ANOVA Flashcards
We use ANOVA instead of multiple t-tests to control the
Error rate (familywise error)
What type of error can you make from familywise error?
Type 1 - you think there’s an effect when there isn’t
Independent groups ANOVA the level of measurement for the IV is
Nominal/caregoric
Independent ANOVA the level of measurement for the DV is
Interval
ANOVA produces an ………statistic
F
ANOVA compares the
Systematic variance to the unsystematic variance
What does k represent?
Number if groups
Instead of n-1 for different ANOVA what do we have to do???
Take the number of groups I.e. K-3 (3groups)
One way ANOVA assumptions
Interval or ratio measurement for DV
Scores randomly sampled from pops if interest
Scores are independent (participants not in multiple groups)
Scores on DV normally distributed
Homogeneity of variance
What test tests homogeneity of variance?
Levenes
If levenes test is not sig variances are assumed
Equal
If levenes test is sig than variances are assumed
Unequal
If normality violated what non parametric test would u use?
Kruskal-Wallis
If homo of variance is violated what tests would u use?
Brown-forsythe or welch f
What is the grand mean
The mean outcome variable of all groups
The bigger the diff between the group means the bigger the difference between the model and the
Grand mean
Total variance is the
Total sum of squares
Model sum of squares is when the variance is calculated
Between groups
Residual sum if squares is where the variance is calculated
Within groups
ANOVA simply analyses the
Variance in scores to determine the source of that variance
How to calculate SD?
Take each score minus the mean. Add up all and the square them
To get the sum of squares SST total we…
Take each score from the mean, square it and add them all up
How do you calculate sum of squares SSM for the model?
Mean of each group minus the grand mean. Square each of the differences. Then multiply each by the n of participants in that group
How to calculate sum of squares residual SSR?
Sum of squares total SST minus the Model Sum of Squares SSM
How many types of degrees of freedom are there with ANOVA?
3
Between groups ANOVA df calculated by
k-1 (k=n of groups)
Within groups ANOVA df calculated
N-k (k= n of groups, n = total sample size)
How do you work out the within groups df?
N (total sample) - k (n of groups)
To calculate the mean squares we
Take the SSM and divide by its df
How is F Calculated
F = MSM divide by MSR
What happens if F is greater than 1?
Indicates the experimental manipulation has some effect above and beyond the effect of extraneous factors
If F is sig in an ANOVA it indicates that there are
Differences among group means that cannot be attributed to error
Sig F does not tell us
How big these differences are or if they have practical importance
Eta squared is just
R squared
Eta squared tells us about the
Effect size in %
Observed power tells us
The % at which we would expect to get the same result if the study was replicated
Power depends on
Effect size
Alpha level
Sample size
ANOVA tell about
The overall effect. Not between each group etc
Ways to make comparisons btwn groups in an ANOVA
Priori comparisons
Post-hoc comparisons
Priori comparisons are comparisons between group means are devised
Before data is collected and the ANOVA performed
Examples of priori comparisons
Multiple independent groups t-tests
Linear contrasts
Nonferrous t
Sidak test
Most common priori comparison
Bonferroni
What do you do with bonferoni?
Take alpha and divide by 3 (amount of groups)
Post hoc comparisons are conducted between groups
AFTER data collected. Look at means and noted which group means appear diff
Common post-hoc tests
Fischers least sig diff Student-Newman-keuls tests Tukeys The Ryan einot Gabriel welch Q procedure Scheffe test Dunnets test
Post hoc with equal variances assumed generally use
Tukey or REGWQ
Post hoc unequal variances use
Games howell
Factorial designs are diff because they look at 2 or more
IVs
In factorial designs each level of every factor is
Paired with each level of every other factor
Factorial designs allow us to establish if
IVs interact with one another. Does the effect of an IV depend on another IV? Ie does learning time and learning setting depend on each other?
A 2x2 ANOVA has
Two IVs
Factorial designs are also
Mixed designs. Comprise of at least one within subjects factor and at least one between subjects factor. Ie new versus old method
Mean square is the
Sum of squares divided by its degrees of freedom
What is a box whisker plot?
Graphically depicts groups of numerical data through quartiles (used this in 1012 assign)
Box whisker plots don’t show the
Mean
