Two-Way Factorial ANOVA Flashcards
what is two-way ANOVA?
one way ANOVA extended to account for other sources of systematic variation
if 2 types of coffee are brewed (caffeinated and decaf). each is treated with no sweetener, artificial sweetener, or sugar. 12 ppl are randomly and equally assigned to one of the 6 formulations. resting HR is measured after the cup is finished.
what test should be run?
what is the DV? IV?
what are the factors? levels?
a two way factorial ANOVA should be run
DV: HR
IV: caffeination and sweetener
Factor A: caffeination
levels: caf and decaf
Factor B: sweetener
levels: no sweetener, artificial sweetener, sugar
what are the two sources of systematic deviation from the coffee example?
caffeination and sweetener type
what are the two questions to be asked with the coffee example?
what is the effect of caffeination AND sugar on HR?
does the increase caused by caffeine and sugar equal the “sum of the parts”, caffeine and sugar effect?
if the lines of a graph are parallel, what does this mean?
the effect is the sum of the parts
no interaction
if the lines of a graph look like they may intersect if extended, what does this mean?
there is an interaction bw the factors
the effect is NOT a sum of its parts
what is an interaction in two way factorial ANOVA?
it implies that the differences among levels of one factor depends on the level of the other factor
2 IV interact with each other and effect the DV
what are some examples of interactions?
the dif in pain relief bw 2 brands of pain meds may also depend on the medium (gelcap or tablet)
dif in consumption of healthy food among socioeconomic classes (low, middle, upper) may depend on proximity to grocery stores (near or far)
when there are 2 factors that need to be tested, what is the test we use>
two way factorial ANOVA
t/f: each factor in factorial ANOVA has multiple levels
tre
factor A has __ levels and is represented by ___
a, tau
factor B has __ levels and is represented by ___
b, beta
the interaction will have _____ levels and is represented by ___
a x b, tau-beta
what distribution does the two way factorial ANOVA use?
F distribution
what are the assumptions of the two way factorial ANOVA?
independence
normality
homogeneity of variance
what are the hypotheses of the two way factorial ANOVA?
factor A:
- H0: tau1=tau2=…=taua=0 (groups defined by factor A have =means)
- Ha: some taui are not 0 (groups defined by factor B have dif means)
factor B:
- H0: beta1=beta2=…=betab=0 (groups defined by factor B have = means)
- Ha: some betai are not 0 (groups defined by factor B have dif means
interaction term:
- H0: tau-beta1=tau-beta2=…= tau-betaab=0 (no interaction bw factor A and factor B)
- Ha: some tau-betaab are not 0 (interaction bw factor A and factor B)
how many hypotheses are there for two way factorial ANOVAs?
3: 1 about 1 IV, 1 about the other IV, one about the interaction term
what does the factor A null hypothesis say?
no differences among factor A levels
what does the factor B null hypothesis say?
no differences among factor B levels
what does the interaction term null hypothesis say?
there is no interaction
what is the decision rule for two way factorial ANOVA?
1) look at the interaction 1st
- if interaction is detected (p less than or equal to 0.05), conduct multiple comparisons on the interaction levels (DO NOT consider the main effects)
- if interaction is not detected (p>0.05), go to step 2
2) test the main effects (factor A and factor B)
- if factor A means differ (p is less than or equal to 0.05), multiple comparisons on factor A levels
- if factor B means differ (p less than or equal to 0.05), multiple comparisons on factor B levels.
- if mean from neither differ (p>0.05), do nothing
if the lines on a graph are parallel, is there an interaction?
nope
if the lines on a graph look like they will intersect if extended, is there an interaction?
yes
if a graph shows 2 horizontal parallel lines, what does this mean?
no interaction
factor A differences
if a graph shows 2 upward diagonal parallel lines, what does this mean?
no interaction
factor B differences
if a graph shows 2 parallel horizontal lines very close/overlapping, what does this mean?
no interaction
no A or B differences
if a graph shows 2 lines forming an X, what does this mean?
interaction
opposite differences
if a graph shows 2 lines increasing, what does this mean?
interaction
increasing differences (AB)
if a graph shows 2 lines, one increasing and one decreasing, what does this mean?
interaction
increasing differences (A)
if a graph shows 2 lines, one going up, and one horizontal, what does this mean?
interaction
increasing differences (B)
an investigator is simultaneously studying the impact of an experimental drug and a relaxation program on insomnia. they randomly and equally assign 80 subjects diagnosed w/insomnia to receive (1) the experimental drug or a placebo, and (2) to participate in the relaxation program or not. after 1 week of Rx, they measure the hours of sleep experiences by each subject. the interaction p value is 0.005, the drug p value is 0.000, and the relax p value is 0.005.
what is the DV? IV?
what is factor A and B?
if there significance in the interaction term?
do we have to look at the main effects?
what is the conclusion?
do we have to run post hoc comparisons?
DV: hours of sleep
IV: drug and relax
factor A: drugs w/levels experimental or placebo
factor B: relaxation program, w/levels received or not received
p<0.05=significance
we do not have to look at the main effects
conclusion: the interaction bw drug and relax program had a significant effect on insomnia (F (1,76)=8.20, p=0.005)
run post hoc
if there are 4 groups, how many pairing do we have?
3+2+1=6 pairing
what is the bonferroni correction for 4 groups?
0.05/6=0.0083
how do we report the results of a two way factorial ANOVA?
a 2 way factorial ANOVA was conducted to examine the effect of [factor 1] and [factor 2] on [DV]
there [was/was not] a statistically significant interaction bw the effects of [factor 1] and [factor 2] on [DV] (F (interaction DF, error DF)=[f-value], p=[p-value])
results indicated that [factor 1/2] [did/did not] have a statistically significant effect on [DV] (F (main effects DF, error DF)=[f-value], p=[p-value]).
post hoc if needed
if a sample data set has 1 group, what is the parametric test?
one sample t test
if a sample data set has 1 group, what is the nonparametric test?
wilcoxon signed rank test
if a sample data set has 2 related groups, what is the parametric test?
paired samples t test
if a sample data set has 2 related samples, what is the nonparametric test?
wilcoxon signed rank test
if a sample data set has 2 independent samples, what is the parametric test?
independent samples t test w/equal variances
independent samples t test w/unequal variances
if a data set has 2 independent samples, what is the nonparametric test?
Mann Whitney U test
if a data set has more than 2 independent samples, what is the parametric test?
one way ANOVA
if a dataset has more than 2 independent samples, what is the nonparametric test?
Kruskal Wallis test
if a data set has more than 2 related samples, what is the parametric test?
repeated measures ANOVA
if a data set has more than 2 related samples, what is the nonparametric test?
Friedman test
if a data set has 2 IVs and independent samples, what is the parametric test?
two way factorial ANOVA
if a data set has 2 IVs and independent samples, is there a nonparametric test?
not that we are learning :)
what are the assumptions tests for one sample t tests and WSR tests?
SW
what are the assumptions tests for paired samples t test and WSR test?
SW
what are the assumptions tests for independent samples t test for equal and unequal variances and MWU?
SW and Levene’s
what are the assumptions tests for one way ANOVA and Kruskal Wallis?
SW and Levene’s
what are the assumptions tests for repeated measures ANOVA and Friedman test?
QQ plot
what are the assumptions tests for factorial ANOVAs?
Mauchly’s test of sphericity
