Means and Statistics
SPSS Tutorial
01
Multiple Analysis
of Variance
(MANOVA)
A MANOVA test is used to model two or more dependent variables
that are continuous with one or more categorical predictor vari-
ables. To explore this analysis in SPSS, let’s look at the following
example.
Example:
An instructor was interested to learn if
there was an academic difference in stu-
dents from different states. She randomly
selected 20 students from each of three
states; California, Arizona, and Colorado
who were a part of the entering freshman
class at the University. She assessed them
based on their English and math placement
tests. The independent variable is the state
and the dependent variables are the scores
on the two placement tests. The results are
as follows.
The first step is to enter the data into the
SPSS data editor. You will need three col-
umns for the three variables. The first
is state, second Math scores, and finally
English scores.
02
To begin the analysis click on Analyze –
General Linear Model – Multivariate.
In the Multivariate Window move Math and
English to the Dependent Variable box and
State to Fixed Factor(s).
Then select Options.
03
Move State to the Display Means for box
and put a check next to Descriptive Statis-
tics, Estimates of effect size, and Ob-
served power. Then Click Continue.
Click Continue in the Multivariate window
and the output will be displayed in the out-
put viewer.
04
There are multiple boxes of information
provided by this analysis. The first box sim-
ply states how many samples there were
for each level of the independent variable.
The Descriptive Statistics box provides the
mean and standard deviation for the two
different dependent variables which have
been split by the independent variables
levels.
05
The next box is the Multivariate tests. This is where we
find the actual results of the one-way MANOVA. We
want to look at the second effect labeled State and the
Wilks’ Lambda row. The Sig column gives the p-value
and we can determine if the results were statistically
significant. Since the p-value = .223 then we see that
there is not a statistically significant difference in the
students academics from different states.
06
To determine how the dependent variables differ for
the independent variables, we need to look at the Tests
of Between–Subjects Effects. Based on the p-values
(Sig.) for Math and English, which are greater than
0.05, State does not have a significant effect on Math
or English results.
SPSS Tutorial
01
Multiple Linear
Regression
Regression begins to explain behavior by demonstrating how dif-
ferent variables can be used to predict outcomes. Multiple regres-
sion gives you the ability to control a third variable when investi-
gating association claims. To explore Multiple Linear Regression,
let’s work through the following example.
Example:
A researcher is interested in studying
four different variables: GPA, motivational
score, IQ, and hours of study. The following
data was collected on a simple random
sample of students.
The researcher wants to examine the re-
lationship between the dependent variable
GPA and the independent variables of Moti-
vational score, IQ, and hours of study.
To begin the analysis, enter the data into
SPSS. There are four variables, so we need
four columns. For questions entering data,
please review the data entry tutorial.
Once the data are entered, click on Ana-
lyze – Regression – Linear.
02
The Linear Regression pop-up window will
open. Move GPA to the Dependent box and
the other three variables to the Indepen-
dent box. Then click OK.
03
The output will be displayed in the output
window.
There are four boxes of output. The first is
a description of the variables entered.
The second box is the Model Summary.
This gives the correlation coefficient r,
the coefficient of determination r2, ad-
justed r2, and the standard error of the
estimate. The correlation coefficient tells
the strength and direction of the linear
relationship. Since r = .968, it is a strong
positive relationship (a positive number
and close to one). The coefficient of deter-
mination tells the proportion of variation
that is account for by the linear relation-
ship between the dependent and indepen-
dent variables.
The third box gives an analysis to show
if there is a statistically significant linear
relationship between the dependent and
independent variables. The p-value of .000
(Sig.) indicates a statistically significant
linear relationship since it is less than 0.05.
04
The last output box gives an individual look
at each of the independent variables as
predictors of GPA.
To interpret this review the p-value (Sig.) for each
of the variables. We can see that Motivation Score
and IQ are statistically significant predictors of
GPA (with p-value <0.05) but Hours of Study is not
(p-value > 0.05). From these results, we see that
collectively these three predictor variables explain
a significant amount of variability in GPA, and individ-
ually, because the slope values are all positive (the B
column in the output table), motivation, and IQ signifi-
cantly predict GPA (as motivation and IQ increase, so
does GPA).
