Week 2 Flashcards
What is the model for an ANOVA?
score = grand mean + treatment effect + residual error
What is residual error?
Differences unique to each person and experimental noise
What are the 3 assumptions of ANOVA?
- homogeneity of variance
- normality
- independence of observation
What two variances produce the F statistic in an ANOVA?
- variance due to the effects of treatment
2. error variance
What is the sum of squares, being the first step toward the calculation of each part of the variance?
A sum of squares is the sum of the squared deviation about some mean, or some multiple of that.
What are the degrees of freedom?
Number of things that were used in the estimation of a particular value.
What is the sum of squares due to total scores?
The difference of a value against the grand mean, squared. Do this for all values in a SS total.
What is a sum of squares due to treatment?
The difference between the overall treatment score against the grand mean, squared.
What is a sum of squares due to the error (overall error)?
Difference between the SS total and the SS treatment is the SS error - the overall amount of unexplained error in the study.
What is the definition of variance?
The SS divided by the degrees of freedom.
What is the df total?
number of observations - 1
What is the df treatment?
number of groups - 1
What is the df error (overall error)?
df total-df treatment.
The bit “left over” is the unexplained variation
What is the mean square?
variance
how is the total mean square variance obtained?
SS total/df total
how is the treatment mean square variance obtained?
SS treat/df treat
How is the total mean square variance obtained?
SS error/df error
How is the F statistic calculated?
the numerator = df treat
divided by
the denominator = df error
Both MS treat and MS error are estimates of the population variance.
While MS error is always a ___ ____
MS treat is _____ ___ _ _ _ _
- true estimate
2. only a true estimate if Ho is true
The further away from 1 F is, the:
less likely it is that the Ho is true
If Ho is true, what does this mean for MS treat and MS error should be:
similar and F should be close to 1
What is one way to see if our F ratio is critical (significant)
We have to check out F ratio against a sampling distribution of F ratios to find the critical value to evaluate how large the F ratio has to be without rejecting the null hypothesis. If F is bigger than critical value, then we can say it’s less than 5% likely that results occurred due to chance (reject the null).
What does the critical value (to determine if the F statistic is great enough to reject the null) vary depending on?
the dfs, the alpha level of interest and direction of hypothesis
What is one way to look at statistical significance?
p value
What is one way to look at psychological significance?
The effect size
What type of effect size expresses the difference between means in terms of the size of the standard deviation of scores in your study?
Cohen’s (and Hedges’ g)
Is Cohen’s d bias? If so, when?
Yes it is positively bias (overly generous) when you have a small sample size.
What is a rough “minimum” for sample size for using Cohens’ d?
100
If you have a small sample size and are worried about Cohens’ d, what’s one way to take the small sample into account so that the data can still be used?
Hedges g - is practically equivalent but has a correction factor to account for the bias from small samples.
Can you interpret hedges g and cohens d in exactly the same way?
pretty much
Can Cohen’s d go above 1?
Yes, it can go way above 1.
What are the R effect sizes?
measures the strength of association between the DV and IV. i.e., how much of the variation in your scores, are associated/due to variation in your IV.
How do you calculate eta squares?
SS treatment divided by SS total
what would an R square score of 0.477 tell us?
That 47.7% of the variance in the DV can be explained by the IV.
In a perfect experiment, what would the R squared value be?
As close to 1 as possible (all score variation is associated with the IV).
