statistically
significant differences among parallel regressions found, create the dummy
variables which should be included in the regression (some of which may have
already been created in Step 14) along with the statistically significant
covariates; then select the

** Step
34**: From the list of variables on
the left, select the (quantitative) dependent (response) variable, and click on
the arrow pointing toward the

** Step
35**: Click on the

** (8) Performing a Repeated Measures
Within-Subjects ANOVA with Checks of Sphericity and Normality Assumptions**

** Step
1**: Identify in the SPSS data file
the quantitative (response or dependent) variables whose means are to be
compared. (The normality assumption can
be checked by using the steps in (2) of the

** Step
2**: Select the

** Step
3**: In the

** Step
4**: Enter the number of
quantitative (response or dependent) variables in the

** Step
5**: Click on the

** Step
6**: Click on the

** Step
7**: Click on the

** Step
8**: Click on the

** Step
9**: Click on the

** (9) Performing a Repeated Measures Mixed
Between-Within-Subjects ANOVA with Checks of Sphericity, Equal Variance and
Covariance, and Normality Assumptions**

** Step
1**: Identify in the SPSS data file
the quantitative (response or dependent) variables whose means are to be
compared whose means are to be compared and the qualitative independent
variable which defines the groups among which the means are to be
compared. (The normality assumption can
be checked by using the steps in (2) of the

** Step
2**: Select the

** Step
3**: In the

** Step
4**: Enter the number of
quantitative (response or dependent) variables in the

** Step
5**: Click on the

** Step
6**: Click on the

** Step
7**: Click on the

** Step
8**: If the qualitative independent
variable has only 2 categories, then go to Step 9; if the qualitative
independent variable has more than 2 categories, then click on the

** Step
9**: Click on the

** Step
10**: Click on the

???????????????

__Performing a logistic regression with checks for
multicollinearity__

1.
Identify in the
SPSS data file the (qualitative-dichotomous) dependent (response) variable, all
quantitative independent (explanatory or predictor) variables, and all
qualitative independent (explanatory or predictor) variables.

2.
For each of the qualitative
independent (explanatory or predictor) variables, add the appropriate dummy
variable(s) to the data file. For a
qualitative variable with *k*
categories, this can be done by defining dummy variables, where the first dummy
variable is equal to 1 (one) for category #1 and 0 (zero) otherwise, the second
dummy variable is equal to 1 (one) for category #2 and 0 (zero) otherwise,
etc.; since *k* - 1 dummy variables are sufficient to represent a
qualitative variable with *k*
categories, the *k*th dummy variable is
not really necessary, and may or may not be used.

3.
The multiple regression routine can be used to check for
multicollinearity (but is __not__ appropriate for statistical analysis,
since the dependent variable is not quantitative); select the **Analyze >**
**Regression > Linear** options, select the (qualitative-dichotomous)
dependent for the **Dependent** slot, and select all quantitative
independent variables and all dummy variables representing qualitative
independent variables for the **Independent(s)** section. Click on the **Statistics** button, and in
the dialog box which appears select the **Collinearity diagnostics**
option. Click the **Continue** button
to close the dialog box, and click the **OK** button to obtain the desired
SPSS output. The desired values for
tolerance and VIF are all available in the **Coefficients** table of the
output.

4.
Make ???????.

5.
From the list of
variables on the left, select the (quantitative) dependent (response) variable,
and click on the arrow pointing toward the **Y-Axis** slot; then select one
of the quantitative independent (explanatory or predictor) variables, and click
on the arrow pointing toward the **X-Axis** slot.

6.
Click on the **OK**
button, after which SPSS output displaying a scatter plot will be
generated. __In order to have the least
squares line appear on the scatter plot, first double click on the graph to
enter the SPSS Chart Editor, and
then select the Elements> Fit Line at
Total options from the main menu (and close the dialog box which appears),
after which selecting the File >
Close options will close the chart editor.
By examining the how the points on the scatterplot are distributed
around the least squares line, a decision can be made as to whether the
linearity assumption about the relationship between the dependent and
independent variables is satisfied.__

7.
Repeat Steps #2
to #5 for each of the quantitative independent (explanatory or predictor)
variables.

8.
For each of the
qualitative independent (explanatory or predictor) variables, add the
appropriate dummy variable(s) to the data file.
For a qualitative variable with *k*
categories, this can be done by defining dummy variables, where the first dummy
variable is equal to 1 (one) for category #1 and 0 (zero) otherwise, the second
dummy variable is equal to 1 (one) for category #2 and 0 (zero) otherwise,
etc.; since *k* - 1 dummy variables are sufficient to represent a
qualitative variable with *k*
categories, the *k*th dummy variable is
not really necessary, and may or may not be used.

