Week 3 Lecture 3 - Independent 1-way ANOVA Flashcards
What does ANOVA mean?
analysis of variance
When is an ANOVA test used?
when we have 1 IV with more than 2 levels
What does an ANOVA test estimate?
whether the pop. means under the different levels of the IV are different
based on sample means
How is ANOVA an extension of the t-test?
F = t^2
What is the familywise error rate?
the probability that at least 1 of a “family” of comparisons, run on the same data, will result in a type 1 error
What does the familywise error rate provide?
a corrected sig. level, expressing the probability of making a type 1 error
How is the familywise error rate calculated?
a’ = 1 - (1 - a)^c
a = level of confidence we’re working to for each comparison (normally = .05)
c = number of comparisons
what type of test is the ANOVA test?
omnibus test
What is the f ratio?
variance between IV levels / variance within IV levels
If F values are close to 0 what does this mean?
small variance BIVL relative to WIVL
If F values are further from 0 what does this mean?
large variance BIVL relative to WIVL
What contributes to variance BIVL?
- manipulation of IV
- individual difference
- experimental error (random and constant error)
What contributes to variance WIVL?
- individual differences
- experimental error (random error)
How do you calculate the grand mean?
Sum of IV level means, divided by the number of IV levels
How is variance partitioned?
1.) calc means for each IV level
2.) calc the grand mean –> sum of IV level means divided by no. of IV levels
3.) Calc WIVL variance –> sum of squared differences between individual values and the corresponding IV level means
4.) calc BIVL variance –> sum of squared differences between each IV level mean and the grand mean
What are the assumptions for an independent 1-way ANOVA test?
- normality
- homogeneity of variance
- equivalent sample size
- independence of observations
If the assumptions for an independent 1-way ANOVA test are seriously violated, what should you do?
use non-parametric equivalent –> Kruskai Wallis Test
How is an F stat reported?
F(dfM, dfR) = f-value, p = p-value
If homogeneity is violated in the I1-W ANOVA, what should you do?
use Welch’s F test
What is Welch’s F test?
DF adjusted to be more conservative
gives slightly higher p-value
How do you report a Welch f value?
F(dfM, dfR) = f-value, p = p-value (Welch)
What is the Model Sum of Squares (SSm)?
sum of squared differences between IV level means and grand mean (BIVL variance)
What is the Residual Sum of squares (SSr)?
sum of squared differences between individual values and corresponding IV level mean (WIVL variance)
How do you calculate SSt?
SSm + SSr
How do you calculate Mean Squared m (MSm)?
SSm / DFm
How do you calculate Mean Squared r (MSr)?
SSr / DFr
How do you calculate an F stat?
MSm / MSr
How many DOF do you need in I1-W ANOVA?
2
1 for BIVL and 1 for WIVL
How do you cal DOF for BIVL in I1-W ANOVA?
k-1 (k = no. of IV levels)
How do you cal DOF for WIVL in I1-W ANOVA?
N - k
What is a post-hoc test?
- used to assess which IV level mean pairs differ
- only used when f-value is sig.
- ran as a t-test but includes correction for multiple comparisons
- there are a choice of corrections, they vary in their risk of Type 1 and Type 2 error
What is the error risks and classifications for the Tukey Honestly Significant Difference (HSD)?
Type 1 error risk = low
Type 2 error risk = high
Classification = “reasonably conservative”
What are the 2 effect sizes that are calculated for ANOVA?
partial ETA^2
Cohens d
What is partial ETA^2?
how much variance in the DV is explained by the manipulation of the IV overall
What are the effect sizes for partial ETA^2?
small > .01
medium > .06
large > .14
How do you calculate partial ETA^2?
SSm / (SSm + SSr)
When do you calculate Cohen’s D?
for each pair in post-hoc tests
