ANOVA
Richard Rivera
(aka Rico)
ANOVA
• In this lesson I will kill two birds with one
stone. You’ll be introduced on how to
– import excel data files into SPSS
– conduct analyses of variance in SPSS
Need some Data Files
• But first, you need to download an Excel
data file.
• Open up your internet Explorer
• Copy and paste the following two links into
the web browser.
http://www.west.asu.edu/statlab/downloads/WorkshopExample.xls
http://www.west.asu.edu/statlab/downloads/WorkshopExample.sav
• Please save them to your Desktop.
Two Topics
• Prepping an Excel spreadsheet to be
imported into SPSS
• Types of Analyses of variance (ANOVA).
Excel spreadsheet
•
•
•
•
•
Each column is indicative of a
variable
First row contains the variable
names
You want to keep the same rules
that apply to variable names in
SPSS
The subsequent rows contain the
data for each case (subject)
Gender has two levels
–
–
•
Age has three levels
–
–
–
•
< 25 = 1
25 - 40 = 2
> 40 = 3
Time has three levels
–
–
–
•
Male = 1
Female = 2
Baseline = time0
Time 1 = time1
Time 2 = time2
Composite scores for “attitude
towards research”
Excel spreadsheet
I sorted the data based on
gender and age
variables for
instructional purposes.
Between subjects (aka
independent
samples)
• What are two
between-subject
factors that have
independent
samples?
– Gender: 2 samples
– Age: 3 samples
Within subjects (aka
related samples)
• What is the one
within-subject factor
that is indicative of
three related
samples?
– Time: 3 samples
Importing Excel Data into SPSS
Stat Lab Staff: you may want to print this slide and follow the SPSS directions below
•
After formatting the data in Excel
– First row contains the variable names
– Other rows contain the data values
•
•
Save and close Excel file
Open up SPSS
– Click on File > Open > Data
– Navigate to the location you save the Excel file
– In “Files of type:” choose either
• Excel (*.xls)
• or All files (*.*)
• Open the Excel file you saved
– You’ll get a dialogue box called: Opening Excel Data Source
• There is a green check mark in box: Read variable names from the list from the first row
of data
• Worksheet: choose the worksheet in which the data is located
• Click the OK button.
– You just imported an excel file into SPSS
Analysis of Variance
• One-way ANOVA
– One between subjects factor
– Example: Age (discrete variable)
• Two-way ANOVA
– Usually consist of two between subjects factors
– Example: Age and Gender
• Repeated Measures
– One-way within subjects ANOVA
• One within subjects factor
• Example: Time
– Two-way between and within subjects ANOVA
• One between subjects factor (e.g., Age)
• And one within subject factor (e.g., Time)
One-way ANOVA
You may want to open the SPSS data file that you downloaded.
•
Differences among 2 or more independent sample means with SPSS
• Analysis of Variance: between subjects factor
•
•
•
•
Analyze > Compare Means > One-Way ANOVA …
One dependent variable (e.g., baseline, time0) goes into the “Dependent List:”
One between subjects factor (e.g., Age) goes into “Factor:”
If the factor has more than three level, click on Post Hoc…
– Click on Tukey and Dunett’s C (unless your instructor wants you to use a
different one).
– Click on continue
•
Click on Options
– Chose
• descriptive Statistics
• Homogeneity of variance test
• Perhaps on Means plot
– Click on continue
•
Click on OK
Descriptive Statistics
Descriptives
time0
N
Under 25
25 - 40
Over 40
Total
33
37
25
95
Mean
14.12
13.24
9.76
12.63
Std. Deviation
3.267
3.840
3.018
3.837
Std. Error
.569
.631
.604
.394
95% Confidence Interval for
Mean
Lower Bound Upper Bound
12.96
15.28
11.96
14.52
8.51
11.01
11.85
13.41
Minimum
7
7
6
6
• The first column contains the three levels of the Age factor.
• The mean column contains the mean “attitude toward statistics”
•Does it appear that there may be an age effect?
•Do you notice a trend?
•Which age group has the greatest mean?