SPSS Tutorial
Two-Way Analysis
of Variance
(ANOVA) – Between
Groups
01
A two-way ANOVA is used to test the equality of two or more
means when there are two factors of interest. When two factors
are of interest, an interaction effect is possible as well. There is an
interaction between two factors if the effect of one of the factors
changes for different categories of the other factor. There are two different options: between groups and within groups. In be-
tween-groups experiments, researchers randomly assign partic-
ipants to independent groups and then expose one group to one
level of the independent variable and the others to the other levels
To explore the two-way ANOVA in SPSS we will use the following
example from the Visual Learner Media Piece.
Example:
A professor at a local University believes
there is a relationship between head size,
the major of the students, and the gender
of students in her biostatistics classes. She
takes a random sample from her three
classes. The data is in the following table.
Notice that the sample size for each set of
categories is the same. (i.e., female and Pre
Med had 4 data values as does male and
Pre Med)
02
A two way ANOVA essentially does three
different hypothesis test. First test for
interaction effect then effect from each of
the two factors if there is no interaction
effect.
The first step is to enter the data into SPSS.
The two-way ANOVA has two factors and
one response variables. This is how the
data is entered into SPSS. One column
for each factor, gender and major. A third
column for the response, head size. The
factors must be quantitative, so we need
to assign numerical values to each level.
For Gender, let Female = 1 and Male = 2. For
Major, let Pre Med = 1, Pre PT = 2, Nursing
= 3, and Health Car Admin = 4. You can use
any values that you choose but make sure
you are consistent and you note the values
assigned.
Once the data is entered, the analysis is
performed by selecting Analyze – General
linear Mode – Univariate.
03
In the Univariate popup box, the factors,
Gender and Major need to be put in Fixed
Factor(s). The response, Head_Size is put
in the Dependent Variable box.
There is an option for selection of Post_Hoc
test on the right of the screen that gives
several options for different Post_Hoc test
that can be performed.
Remember that a Post_Hoc test is only
need if there is significant difference found.
Therefore, the two-way ANOVA should be
run first. Select continue, then interpret
the output in the output window.
The fist output box gives the sample size
for each of the factors.
The second output box gives the two-way
ANOVA table. Remember to test for inter-
action, looking at Gender*Major first. Then,
if there is no significant effect, go on to look
for a significant effect due to Gender and
Major separately.
Putting all the statistical conclusions
together we can see that there is no
effect from the interaction of gender and
major on the head circumference and
there is no effect on head circumference
due to major but there is an effect due
to gender on head circumference at a
statistically significant level of 0.05.
04
SPSS Tutorial
01
Mann-Whitney
U Test
The Mann-Whitney U test is used to test for a significant differ-
ence between two samples but the data either does not meet the
normality assumption needed for the independent samples t-test
or the variables are ordinal.
Example:
A group of students are interested in
discovering if music with or without words
has an impact on student rating of class
experience. During class work, students in
one class were played music with no words
and students in the other class were played
music with words. Students were asked
to rate their class experience on a scale
of 1 to 5 with 1 being the worst and 5 being
the best. The following data was collected
where 1 is for music without words and 2 is
for music with words.
To perform the Mann-Whitney U test in
SPSS, first enter the data. Review the data
entry tutorial if there are any questions
about data entry. The data is entered in two
columns.
It is important to note that in the variable
view tab, you need to set the Measure
(scale of measurement) for the two vari-
ables. Music Type is nominal (it is a name or
label) and the Class Rating is scale (specifi-
cally it is the ordinal level of measurement,
review the visual learner media piece).
02
Once the data is entered, the analysis is run
by going to Analyze – Nonparametric Tests
– Independent Samples.
The Nonparametric Tests Two or More
Independent Samples window will open.
There are three tabs at the top of the win-
dow. It will start on the Objective tab. The
default setting of Automatically
compare distributions across groups
should be selected. Then go to the Fields
tab.
03
In the Fields tab move the Class_Rating to
the Test Fields box and Musics_Type to the
Groups box. Select Run.
The output window will open with the
Hypothesis Test Summary. To get the
detailed output, you will need to double
click on the Hypothesis Test Summary.
A pop-up output window will open when
you double click.
04
The left hand side of the viewer displays the
Hypothesis Test Summary and the right-
hand side provides more detailed informa-
tion.
