other ANOVAS
one way anova
design where one variable has been manipulated
ANCOVA
second variable considered and entered as a covariate
Factorial Anova
designs where there are multiple factors (IV's)
must be categorical
DV= single continuous variable
Two way ANOVA
factorial anova -effect of two IVs on a dependant variable
2 IVS manipulated!
Two way independent ANOVA
variables manipulated - different P in each condition
(+) advantages:
(+) ability to analyse interactions. ie drug A and drug B have no individual effects but could interact
separate one-way anovas (one with drug A and B) would not look at interactions
(+)more powerful:
adding factors can help reduce the error term by accounting for variance that would otherwise be unexplained
EXAMPLE
'beer google' effect
'after alcohol had been consumed subjective perceptions of physical attractiveness are inaccurate'
48 students
IVs:
Alcohol consumed (none/2/4)
three levels #
Gender: male and female ( 2levels)
DV
Attractiveness rating
ANALYSIS
output:
look at Levene's test
non significant is good!
F(5,42), 1.53, p=.202
Tests of between subjects effects
look at the 2 iv lines
Gender =F(1,42)=2.03, p=.161
Alcohol: F(2,42), 20.07, p<.001
Interaction: Tests of between subjects effects
gender*alcohol : F(2,42), 11.91, p<.001
'overall the amount of alcohol influenced attractiveness of the mate selected by participants, F(2,42)=20.07, p<.001). there was no main effect of the participants gender on the attractiveness of the selected mate (F(1,42) =2.03, p=.16).
breaking down the main effect : with plots 
look at descriptives : the means !
not every plot will be the same : not every group will be significantly different to the others - got to test this!
breaking down the main effectwith planned and post hoc
one tailed = planned - directional
two tailed - non directional- post hoc
levenes significant:
Games Howell
different number of participants in each condition?
Slightly
very
not sig? #
Gabriel
Hochbergs GT2
NO
how many pairwise comparisons are to be made
Few
Many
Boneferroni
Tukey
IF 3+ CONDITIONS in the IV #
OUTPUT
Multiple comparisons table:
none compared to 2 & 4 Pints
2 compared to none & 4
4 compared to none and 2
use this table and the Descriptive statistics to breakdown the main effect.
signigifactly lower attractiveness after 4 pints compared to after 2 pints:
significantly lower after 4 pints compared to no alcohol
after 4 pints (M-46.56, SD= 14.34) compared to 2 (M=64.69, SD=9.91, p<.001).
after 4 compared to no alcohol (M=63.75, SD=8.47, p<.001)
NO significant difference between 2 pints and no alcohol (p=1.00)
breaking down the interaction effect
hints as to when its significant:
Non-parallel lines- interaction graph - depends on the degree which they are not parrallel
Crossing lines on an interaction graph
doesn't ALWAYS mean significant #
PLOTS
line plots
males attractiveness ratings overall after alocohol levels is lower than women
Have to run separate independant measures T-Tests
split by alcohol consumption- to compare men and women
look at the INDEPENDANT SAMPLES T TESTS
there was a gender difference when 4 pints were consumed (t(14)=-4.78, p<.001
there was no gender difference when non alcohol was consumed (t(14)= 1.543, p=.145.
there was no gender difference when 2 pints were consumed (t(14)= .876 , p=.396
need to apply boneferroni correction
(0.5/3)
significant gender difference- when drinking 4 pints - males have lower attractiveness ratings after 4 pints (m= 35.63, SD= 10.84) than women (m=57.5,SD=7.07)
interaction conclusion:
there was a signifigant interaction between the amount of alcohol consumed and the gender of the person selecting a mate, on the attractiveness of the mate selected (F(2,42)=11.91, p<.001).
This indicates that male and female genders were affected differently by alcohol. specifically, there was a significant gender difference after 4 pints of alcohol consumption (t(14)=-4.78, p <.001).
Males choose signifigantly less attractive mates after 4 pints than females (males M=35.63, SD=10.84); females: M=57.50, SD=7.07). Attractiveness of the chosen mate did not differ between men and women after 2 pints (t(14)=.87, p=.40) or after no alcohol consumption (t(14)=1.54, p=.15)
writeup
Which type of ANOVA did you use? what are your predictions? IV's, how many IVs and how many levels? DV?