9.
Select the **Analyze >**
**Regression > Linear** options to display the **Linear Regression**
dialog box.

10. From the list of variables on the left, select the
(quantitative) dependent (response) variable, and click on the arrow pointing
toward the **Dependent** slot; then select
each independent (explanatory or predictor) variable, and click on the arrow
pointing toward the **Independent(s)** section (where selection of more than
one variable is permitted).

11. Click on the **Plots**
button to display the **Linear Regression: Plots** dialog box. From the list of variables on the left,
select *ZRESID*, and click on the arrow
pointing toward the **Y** slot; then select *ZPRED*, and click on the arrow pointing toward the **X**
slot. __This will generate a scatter
plot with standardized predicted values on the horizontal axis and standardized
residuals on the vertical axis, so that a decision can be made as to whether
the homoscedasticity assumption is satisfied__.

12. In the **Standardized
Residual Plots** section of the **Linear Regression: Plots** dialog box,
select the **Histogram** option and the **Normal probability plot**
option. __This will generate a
histogram and a normal probability plot for standardized residuals, so that a
decision can be made as to whether the normality assumption is satisfied__.

13. Click on the **Continue**
button, and then click on the **Statistics**
button to display the **Linear Regression: Statistics** dialog box. In the **Regression
Coefficients** section, make certain that the **Estimates** option is selected, select the **Descriptives**
option to generate means, standard deviations, and the Pearson correlations,
and select the **Collinearity diagnostics** option to generate information
about whether multicollinearity could be a problem; also, select the **Confidence
intervals** option to set the desired (two‑sided) confidence level
(which will generally be 100% minus the significance level, i.e., if the
significance level is 0.05 (5%), then the confidence level will be 0.95
(95%)). __This will generate confidence
intervals for the slope and for the intercept in the regression__.

14. Click on the **Continue**
button, and then click on the **Save**
button to display the **Linear Regression: Save** dialog box. In the **Residuals** section, select the **Standardized**
option to save the standardized residuals as part of the data. __This allows further analysis to be
performed using the standardized residuals__.

15. Click on the **Continue**
button, and then click on the **OK**
button, after which the SPSS output will be generated.

16. The scatter plot with standardized predicted values on
the horizontal axis and standardized residuals on the vertical axis, requested
in Step #8, will be displayed on the SPSS output without a horizontal line at
zero; since this line can be helpful in examining this plot, the instructions
in Step #5 to have the least squares line appear on the scatter plot can be
used to add this horizontal line at zero.

Methods to decide which of
many predictors are the most important to include in a model are available with
SPSS by doing the following:

1.
Select the **Analyze >**
**Regression > Linear** options to display the **Linear Regression**
dialog box.

2.
From the list of
variables on the left, select the (quantitative) dependent (response) variable,
and click on the arrow pointing toward the **Dependent**
slot; then select each independent (explanatory or predictor) variable, and click
on the arrow pointing toward the **Independent(s)** section (where selection
of more than one variable is permitted).

3.
In the **Method**
slot, select the desired method for variable selection (such as the **Stepwise**
option).

4.
Click on the **Continue** button, and then click on the **Statistics** button to display the **Linear
Regression: Statistics** dialog box.
In the **Regression Coefficients**
section, make certain that the **Estimates**
option is selected, and select the **R squared change** option; also, select
the **Confidence intervals** option to set the desired (two‑sided)
confidence level (which will generally be 100% minus the significance level,
i.e., if the significance level is 0.05 (5%), then the confidence level will be
0.95 (95%)). __This will generate confidence
intervals for the slope and for the intercept in the regression__.

5.
Click on the **OK** button, after which the SPSS output
will be generated.

__Generating a correlation matrix__

????????????????