According to the Mann-Whitney U test, there is a
statistically significant difference based on the p-value
(Exact Sig. (2 sided test)) = .013. Group 1, which listened
to the music with no words (Mean Rank of 19.43),
reported a higher rating of the class than the group
that listened to music with words (Mean Rank of 11.57).
According to the Mann-Whitney U test, there is a
statistically significant difference based on the p-val-
ue (Exact Sig. (2 sided test)) = .013. Group 1, which
listened to the music with no words (Mean Rank of
19.43), reported a higher rating of the class than the
group that listened to music with words (Mean Rank
of 11.57).
SPSS Tutorial
01
Kruskal-Wallis
Test
The Kruskal-Wallis Test is used when you want to test to see if
there is a significant difference between two or more samples but
the assumption for the One-Way ANOVA are not met, either the
data is not normally distributed or the data is at an ordinal level of
measurement. To explore this technique in SPSS, let’s look at the
following example.
Example:
A study was done to see if music type (1
= Country, 2 = Classic, 3 = Rock, and 4 =
Jazz) had an effect on students perception
of their performance on an in-class exam
when students listened while taking the
exam. A class of 40 students were given
an exam and were asked to listen to one
of four types of music with head phones
during the exam. Ten students listened to
each type of music. They were ask to rate
how well they thought they performed on
the exam at the end on a scale of 1 to 5 with
1 being the worst and 5 being the best. Us-
ing the data below, we want to determine if
there is a statistically significant effect on
students perception of their performance
due to the type of music listened to.
The first step to performing the analysis in
SPSS is to enter the data. The data is en-
tered in two columns, one for Music Type
and one for Perception. Please review the
data entry tutorial for questions on data
entry.
The Kruskal-Wallis Test requires the
assignment of the level of measurement
be assigned for each of the variables in
the Measure column in the variable view
tab. Music Type is at the nominal scale and
Perception is Interval but in SPSS both
Interval and Ratio are called scale.
02
Once the measure is set, the analysis is run
by selecting Analyze – Nonparametric –
Independent Samples.
The Nonparametric Tests Two or More
Independent Samples box will open. There
are three tabs at the top of the box.
Objective is the first and the default setting
of Automatically compare distributions
across groups will be selected.
03
Select the second tab, Fields. In this tab
move Perception to the Test Fields box and
the Music Type to the Groups box.
The last tab is the Settings tab. In this tab,
first select Customize Test and then Kru-
skal-Wallis 1-way ANOVA K samples. Then
click Run.
The Hypothesis Test Summary is displayed
in the output window. To get a detailed
view for interpretation, double click on the
Hypothesis Test Summary.
A pop-up output window will open with the
results of the test.
The left side of the screen is the
Hypothesis Test Summary and the right is
a more detailed look at
the test.
04
The p-value (Asymptotic Sig. (2-sided test)
= .004) shows there is a statistically signif-
icant effect on the perception of student
performance due to the type of music
listened to. To see which levels of the inde-
pendent variables are significantly differ-
ent from each other, the Pairwise Compar-
isons will need to be selected under View
at the bottom of the pop-up window.
The detailed report allows us to see which
types of music are statistically different.
The p-values for Rock – Country and Rock
– Jazz show significant findings (they are
less than .
05
). This implies that there is a
statistically significant difference between
student perception on exams when listen-
ing to Rock and Country and Rock and Jazz
music.
A separate pop-up window will open,
the right side of the screen will have the
detailed report.
05
Descriptive Statistics Worksheet
Directions: Answer each question completely, showing all your work. Refer to the SPSS tutorials located in the Topic 4 materials as needed. Copy and Paste the SPSS output into the word document for the calculations portion of the problems. (Please remember to answer the questions you must interpret the SPSS output).
1. A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).
Participant
Hours of Exercise
Life Satisfaction
1
3
1
2
14
2
3
14
4
4
14
4
5
3
10
6
5
5
7
10
3
8
11
4
9
8
8
10
7
4
11
6
9
12
11
5
13
6
4
14
11
10
15
8
4
16
15
7
17
8
4
18
8
5
19
10
4
20
5
4
2. Find the mean hours of exercise per week by the participants.
3. Find the variance of the hours of exercise per week by the participants.
4. Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.
5. Describe the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction.
6. Develop a model of the linear relationship using the regression line formula.
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