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Suggested answers for
case study 1
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Statistical tests
Testing normality: The two normality tests available in PAST are
Chi-square for samples larger than about 30, and Shapiro-Wilk for samples
smaller than about 50. In our case we can use the Chi-square for all
samples (L1, L2 and L3). For L3 the Shapiro-Wilk test can also be applied,
and both tests are therefore acceptable.
The tests show, in accordance with the visual impression from the
histograms, that L1 and L2 are higly non-normally distributed, while
normality for L3 cannot be rejected.
Non-normality for two of the three samples means that the F, t or ANOVA tests
cannot be used for testing equality. Both the
Kolmogorov-Smirnov test (testing for general equality of the distributions)
and the Mann-Whitney U (testing for equality of the medians) reject the
hypothesis of equality of any pair - admittedly with a relatively high
p value (low significance) in the case of Kolmogorov-Smirnov for L1 and L2.
In short, the samples are all taken from different populations.
Regression and growth rates
At a significance level of 0.05, the null hypothesis of isometric growth
(that is, a=1 in a log-log regression) cannot be rejected for any
of the samples. We therefore assume isometric growth.
Comparison of growth rates
L1, L2 and L3 have slopes of 0.84, 0.82 and 0.91 respectively. The F and t test
rejects equality of all pairs of slopes at very high significance, even
though the slope values are rather close to eachother.
The allometric growth constants do seem to differ from eachother,
supporting the erection of subspecies.