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242 (w7 on) - Coggle Diagram
242 (w7 on)
One-way ANOVA
More levels of an independent variable
means we can test multiple and more specific predictions.
All possible predictions when you have only 2 levels of a single independent variable:
Group 1 =/= group 2 (two tailed)
Group 1 >(or <) group 2 (one-tailed)
One example of a prediction you can make when you have 3 levels of your IV:
Group 1 will be significantly greater than Group 3, and Group 2 will be significantly greater than Group 3, and Group 1 will be significantly greater than Group 2.
Group 1 > group 2 > group 3
Why would we want to test more specific predictions?
We want to test the
most specific prediction possible
based on a hypothesis that we have identified from a theory.
More specific predictions
demonstrate greater understanding
of a certain mechanism.
More specific empirical demonstrations are more likely to be contributing meaningfully to our collective understanding and lead to a more refined knowledge of the phenomenon we are investigating.
Why not just do multiple tests?
This would increase our risk of making a
Type 1 error
Why does the Type 1 error rate increase when we do multiple t-tests?
Alpha = 0.5, we accept that there will be a 5% chance of rejecting the null hypothesis when the null is, in fact true.
If the a = .05 for each test we run, the probability of committing one type-1 error increases if we do multiple tests.
E.g. the probability of type 1 error becomes 14.26% when we conduct three t-tests
How can we test a prediction about three groups while keeping the type-1 error rate at .05 & without having to run multiple studies?
One-way ANOVA
(when we reject the null hypothesis when the null hypothesis is true / false positive).
What an ANOVA can tell us:
Whether or not it is more likely that groups come from a common population.
If p is significant, we reject the null hypothesis, it is NOT likely that these groups come from a common population.
The MOST likely explanation is that at least one of these groups is drawn from a different population.
What the one-way ANOVA cannot tell us.
Which groups differ from which other groups and how those groups differ from each other.
We might look at the descriptives to see which groups differ.
One-way ANOVA as a gateway analogy:
If ANOVA is significant:
At least one group is different, so the gate opens. Now you can examine your data further to find out which specific groups are different from which other groups.
If the ANOVA is not significant:
None of these groups are different, so the gate does not open. You do not get to examine your data further to find out what groups are different.