Lab assignment 4: ANOVA with SPSS
Analysis of Variance, or ANOVA, is a statistic designed to examine, basically, if variability between means of groups is significantly greater than variability of scores within groups. This lab assignment will address the simplest form of ANOVA: a "one-way" ANOVA. In a one-way ANOVA, you have two or more groups (usually 3 or more groups) that represent different levels of an IV. You perform the ANOVA to examine if the means of these groups differ on some continuous DV.
For instance, suppose I am interested in whether professors from different departments differ significantly in terms of how many publications they have. To address this question I find five psychology professors, five engineering professors, and five sociology professors. I then find out how many publications each professor has. The scores are entered in SPSS as follows:
dept pub
1 8
1 9
1 6
1 8
1 10
2 2
2 5
2 9
2 2
2 3
3 0
3 5
3 7
3 5
3 1
Note that "dept" stands for "department," the categorical independent variable. For this variable, 1 represents psychology, 2 represents computer engineering, and 3 represents sociology. The dependent variable, "pub," stand for number of publications.
To conduct a one-way ANOVA on these data, I would do as follows:
1. Click on Analyze on toolbar.
2. Drag to Compare Means
3. Click "One Way ANOVA"
4. Dependent variable is "pub"
5. Factor is "dept"
6. Next, click on "POST HOC."
7. Choose "Tukey" (the most common post-hoc test); hit "continue"
8. Go to "Options"
9. Choose "descriptive"; hit continue.
10. Click paste
11. Go to the .sps file and highlight the relevant commands.
12. Click on "run."
Here's what you'll see:
Descriptives
PUB
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N |
Mean |
Std. Deviation |
Std. Error |
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1.00 |
5 |
8.2000 |
1.4832 |
.6633 |
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2.00 |
5 |
4.2000 |
2.9496 |
1.3191 |
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3.00 |
5 |
3.6000 |
2.9665 |
1.3266 |
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Total |
15 |
5.3333 |
3.1773 |
.8204 |
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ANOVA
PUB
|
|
Sum of Squares |
df |
Mean Square |
F |
Sig |
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Between Groups |
62.533 |
2 |
31.267 |
4.761 |
.030 |
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Within Groups |
78.800 |
12 |
6.567 |
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Total |
141.333 |
14 |
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Multiple
Comparisons
Dependent
Variable: PUB
Tukey HSD
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Mean Difference (I-J) |
Std. Error |
Sig. |
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(I) GROUP |
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(J) GROUP |
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1.00 |
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2.00 |
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4.0000 |
1.6207 |
.071 |
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3.00 |
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4.6000 |
1.6207 |
.037 |
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2.00 |
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1.00 |
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-4.0000 |
1.6207 |
.071 |
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3.00 |
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.6000 |
1.6207 |
.928 |
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3.00 |
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1.00 |
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-4.6000 |
1.6207 |
.037 |
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2.00 |
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-.6000 |
1.6207 |
.928 |
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*
The mean difference is significant at the .05 level.
When reporting results from an ANOVA, you typically report whether the overall F is significant in the text of your Results section. For this example, that would look about like so; this information comes from the second component of the SPSS printout (above):
The one-way ANOVA revealed that number of publications differed significantly as a function of department (F(2, 12) = 4.76, p < .05). For means, standard deviations, and specific contrasts between means that were significant, see Table 1. The Tukey post-hoc test revealed that psychology professors had significantly more publications than sociology professors*. No other specific post-hoc contrasts were significant.
___________________________________________________________
Note that in the text above, the numbers that follow "F" refer to the two different degree of freedom terms. The inclusion of this information gives the reader a sense of the number of groups and the number of participants in each group.
From the first part of the above-SPSS printout, you are primarily interested in the means and standard deviations. I would make a table summarizing these numbers like so:
______________________________________________________
Table 1
Means and Standard Deviations Pertaining to Number of Publications across three Academic Departments
Department Mean Standard Deviation
Psychology 8.20a 1.48
Engineering 4.20 2.95
Sociology 3.60b 2.97
N = 5 for all groups; Means with different subscripts differ significantly from each other using the Tukey post-hoc test.
_________________________________________________________
The subscripts from that table come from the output regarding post-hoc tests. If two particular means are significantly different from each other with the Tukey test, indicate so by using different subscripts to demarcate them.
Assignment:
1. Open up the made-up data. Compute a one-way ANOVA seeing if scores on one of the continuous variables differs as a function of year in college (1 = first-year, 2 = sophomore, 3 = junior, 4 = senior). Be sure to obtain both descriptive statistics and post-hoc statistics (as in example above).
Write up a brief report summarizing (a) the hypothesis being addressed, (b) the nature of the data being examined, (c) the analyses being conducted, (d) the results (including text in the Results section and a table), and (e) implications of the results.
Hand in:
i. the report including the text and a separate table.
ii. The output (.spo) file.
2. ANOVA on data collected in class.
Get into groups of 3 or 4. Think of a hypothesis regarding naturalistic student behavior that would include at least three groups. For instance, you could measure speed of walking among different majors; simply measure walking speed of individuals in specified areas and then ask them their majors. You might even be able to think of something more interesting than that! It would be nice, but not mandatory, if you could come up with a study that was based on a specific hypothesis with some rationale.
A. Conduct a one-way ANOVA to determine if scores on the dependent variable differ significantly across the three conditions of the independent variable. Be sure to obtain both descriptive statistics and post-hoc statistics (as in example above).
B. Write up a brief report summarizing (a) the hypothesis being addressed, (b) the nature of the data being examined, (c) the analyses being conducted, (d) the results (including text in the Results section and a table), and (e) implications of the results.
C. Hand in:
i. the report including the text and a separate table.
ii. The output (.spo) file.
_____________________________________________________________________________
*Please note the hypothetical nature of this example!