PS2024 Statistics - ANOVA

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what does degrees of freedom actually mean?
how many numbers in a set are free to vary (usually N-1)
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What is the relationship between ** and MS?
MS = **/df
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what does the F ratio actually calculate?
treatment effects
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If there were no treatment effects, what should F be in theory?
1
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What are the 3 assumptions of BS ANOVA?
normality, independence, and homogeneity of variance
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how is homogeneity of variance measured?
the Fmax test.
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How would you report an F ratio formally?
F(df effect, df error) = F, p level, MSE
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Why is the repeated measures ANOVA more sensitive to treatment effects?
because it removes individual difference, which reduces the SSerror
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what are the assumptions of sphericity, necessary for a RM ANOVA?
correlations between treatment conditions should be equal, homogeneity of covariance
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what does homogeneity of covariance mean and how is it calculated?
the differences between pairs of scores should be roughly equal, and a significant Mauchley's test means this is NOT the case.
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What can you do if the assumption of sphericity is violated?
Use the Greenhouse-Geisser correction, which makes the F test more conservative.
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What is the difference between pairwise comparisons and complex comparisons?
complex comparisons use averages to compare
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which post-hoc test only looks at pairwise comparisons?
Tukey
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which post hoc test looks at all possible comparisons?
Scheffe
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which post hoc test looks at only a sub set of comparisons?
Dunnett
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which post hoc test adjusts probability level rather than critical F value?
Bonferroni
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which post hoc test would you typically use for a repeated measures design?
Bonferroni
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why not use a t test to compare means instead of post-hoc testing?
it would be too liberal, because it doesn't use the family-wise type 1 error rate
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what are 2 advantages of using 2-way factorial ANOVA?
more realistic and more economical
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what is a mixed-model ANOVA?
involves between subject and within subject factors
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what is the rule for error terms in mixed-model ANOVA?
any time there is a within-subject component, use the WS error term.
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what is the follow up strategy recommended by Keppel?
test interaction. Significant? test simple effects. Significant? test simple comparisons.
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what is within cell error?
an average of all the variances from all the cells in the design, must be calculated.
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why is statistical significance (p value) not a good measure of treatment effects alone?
F statistics are dependent on sample size
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what do effect sizes measure?
the strength of an effect
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What is the difference between eta and omega effect sizes?
use eta when only referring to your own sample, use omega when you want to generalise
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what is the difference between original and partial effect sizes?
use partial when there is a multi-factorial design
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what is a type 1 error?
false positive
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what is a type 2 error?
false negative
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what does alpha indicate?
the chance of making a type 1 error
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what does beta indicate?
the chance of making a type 2 error
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what is the relationship between power and beta?
power = 1-beta
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what are 3 dangers of underpowered studies?
statistically significant results found less, non-significant results can't be interpreted, and inconsistent results within a field.
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to ensure power in a study, what is the recommendation?
calculate necessary sample size in advance, using alpha, power, and effect size as input.
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What is the relationship between ** and MS?

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MS = **/df

Card 3

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what does the F ratio actually calculate?

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Card 4

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If there were no treatment effects, what should F be in theory?

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Card 5

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What are the 3 assumptions of BS ANOVA?

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