Week 2: One-way ANOVA, SS, Df, MSE, Fstat, Effect sizes Flashcards
what is the underlying ANOVA equation?
Score = Grand mean + treatment effect + residual error (measurement and individual differences)
Essentially, how does ANOVA break down variance? and what does the comparison of this breakdown produce?
Into 2 parts
- Variance due to treatment
- Error variance
Comparison of these two variances produces the F STATISTIC
What are the assumptions of a between ANOVA?
Homogeneity of variance: SD for all groups is about the same
Normality: error is normally distributed
Independence of observation: truly between design
What are degrees of freedom?
They represent the number of independent pieces of data, or values that are free to vary after a mean has been estimated
Can have total, treatment and error df
What is the calculation for total degrees of freedom?
Number of observation - 1
N-1
What is the calculation for treatment degrees of freedom?
Number of groups - 1
k-1
What is the calculation for error degrees of freedom?
df(total) X df(treat)
k(N-1)
What is mean square?
Variance. Obtained by dividing the sum of squares for each effect by the corresponding degrees of freedom
So for total =SS(total)/Df(total)
Treatment = SS(treat)/Df(treat)
Error = MSE/df(error)
F statistic calculation?
MS(treatment)/MS(error)
What can the F statistic tell us about the null hypothesis?
Because of the way is is calculated, if the null is true these values should be similar and therefore F= close to 1
The further away from 1 F is, the less likely it is that the null is true
How do you set up data in jamovi for a one-way ANOVA?
One column for each IV and the DV
One row for each participant
How do you do a one-way ANOVA in Jamovi?
ANOVA -> ANOVA
Drag DV into the dependent variable box
IV into fixed factors
Descriptives (explore)
What do we do then if the ANOVA output is significant (one-way)?
Click on the post hoc section under analysis
Put IV into the box on the right and click on post hoc desired - typically tukey
Can go into estimated marginal means - get a plot
Reporting a one-way ANOVA?
Means, SD, sample sizes
F(dfb,dfw) = F, p = p
Significant:
Tukey post hoc tests at an alpha level of 0.05…
What is the difference between statistical significance and psychological significance?
Statistical: tells us whether it would occur by chance or not - relates to alpha
Psychological: Asks whether a finding is meaningful - relates to effect size
What are d family effect sizes and what do they do?
Cohens d, hedges g, cohens f
They quantify the size of the difference between means in terms of SD units
What are R family effect sizes and what do they do?
Eta squared, omega squared, adjusted Rsquared
Look at how strongly associated the IV and DV are
Explain cohens D
part of d family so looks at the difference in means in terms of their SD
The further away this is from 0, the larger the effect
What is considered a small, moderate and large cohens d?
- 2 small
- 5 moderate
- 8 large
Is cohens d biased at all? how do you correct this?
It can be biased when you have a smaller sample size (overly generous for treatment effect)
- apply a correction factor. in this case you can use hedges g. It is equivalent to cohens d but accounts for small sample size bias
What is cohens f?
Used when there are 3+ means
1/2 D so a small is 0.1, moderate 0.25, large 0.4
What is eta squared and r squared?
They are squared correlations between the IV and DV
=SS(treatment)/SS(total)
Gives a score between 1 and 0
close to 1 as possible is best but not common in psychology
What does it mean if we have a smaller eta squared?
There is more variation in DV measurement from other things, not IV
How would we interpret, say an eta squared value of 0.477?
Means that 47.7% of the variance in the DV can be explained by the IV
Eta squared and Rsquared can be biased… what can we use instead?
Effect stengths?
Omega squared and adjusted R squared
(eta squared can be biased because the means are sample means derived from a larger population)
Small effect - 0.02, medium - 0.15, large - 0.35
What are confidence intervals?
Interval estimate that attempts to set limits which have a high level of encompassing the true population mean
Explain a 95% confidence interval
If we repeated 100 times, 95% of these will include the true population mean
In relation to confidence intervals, how do we know if the difference in means is statistically significant?
If 0 is outside range (doesn’t contain null hypothesis value)
