Task 5 Flashcards
The samples in ANOVA are
a) dependent
b) independent
independent
In ANOVA normality is assumed, true or false?
true
How can we assume normality?
basic check - histogram
What to do if normality is violated
ensure samples are “large enough” -> CLT
Do we assume equal variances?
Yes
How do we check for equal variances?
Levene’s test
What to do if equal variances assumption is violated?
ensure sample size are “equally large”
Sum of squares?
a) SSG
b) SSW
c) SST
variation
a) between groups
b) within groups
c) total
Mean square?
average variation (variance)
Which sum of squares is for taking error into account?
SSW
Which df takes into df of erro?
DFW
What is a p-value in relation to ANOVA?
the probability of the F calculated or an even larger one if Ho is true
What does a one-way ANOVA enable us to compare?
2 or more independent samples
What is the general ANOVA model?
Yij = μ + ai + Eij
Yij: the individual score of a person j in group i
μ: the effect of constant factors (they are the same in every condition- its what all 3 samples have in common)
ai: the effect of the research factor (independent variable) e.g. no effect ai=0, increase in sales ai=+1
- > to calcualte group effect a1 = μ - ui (ui is the group mean)
Eij: the effect of remaining factors/effect of chance or individual differences aka “error” as they are not explicitly measured
-> to calculate Eij = Yij - ui (ui is the group mean)
The sum of all ai’s always equals
0
The sum of all Eij’s always equals
0
How to calculate how much one person deviates in a population?
Yij - μ
What acts as explained and unexplained variation?
explained - SSG
unexplained - SSW
What is the Ho?
u1=u2=u3 (i.e. no group effect e.g. no influence on advertising)
What is the Ha?
Not all u’s equal
Does accepting Ha mean there is definitely effect from the dependent variable?
No there may be the effect of chance or error
How can we determine normality? (only need to know about histograms)
Explore output
- Skewness = 0 if normal
- > rule of thumb: the skewness of the sample can lie within -1 and +1 to e considered normal
- > positive means skewed right and vice versa - Kurtosis (flatess) = 0 if normal
- > same rule of theumb
- > positive means high point and vice versa
What is always an unbiased estimator of the so-called error variance?
the variance within a group (MSW) is an unbiased estimator of error variance: the dispersion in the population due to remaining factors
What is s^2p equal to in anova?
MSW
What is the most efficient error estimate and why?
MSW/s^2p as they use all participants
What is ALSO an unbiased estimator of error variance if Ho is true?
MSG as if the group means differ there is variance between the groups i.e. sampling error you may have just coincidentally picked more picky people for one sample
What is the average value of the sampling distribution F?
1
What is the expected value of F and why?
MSG and MSW are unbiased estimators of the same thing therefore should equal 1 however they are independent estimates so one time we draw the sample and MSG will be bigger than MSW
When are BOTH MSG and MSW unbiased estimates of error variance?
when Ho is not true
When do we reject Ho according to the F-statistic?
when it is larger than 1
How do we find out which mean is different?
do the 3 possible t-tests and the p-values of each
then conduct bonferroni correction which divides the significance level by the number of comparions
compares the p-values to this p-value
What does ANOVA compare?
The variability within groups vs between groups
The larger the sample, the larger the ___
power
