Week 3: ANOVA assumptions, power and mean comparison 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
How do you test the assumption of homogeneity of variance?
Levenes test
- if statistically significant the null is rejected. this means that there is a difference somewhere do homogeneity is violated
What do you do if Levenes test is significant?
You can look up density plots to find the culprit
can be violated without grave consequences as long as sample sizes are equal
What can you use to test the assumption of normality?
Shapiro WIlk
If significant, assumption of normality is violated
can also look at histograms, distribution plots, skewness and kurtosis
What happens if normality is violated?
Typically its not a big issue
ANOVA still tends to be robust in terms of normality violations
How do you report that you have used a non-parametric version of an ANOVA?
‘Similar results were found using non-parametric….’
What are quantile-quantile plots?
They look at normality assumption.
Chop data up into how many scores are in each quantile and compare it against what we would expect in that quantile for a normal distribution.
Straight line = perfect
Deviations = bad
What happens to the ANOVA if assumptions are violated?
If you arent confident, can use non-parametric versions of the test
This can then increase confidence in results
What is skewness of data?
Deviations from typical bell curve of data distribution
- asymmetrical
Explain positive and negative data skewness
Negative skew: Have a long tail towards low values in the data (more low scores than expected)
Positive skew: long tail towards high values (more high scores than expected)
No skew value?
0 - perfectly symmetrical
What values are considered moderately skewed?
Between -1 and -0.5
or
Between 0.5 and 1
What values are considered highly skewed?
(-/+) 1+
Skewness in Quantile-Quantile plots?
If data drops below the line, it is skewed to the left or negatively skewed
If data rises above the line, it is skewed to the right or is positively skewed
What is kurtosis?
It is a measure of tailedness in data distribution curve
how light or heavy-tailed the data is
What is leptokurtic distribution (kurtosis)?
People scoring closer to the average (light tailed)
What is platykurtic distribution (kurtosis)?
Wider spread of scores so maybe more heavy tailed
What is the optimal kurtosis value?
It is reported in terms of how much excess skew there is - so the optimal would be 0!!!
How do you know when to reject normality in terms of kurtosis?
You are given a standard error as well as a skewness value - these can be used to determine a z-score
z score = Value of kurtosis/standard error
If z score is less than -2 or more than +2, reject normality
What is power?
The probability of correctly rejecting the null
finding a difference between means if it is there
What is power associated with?
Type 2 errors
when do type 2 errors typically occur?
when alpha level is too strict
or
outlier increases error variance so hard to see treatment effect clearly