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Page Title:
Table L-7. Tests of Assumptions and Parametric Hypothesis Tests on Untransformed and Log10-Transformed Bioaccumulation Exampl... |
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 The data in Table L-6 were analyzed using SAS program BIOACC
(Section L.4.2), and the results are reported in Tables L-7 and L-8. The
probability value for Shapiro-Wilk's Test (2) was >0.01 (a level in Table L-2 for
N = 20, balanced data), indicating no significant departure from normality. If the
raw data had failed the normality test, then a log transformation (3) would be
applied and the Shapiro-Wilk's Test rerun (2). If the log-transformed data still
departed significantly from normality, then nonparametric hypothesis testing
procedures would be performed (Figure L-4b).
The P-value for Levene's Test (4) was >0.10 (a level in Table L-2, n = 5,
balanced data), indicating that assumption of equality of variances need not be
rejected for the raw data. If the variances had been significantly unequal, a log
transformation would have been applied (3) and the tests of assumptions (2,4)
rerun. Data that passed the normality test but failed the test for equality of
variances would be analyzed using a t-test for each dredged sediment - reference
sediment comparison (5).
Table L-7
Tests of Assumptions and Parametric Hypothesis Tests on
Untransformed and Log10-Transformed Bioaccumulation Example
Data
Null Hypothesis: Mean Dredged Material Bioaccumulation Equals Mean Reference
Bioaccumulation1
Test
Test Statistic
a
Conclusion
Normality Assumption:
Shapiro-Wilk's Test
Untransformed data
0.511
0.01
Do not reject
W = 0.958
Log-transformed data
0.921
0.01
Do not reject
W = 0.980
Equality of Variances Assumption:
Levene's Test
Untransformed data
0.134
0.10
Do not reject
F = 2.15
Log-transformed data
0.129
0.10
Do not reject
F = 2.19
Null Hypotheses:
Sediment 1 = Reference
LSD Test
Untransformed data
0.0028
0.05
Reject
t = 3.76
Log-transformed data
0.0011
0.05
Reject
t = 4.45
t-Test (unequal variances)
0.0020
0.05
Reject
Untransformed data
t = 5.30
<0.0001
0.05
Reject
Log-transformed data
t = 7.04
Sediment 2 = Reference
LSD Test
0.0063
0.05
Reject
Untransformed data
t = 3.20
0.0025
0.05
Reject
Log-transformed data
t = 3.84
t-Test (unequal variances)
0.0129
0.05
Reject
Untransformed data
t = 3.33
0.0020
0.05
Reject
Log-transformed data
t = 4.34
Sediment 3 = Reference
LSD Test
0.0688
0.05
Do not reject
Untransformed data
t = 1.65
0.0295
0.05
reject
Log-transformed data
t = 2.20
t-Test (unequal variances)
0.0523
0.05
Do not reject
Untransformed data
t = 2.03
0.0495
0.05
Reject
Log-transformed data
t = 1.98
1
Based on tests of assumptions, appropriate statistical tests of null hypotheses are underlined.
Other test results are included for illustration only.
L31
Appendix L
Statistical Methods
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