Maximum
20
20
18
20
F-test
ANOVA
time0
Between Groups
W ithin Groups
Total
•
•
Sum of
Squares
293.219
1090.886
1384.105
df
2
92
94
Mean Square
146.610
11.857
F
12.364
Sig.
.000
The F-test looks tells us if there is an age effect.
Is the F-test significant?
– Look at the p value (in column called Sig.)
– Is it less than an alpha of .05?
•
•
However, the F-test does not tell us which pair of means are significantly
different.
We look at the multiple comparisons for that.
Multiple Comparisons
Multiple Com pari sons
Dependent Variable: time0
Tukey HSD
(I) age
Under 25
25 - 40
Over 40
Dunnett C
Under 25
25 - 40
Over 40
(J) age
25 - 40
Over 40
Under 25
Over 40
Under 25
25 - 40
25 - 40
Over 40
Under 25
Over 40
Under 25
25 - 40
Mean
Difference
(I-J)
St d.
.878
4.361*
-.878
3.483*
-4. 361*
-3. 483*
.878
4.361*
-.878
3.483*
-4. 361*
-3. 483*
E rror
.824
.913
.824
.891
.913
.891
.850
.829
.850
.873
.829
.873
Sig.
.538
.000
.538
.001
.000
.001
95% Confidenc e Interval
Lower Bound Upper Bound
-1. 09
2.84
2.19
6.54
-2. 84
1.09
1.36
5.61
-6. 54
-2. 19
-5. 61
-1. 36
-1. 20
2.96
2.31
6.42
-2. 96
1.20
1.33
5.64
-6. 42
-2. 31
-5. 64
-1. 33
*. The mean differenc e is significant at the .05 level.
•Mean difference column was calculated by subtracting the means
for age categories in column (j) from means for age categories in
column (I).
•If there is an asterisk, the mean difference is significant.
Two-way ANOVA
• Example: two between subjects factors
• Analyze > General Linear Model >
Univariate…
• Dialogue box titled Univariate
– Dependent variable: move one dependent
variable (e.g., baseline: time0)
– Fixed Factor(s): move in the between subjects
factors (e.g., Gender and Age).
Dialogue box titled Univariate
(continued)
• Click on Plots
– Move one of factors into horizontal axis and
the other into separate lines
– Click Add
– If you wish, you can do the inverse of that,
then click add again
– Click Continue
Dialogue box titled Univariate
(continued)
• Click on Post Hoc…
– Choose only factors that have three or more
levels. (e.g., Age).
– Click on Tukey and Dunett’s C (unless your instructor
wants you to use different ones).
– Click on continue
Dialogue box titled Univariate
(continued)
• Click on Option…
– Choose Descriptive statistics
– Homogeneity tests
– Click on continue
• Click on OK
Repeated Measures
• Within Subjects ANOVA example
• Analyze > General Linear Model > Repeated
Measures…
• Dialogue box: Repeated Measures Define
Factor(s)
• Within-Subject Factor Name:
– Change name to: time
– Number of levels: 3 levels (i.e., baseline, time0, and
time1)
– Click on Add
– Click on Define
Dialogue Box: Repeated Measures
• Within-Subjects Variables (time):
– Choose the three variables (time0, time1,
time2) the insert them in the correct order.
– Between-Subjects Factor(s):
• Insert the factors that you are interested in.
• In this case, enter in Age.
Dialogue Box: Repeated Measures
(continued)
• Click on Plots
– I recommend that you move the Time factor
into horizontal axis and the other (Age) into
separate lines
– Click Add
– Click Continue
Dialogue Box: Repeated Measures
(continued)
• Click on Post Hoc…
– Choose only factor(s) that have three or more
levels. (e.g., Age).
– Click on Tukey and Dunett’s C (unless your instructor
wants you to use different ones).
– Click on continue
Dialogue Box: Repeated Measures
(continued)
• Click on Option…
– Choose Descriptive statistics
– Homogeneity tests
– Click on continue
• Click on OK
Results Coach
• In many instances there is a results coach
in SPSS for certain types of output.
• In the SPSS output, you can right click on
a table and choose “results coach”
• Results coach, which uses an example
from a different data set, will introduce you
to some of the concepts in the tables.
• Good luck!