week 9 Flashcards
independent group anova
ANOVA tests the difference between
more than two groups
what is multiple comparison bias
every time you carry out a t-test within the same set of data you increase chance of making type 1 error (inflating alpha)
f-ratio allows us to
determine if two variances are equal
if treatment and error are equal f-ratio will be
1
as treatment variance gets larger in relation to error variance what happens to f-ratio
it exceeds 1 (gets larger)
t/f: the larger the f-ratio, the more statistically significant effect
true
the f-ratio is an
omnibus test
characteristics of single-factor independent group ANOVA
- one independent variable
- one dependent variable
- subjects are randomly assigned
treatment variance is variability due to action of our
independent variable
assumptions of independent ANOVA
- independent random sampling
- normality
- homogenity of variance
anova is based on the assumption that
errors will be normally distributed
when is the grand mean equal to the average of group means
when group sizes are equal
what does no variability within groups suggest
no measurement error within the study
total df formula
N-1 (participants - 1)
treatment effect df formula
k-1 (number of groups -1)
error df formula
N-K or df total - df treatment
f distribution in an anova is
never split
eta square (n^2)
proportion of variance accounted for
how to conduct a pairwise comparison
post hoc test
tukeys HSD
post hoc test that computes multiple t-tests while controlling for the inflation of type 1 error that results from multiple comparissons
what do the letters in q(kv) represent
k= number of treatment groups
v= error DF
look up on table
what does anova allow for
Allows us to partition the total variability of our data into “explained variance” and “unexplained variance”
what kind of ratio is the test statistic anova
f-ratio
bonferroni correction
It is the idea that the inflation of type 1 error is only a problem if the experiment-wise alpha is larger than our tolerance for error
- adjusts the per-comparison alpha so that the “inflates alpha” is not acceptably high
- if you know how many comparisons your making you can just adjust the per-comparison alpha to a value that when multiplied by your number of calculations is not acceptably high
- this is not something we will use
bonferroni leads to a
substantial reduction in your power
variance partitioning
splitting total variance into treatment and error variance
anova null hypothesis
that all means are equal to eachother
what are the characteristics of single anova
- one independent variable (IV)
- the IV must have multiple levels - one dependent variable (DV)
- subjects are randomly assigned to the levels of the IV or random representations of the levels of the IV
- a subject can be a member of only one group or level (ie. groups are independent)
anova is based on the fact that your errors will be
normally distributed
homogeniety of variances
variances are equal to eachother
k =
number of groups
What is the sum of squares for the error effect equal to
The weighted sum of the variances for each treatment group
- weighted by the n-sizes of each treatment group
what is included in anova summary table
- source (column that defines source of variance)
- SS (sums of squares, columns that lists the variance numerators)
- df (column that lists the variance denominators)
- MS (mean squares, the variance estimates, when you divide the SS for a variance component by it’s df you get a mean square)
- F
three sources of variance
treatment, error, total
how to calculate ms
ss/df
how is f ratio in anova calculated
MStreatment/MSerror
when looking up critical values of F the alpha is never
split
what effect size estimate is not useful for independent ANOVA
cohens d
what effects size is useful for anova
eta square (proportion of variance in dependent variable predicted by the independent variable
what kind of analysis is anova
regression analysis
anova predicts interval or ratio data using
categorical (nominal or ordinal) independent variable
when is anova robust to the assumtion of homogeneity of varience
when n sizes are equal