Asusmptions met? homogeneity of variance or sphericity- report stats even if NS
first main effect sig? if yes interpret where differences occurred-
if 2 conditions -only MEANS
If 3+ need further contrasts (planned or post hoc)
is the second IV main effect significant? same as before
Is the interaction significant? yes , interpret where those differences occurred. Take one IV do the comparisons across the other IV differ within each level of IV (a)?
Graphically represent any sig findings!
what is the answer to your question? refer to predictions do the findings support or contradict ?
Two way repeated anova
EXAMPLE
Question? are looks or personality more important when choosing a date?
10 p meet 9 actors who differed in looks and personality-rated them on how much they would like to see them again.
2 IVS
Personality , (lots of charisma, average charisma, no charisma)
LOOKS (attractive, average, ugly) 3 levels
2x3 repeated anova
Sphericity
mauchleys test: need to meet assumption for Looks? W=.90, X2 (2) =0.81, p=.667 - assumption met
Personality?W=.85, X2(2)=1.29, p=.524
looks *personality? W=.05, X2 (9) =22.76, p=.008
Significant? so use corrected F test!
if e=<.75 use the GG
If > .75 use Huynh-Feldt
W=.05, x2(9)=22.76, p=.579
Main effect one: look at the within subjects Effects
was there a significant main effect of looks?
Yes F(2,18)=66.44, p<.001
when we ignore all other variables ratings different for attractiveness , average and unattractive dates
LOOK AT EMMS and post hocs to interpret
particpants gabe
MIXED ANOVA
one or more IV's use different participants in different conditions
one or more Ivs use same p's in different conditions
when all IVs have different ps =2 way independent measures ANOVA
all IV's the same p's = 2 way repeated measures ANOVA
same and different Ps= 2 way mixed design anova
FACTORIAL ANOVAS
two way mixed ANOVA
IVs- gender of P? looks of date ? Attractive, average, ugly- ignore charisma
DV- how much participants would like to see the dates again
example -the gender factor -does the importance of looks differ for male and female participants ?
iv 1 - gender = independant groups 1
iv 2 = attractiveness - repeated measure
check for sphericity
check levenes test of equality of measurement
of the repeated IV- needs to be non signifigant- w(2), .960, p=.708
for the independent IV- for each level- attractive - F(1,18),077, p=.785, not signifigant so there is equal error of variences
Between subjects effect
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within subjects effect
ANALYSIS OF THE MAIN EFFECT
tests of within subjects effects
look at the mian effect of looks and the interaction
use the error df and the experimental df
main effect is signifigant
First line if ssphericity assumed or greenhouse-geisser if not - F(2,36)= 423.73, p<.001
interaction F(2,36)=80.43, p<.001
look at the main effect of gender
BETWN SUBJECTS EFFECTS _ F(1,18)=.005, p=.946
also look at the means and descriptive stats- to see the differences- when we ignore all other variables ratings were differenct for attractive average and ugly dates (F(2,36)=423.73,p<.001)
look at estimates table for the differences - participants rated attractive actors (M-=82.1) more highly than average (M=67.7,p<.001) or ugly (M=55.82, p<.001) actors
pairwise comparisons table = the comparison of the different IVs rated average looking actors highly more attractive than the ugly actors (p<.001)
analysis of the interaction
using the means create plots to see the interaction effect
graph suggests that the male and female participants give similar ratings for average looking people- but men rate attractive people higher than women do, whereas women rate ugly actors higher than men do
ratings of different levels of attractiveness were different in men and women (F(2,36)=80.43, p<.001)-look at graph to interpret
both male and female interest decreases as attractiveness decreases , but this decrease is more pronounced for men
breaking down the interaction
could split file by gender
run repeated measures ANOVA on looks for the male and female participants
does each gender show a main effect of looks?
could do Bonferroni corrected post hocs
or run pairwise t tests for each level of looks and correct with boneferroni but this increases family wise error
could also - split file by looks comparing male vs female for 3 levels - independent t tests- m and female in different groups sig = 0,05/ number of comparisons
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write up
is the second iv sig? yes interpret and if 2 -need means if 3 need contrasts p or ph
is the interaction sig? yes interpret differences - take one IV do comparsions across the other IV differ within each level of the IV(a)
is the first main effect sig? if yes interpret where differenves occur- if 2 conditions only need means- if 3 need further contrasts - planned or post hoc
graph signifigcant finsings
were assumptions met ? report stats even if NS homogeneity of varience or sphericity
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what type of ANOVA used? to address the question? predictions? ivs? how many and levels? DV?
three way anova
example : how doess the type and amount of Christmas treats consumed affect the speed which elves and fairies diliever gifts?
