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ANOVA

ANOVA

1. Aims and Learning Objectives

The aim of this workshop is to use SPSS to carry out an Independent Measures ANOVA and a Repeated Measures ANOVA.

After this workshop you will be able to:

  • Use SPSS to carry out an Independent Measures ANOVA and a Repeated Measures ANOVA.
  • Determine when an Independent Measures ANOVA and a Repeated Measures ANOVA should be used.
  • Produce illustrative and descriptive statistics for both tests.
  • Copy and paste the illustrative statistics into Microsoft Word.

2. What is ANOVA?

ANOVA is an acronym for Analysis of Variance. It is used with parametric levels of data. There are two main/simple types based on experimental design; these are: Independent Measures ANOVA (Between Subjects ANOVA) – (3 groups 1 condition)

Repeated Measures ANOVA (Within Subjects ANOVA) – (1 group 3 conditions).

In both the dependent is the score or condition and the factor affecting them is the group.

Post Hoc Tests

ANOVA can tell you whether there is a significant difference either between subjects or within subjects simultaneously, but it does not tell you where that significance lies. This is important especially when our hypothesis is one-tailed. Descriptive and illustrative statistics can be used to try and infer a direction or difference between each variable. However, Post Hoc tests are able to tell us the significant difference between each of the variables. It is possible for an ANOVA to be significant but for two of the variables to show no significance. There are a number of Post Hoc tests that you can choose from. The one that is more commonly used is the Tukey test for Independent Measures ANOVA and a Bonferroni for a Repeated Measures ANOVA.

3. Scenario 1:

In an experiment, participants were tested to see how many minutes they could juggle assorted office equipment after varying periods of sleep. Column A gives the number of minutes completed and Column B shows groups. Group 1 had not slept for 72 hours, group 2 for 48 hours and group 3 for 24 hours.

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The following tables will now appear in the Output window.

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5. Descriptive Statistics

From the descriptive statistics presented, there appears to be some differences in the mean juggling times between the three levels or groups of sleep deprivation. From the data, one could surmise that sleep deprivation adversely affects participants’ ability to juggle as measured by time. However, to see if this relationship is significant, scrutiny of the ANOVA results needs to be applied.

  • The Tests of Between-Subjects Effects table displays the results of the ANOVA.
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From these results, there is a significant difference between the three sleep deprived groups in their juggling abilities (F(2,12)=6.463, p<.05). Therefore, we can surmise that a greater level of sleep deprivation is significantly related to lesser juggling skills! However we don’t know whether there are significant differences between all groups, or just some.

6. Illustrative Statistics

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7. Post-Hoc Tests

The post-hoc results compare individual groups against each other to see if there are

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significant differences between groups’ means.

For instance, the difference between the mean juggling times for those with 72 hours sleep deprivation and 48 hours deprivation is not significant (p=.873). Conversely, the difference in times between 72 hours without sleep and 24 hours without sleep is significant (p=.015). This significant effect can clearly be seen in the line chart above. The post hoc tests therefore give a more detailed statistical account of the data. We may conclude that sleep deprivation adversely affects juggling ability, but after 48 hours no sleep it does not have significantly greater effects.

8. Scenario 2

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9. Repeated Measures ANOVA

Go to the Analyze pull-down menu and select General Linear Model and then scroll across to GLM -Repeated Measures.

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Follow the procedure outlined earlier for the illustrative statistics. And click OK for the results.

Results

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Again the Descriptive Statistics table displays the standard deviation and mean.

From the descriptive statistics shown, we can see some differences in the mean distance in meters that our participants ran away. It could be inferred that as Luton (the dog) became more agitated the subjects ran away increasingly more on average…. Unsurprisingly! However, we need further analysis to ascertain if these differences are significant…

There are many tables that are superfluous to our needs – scroll down to one shown here. The line you need to look at is the sphericity assumed df, F and p values

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There is a significant difference in the difference run by participants between the three conditions of ‘Luton’

(F(2,8)=9.043, p<.05)

The Illustrative Statistics

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Post Hoc Tests

Whilst there is a significant difference between the three conditions, the descriptive means plotted on the line chart suggests that this significance may not necessarily be between all conditions. We therefore need to look at our Bonferroni post-hoc test to observe where the significant differences lie.

Look at the pairwise comparison table…

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In comparing conditions 1 & 2 (barking and hungry), no significant differences were found in how far our participants ran away p>0.05 (.374).

Conditions 2 & 3 were significantly different from each other p<0.05 (.033) as were conditions 1 & 3 p<0.05 (.016).

10. Non-parametric test equivalents

Where an experimental design requires ANOVA analysis, but the data collected is of a non-parametric ordinal nature, non-parametric ANOVA equivalents should be utilised. These tests follow a simple procedure and can be located using the following instructions.

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A repeated measures ANOVA’s non-parametric equivalent is the Friedman (known to SPSS as a K related samples)

An independent measures ANOVA non-para equivalent is the Kruskal-Wallis (known to SPSS as a K independent samples).

Both require similar determination of dependents and factors as in ANOVAs.

However, the output though not similar, is less complicated and garrulous.

Summary

The design of the experimental scenarios clearly reflects the layout of the data and the choice of ANOVA. Basically, in independent measures ANOVA’s the data includes one condition column of raw scores and one group column consisting of three groups. Repeated measures designs consist of 1 group entering into 3 separate conditions, thus columns. It is these data layouts and clarity over the number of groups and conditions involved that dictate the type of ANOVA analysis. Finally, it is imperative that means are described in order to see differences between groups or conditions.

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