Friday, August 2, 2013

Stats: Independent ANOVA


 
Last time we looked at how to do a correlational analysis, today we look at the independent ANOVA. This examines whether the means of 2 or more separate samples are significantly different. An example might be a control group vs. a group with intervention A vs. a group with intervention B. Our research question is – are the means for the 3 groups significantly different from each other? The independent variable is condition (control, group A or group B), the dependent variable is the scores on a test. Our null hypothesis is that there will be no difference between the groups. An important point: our ANOVA will only tell us if there is a significant difference present, it will NOT tell us, which groups are different from each other. To find this out, we will need to post hoc tests (more on this later). Let's do an example together. So open SPSS and enter the following data for your samples:

Under Variable view (see tab at bottom of page). It should look like: 

Name
Type
Width
Decimals
Label
Values
Ignore the rest
Condition
numeric
8
0
Condition
*(see below)
Ignore the rest
score
numeric
8
0
Score
None
Ignore the rest

 *For condition, labels: 1= control; 2 = group A, 3 = group B 

Go back to Data View and enter the following: 

Condition
Score
1
5
1
3
1
7
1
2
1
6
2
6
2
7
2
9
2
10
2
8
3
4
3
8
3
7
3
9
3
5

Go to Analyze/ General Linear Model/ Univariate. Move your score variable into Dependent Variable. Move condition into Fixed Factors. Go to Post Hoc (button on right side of variable screen), move condition into right box for post hoc tests. For now, choose Tukey's test (note, there are many different post hoc tests, check a stats book or the SPSS book listed below to choose the correct one for your data). Press continue to return to the variable screen. Go to Options, move Overall and condition to right to display means. Also, check descriptive statistics. Press continue to return to the variable screen. Press ok. 

Your results should look like the following:
 
Descriptive Statistics
Dependent Variable: Score
Condition
Mean
Std. Deviation
N
control
4.60
2.074
5
group A
8.00
1.581
5
group B
6.60
2.074
5
Total
6.40
2.293
15
 
Tests of Between-Subjects Effects
Dependent Variable: Score
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
29.200a
2
14.600
3.946
.048
 
614.400
1
614.400
166.054
.000
condition
29.200
2
14.600
3.946
.048
Error
44.400
12
3.700
 
 
Total
688.000
15
 
 
 
Corrected Total
73.600
14
 
 
 
a. R Squared = .397 (Adjusted R Squared = .296)
 
Multiple Comparisons
Dependent Variable: Score
 Tukey HSD
(I) Condition
(J) Condition
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
control
group A
-3.40*
1.217
.040
-6.65
-.15
group B
-2.00
1.217
.266
-5.25
1.25
group A
control
3.40*
1.217
.040
.15
6.65
group B
1.40
1.217
.503
-1.85
4.65
group B
control
2.00
1.217
.266
-1.25
5.25
group A
-1.40
1.217
.503
-4.65
1.85
Based on observed means.
 The error term is Mean Square(Error) = 3.700.
* The mean difference is significant at the .05 level.
 
What does this mean? There is a significant difference between the 3 groups (see where I marked in blue above). This does not tell which groups are different from each other, to find this out we did Tukey's post hoc tests and found that the control varied significantly from group A (see data marked in yellow above), no other groups differed. So let's write it up as you would in your paper: 

An independent ANOVA was conducted comparing the control group (M = 4.6; SE = .86) to group A (M = 8.0; SE = .86) and group B (M = 6.6; SE = .86). The result (F(2, 12) =3.95, p= .048) indicates that there is a significant difference between the groups and the null hypothesis is rejected. Tukey's post hoc tests examined which groups differed. It was found that only the control group and group A differed (p< .05).

A great resource for SPSS is
Pallant, J. (2013). The SPSS Survival Manual, 5th edition. Open University Press. 

Next time, we will look at repeated measures ANOVA. Do you have an issue or a question that you would like me to discuss in a future post? Send me an email with your ideas. leann.stadtlander@waldenu.edu

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