9 elves and 9 fairies delievered gifts to 4 separate houses
three independent variables
for 2 of the houses , drank sherry before work- once they had one glass once they had 2 glasses
for two of the houses they ate a mince pie , once no pie and once 2 pies
VARIABLES
three IVS-
Dose
Helper
Type of treat
Mince pies
Sherry
1
2 of each
fairy or elf
within subjects
within subjects
between subjects
DV
time taken to deliver presents to the house in seconds
2 x 2 x 2 three way mixed anova
only two levels so don't need POST HOCS
analysis
only two levels of each repeated IV: only one set of differences for each IV, nothing to compare the variance of those differences against-
ASSUME SPHERICITY
Look at levenes test of equality of variances
needs to be NOT signifigant - here :
time taken to deliever presents after 2 sherry
time taken after 1 mince pie
Time taken to deiliever after 1 Sherry
time taken after 2 mince pies
F(1,16)= 3.797,p=.069
F(1,16),2.953, p=.105
F(1,16)=.204, p=.658
F(1,16)=1.003,p=.331
MAIN EFFECT OF HELPER
look at between- subjects effects
measure_1 table
yes there is a significant effect of the type of helper - main effect- F(1,16)=14.4, p=.002
if we ignore the type of treat consumed and how many of these were consumed , elves and fairies differed in their delievery speeds-
look at estimated marginal means - to interpret
look at table 1. ----- measure3 one means and std error
elf (M=22.16) fairy (M=26.02) , fairies took sig longer to deliever presents than the elves
Tests of Within Subject effects
for the main effects and interactions of the other two within subjects factors
type of treat- F(1,16)= 56.32, p<.001 there was a significant main effect of type of treat-ignore how many treats consumed and type of helper , deleivery time was slower after consuming certain types of treat
interaction of type of treat and helper
no post hoc needed as only have two levels :
mean delievery times higher after sherry (M=28.44) than mince pies (M=19.75) that is independent of the type of helper it took longer to deliever presents after having sherry than after mince pies (EMMS)
there was a significant interaction between the type of treat consumed and whether the helper was an elf or a fairy,
F(1,16)=11.74, p=.003
the effect of type of treat on delivery times was different for elves than for fairies
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look at emms- difference between treats different for fairies and elve
delivery times= after eating mince pies similar for elves (M=19.8) than for fairies (M=19.69) thn after drinking sherry, when fairies (M=32.35) took longer than elves (M=24.52) to deliver presents
Main effect of DOSE
there was a signifigant main effect of dose - F(1,16)=232.08, p<.001
when we ignore the type of treat and whether the helper was an elf or a fairy -delievery time was slower after consuming certain amounts of treats
means : men delievery times were greater after two treats (M=32.96) thn after one treat (M=15.22)
loger to deliever presents after helpers had two treats than onl having one
INTERACTION> dose and helper
There was a signifigant interaction between amount of treats consumed and whetehr tne helper was an elf or fairy F(1,16)=9.60, p=.007
effect of amount of treats on delivery times different for elves than for fairies
interaction emms - difference in delievery times was greater after having two treats in faireies than elves -
Delievery times = after one treat similar times for elves (M=15.09) and fairies (M=15.35than after two treats , when f took (m=36.69) took longer than elves (M=29.22) to deliver presents
interaction between type of treat and dose
there was a sig intercatioi between type and amount of treats consumed on delivery times , F(1,16)=29.95, p<.001
the effect of type of treats on delivery times different depending on amount of treats consumed
difference indelievry times after having two treats compared with one treat greater for sherry than fro mince pies - delievru times more similar after one sherry (M=16.20) and one mince pie (M=14.24) than after two treats when delivery took longer after having sherry (M=40.67) than after having mince pies (M=25.25)
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