Standardizing the residuals by estimates of standard deviation by segment-group and year leads 
to improvement in both normality and homogeneous variance. However, both non-normality 
and heterogeneous variance remain statistically significant. 
Tests for Normality for standardized residuals 
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Levene’s test for standardized residuals 
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Again the heterogeniety seems to be associated with segments which suggests that the grouping 
algorithm could be improved. 
SPRING: 
Similar to summer results, without standardizing for heterogeneous variance, the In(chl) 
residuals from the Year X Segment model seem to be fairly close to a normal distribution. The 
normality test show significant departure from normality but the p-value is larger than for 
Summer. 
Tests for Normality for un-standardized residuals 
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The Shapiro-Wilk statistic of 0.994 shows that the residuals are very highly correlated with the 
expected residuals from a normal distribution. The normal probability plot shows very high 
concordance between the expected residuals and the observed residuals and like the result for 
summer, the departure from normality appears as outlier points in the extreme tails of the 
sample. 
Levene’s test shows that the data do exhibit heterogeneous variances even in the log-metric. This 
heterogeniety seems to be associated with changing variance over both segments and years. 
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55 
