MARE 250

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Analysis of Variance (ANOVA) II
MARE 250 Dr. Jason Turner
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Assumptions for One-Way ANOVA
Normality and Equal variance is more difficult to
test with multiple populations Another way to
assess Residual the difference between the
observation and the mean of the sample containing
it IF Normality and equal variances assumptions
are met THEN normal probability plot should be
roughly linear THEN residuals plot should be
centered and symmetric about the x-axis
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Assumptions for One-Way ANOVA
What?
A. Residuals centered and symmetric about the
x-axis normally distributed, equal variances B.
Residuals curved data not normal C. Residuals
cone shaped variances not equal
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Assumptions for One-Way ANOVA
Four-in-one Plot Probability plot, Residuals
versus fitted Histogram, Residuals versus order
Are residuals centered and symmetric?
Are residuals distributed in a random pattern?
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Non-Parametric Version of ANOVA
Kruskal-Wallis
If samples are independent, similarly distributed
data Use nonparamentric test regardless of
normality or sample size Is based upon median of
ranks of the data not the mean or variance
(Like Mann-Whitney) If the variation in mean
ranks is large reject null Uses p-value like
ANOVA Last Resort/Not Resort low sample size,
bad data
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Non-Parametric Version of ANOVA
Kruskal-Wallis Test _ Urchins versus Distance
Kruskal-Wallis Test on _ Urchins Distance
N Median Ave Rank Z Deep
50 3.000000000 208.2 6.90 Middle
75 0.000000000 153.2 1.94 Shallow
150 0.000000000 107.0 -7.08 Overall
275 138.0 H 64.49 DF 2
P 0.000 H 103.96 DF 2 P 0.000
(adjusted for ties)
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When Do I Do the What Now?
Well, whenever I'm confused, I just check my
underwear. It holds the answer to all the
important questions. Grandpa Simpson
If you are reasonably sure that the distributions
are normal use ANOVA Otherwise use
Kruskal-Wallis
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For Friday
Two-Way ANOVA with Urchin data Was last week a
complete waste of time or did we get some
workable data?