One-way ANOVA

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 members of different majors differ from one another in terms of how “cool” they are. To address this question I find five psychology majors, five engineering majors, and five sociology majors. I administer the SUNY Coolness scale to each participant. The scores are entered in SPSS as follows:

group      cool

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

In this case, ‘group’ corresponds to my categorical, independent variable. For this variable, 1 represents psychology major, 2 represents engineering major, and 3 represents sociology major. The continuous scores on the cool scale are such that high scores represent cooler participants.

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 ‘cool’
5. Factor is ‘group’
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:

Table 1
Table 2

Table 3

Table 4

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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 coolness scores differed significantly as a function of college major (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 students were significantly cooler than sociology majors.No other specific post-hoc contrasts were significant.
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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:
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Table 1

Means and Standard Deviations on Coolness Variable across three College Majors

Major                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.
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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 Don’s data (it can be found here). Don was interested in the psychological effects of receiving ideal-self confirming versus ideal-self disconfirming feedback from a psychologist. To manipulate this variable, Don had a several individuals complete a personality measure. He then had an ‘experimenter’ provide them with feedback. The feedback was randomly-assigned to fit one of three categories: confirming, neutral, or disconfirming. In Don’s data file, the variable ‘group’ corresponds to this independent variable. This variable is coded as such: 1 represents confirming feedback, 2 represents neutral feedback, and 3 represents disconfirming feedback.

Don then measured several dependent variables including their total mood scale (indicated as the variable ‘mood_tot’ in his data file). This mood scale was the same one used in my jealousy study (higher scores mean more psychological discomfort).

A. Conduct a one-way ANOVA to determine if total mood scores differ significantly across the three conditions of the group 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 (.spv) 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.

A. Conduct a one-way ANOVA to determine if total mood scores differ significantly across the three conditions of the group 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 (.spv) file.

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