Comparisons of Water Quality by River Section and Stratum

Comparisons of water quality by river section and stratum

Salinity

Two Way Analysis of VarianceWednesday, July 29, 2009, 9:56:55 AM

Data source: Data 1 in Environmental.SNB

General Linear Model

Dependent Variable: +ln(col(4))

Normality Test:Failed(P < 0.050)

Equal Variance Test:Failed(P < 0.050)

Source of Variation DF SS MS F P

section 2 280.008 140.004 126.401 <0.001

Stratum 1 0.173 0.173 0.156 0.693

section x Stratum 2 3.018 1.509 1.362 0.257

Residual 1044 1156.351 1.108

Total 1049 1493.001 1.423

The difference in the mean values among the different levels of section is greater than would be expected by chance after allowing for effects of differences in Stratum. There is a statistically significant difference (P = <0.001). To isolate which group(s) differ from the others use a multiple comparison procedure.

The difference in the mean values among the different levels of Stratum is not great enough to exclude the possibility that the difference is just due to random sampling variability after allowing for the effects of differences in section. There is not a statistically significant difference (P = 0.693).

The effect of different levels of section does not depend on what level of Stratum is present. There is not a statistically significant interaction between section and Stratum. (P = 0.257)

Power of performed test with alpha = 0.0500: for section : 1.000

Power of performed test with alpha = 0.0500: for Stratum : 0.0500

Power of performed test with alpha = 0.0500: for section x Stratum : 0.104

Least square means for section :

GroupMeanSEM

lower 2.318 0.0608

middl 1.327 0.0568

upper 0.982 0.0644

Least square means for Stratum :

GroupMeanSEM

W 1.529 0.0573

M 1.557 0.0405

Least square means for section x Stratum :

GroupMeanSEM

lower x W 2.361 0.105

lower x M 2.276 0.0608

middl x W 1.2370.0859

middl x M 1.417 0.0744

upper x W 0.989 0.105

upper x M 0.976 0.0744

All Pairwise Multiple Comparison Procedures (Tukey Test):

Comparisons for factor: section

ComparisonDiff of MeanspqPP<0.050

lower vs. upper 1.336 3 21.330 <0.001 Yes

lower vs. middl 0.991 3 16.844 <0.001 Yes

middl vs. upper 0.345 3 5.678 <0.001 Yes

Temperature

Two Way Analysis of VarianceWednesday, July 29, 2009, 10:12:42 AM

Data source: Data 1 in Notebook 3.SNB

General Linear Model

Dependent Variable: ln(x+1)

Normality Test:Failed(P < 0.050)

Equal Variance Test:Failed(P < 0.050)

Source of Variation DF SS MS F P

section 2 0.360 0.180 6.267 0.002

Stratum 1 0.000249 0.000249 0.00869 0.926

section x Stratum 2 0.0234 0.0117 0.408 0.665

Residual 1044 29.955 0.0287

Total 1049 30.518 0.0291

The difference in the mean values among the different levels of section is greater than would be expected by chance after allowing for effects of differences in Stratum. There is a statistically significant difference (P = 0.002). To isolate which group(s) differ from the others use a multiple comparison procedure.

The difference in the mean values among the different levels of Stratum is not great enough to exclude the possibility that the difference is just due to random sampling variability after allowing for the effects of differences in section. There is not a statistically significant difference (P = 0.926).

The effect of different levels of section does not depend on what level of Stratum is present. There is not a statistically significant interaction between section and Stratum. (P = 0.665)

Power of performed test with alpha = 0.0500: for section : 0.846

Power of performed test with alpha = 0.0500: for Stratum : 0.0500

Power of performed test with alpha = 0.0500: for section x Stratum : 0.0500

Least square means for section :

GroupMeanSEM

lower 3.253 0.00978

middl 3.278 0.00915

upper 3.304 0.0104

Least square means for Stratum :

GroupMeanSEM

W 3.279 0.00922

M 3.278 0.00652

Least square means for section x Stratum :

GroupMeanSEM

lower x W 3.261 0.0169

lower x M 3.246 0.00978

middl x W 3.2770.0138

middl x M 3.280 0.0120

upper x W 3.299 0.0169

upper x M 3.308 0.0120

All Pairwise Multiple Comparison Procedures (Tukey Test):

Comparisons for factor: section

ComparisonDiff of MeanspqPP<0.050

upper vs. lower 0.0504 3 5.004 0.001 Yes

upper vs. middl 0.0252 3 2.580 0.162 No

middl vs. lower 0.0252 3 2.662 0.144 No

Dissolved Oxygen

Two Way Analysis of VarianceWednesday, July 29, 2009, 10:06:05 AM

Data source: Data 1 in Notebook 2.SNB

General Linear Model

Dependent Variable: ln(x+1)

Normality Test:Failed(P < 0.050)

Equal Variance Test:Failed(P < 0.050)

Source of Variation DF SS MS F P

section 2 0.490 0.245 1.915 0.148

Stratum 1 3.864 3.864 30.235 <0.001

section x Stratum 2 1.007 0.504 3.940 0.020

Residual 1044 133.424 0.128

Total 1049 140.008 0.133

Main effects cannot be properly interpreted if significant interaction is determined. This is because the size of a factor's effect depends upon the level of the other factor.

The effect of different levels of section depends on what level of Stratum is present. There is a statistically significant interaction between section and Stratum. (P = 0.020)

Power of performed test with alpha = 0.0500: for section : 0.199

Power of performed test with alpha = 0.0500: for Stratum : 1.000

Power of performed test with alpha = 0.0500: for section x Stratum : 0.567

Least square means for section :

GroupMeanSEM

lower 2.031 0.0206

middl 2.039 0.0193

upper 1.985 0.0219

Least square means for Stratum :

GroupMeanSEM

W 1.953 0.0195

M 2.084 0.0138

Least square means for section x Stratum :

GroupMeanSEM

lower x W 1.938 0.0357

lower x M 2.124 0.0206

middl x W 1.9520.0292

middl x M 2.126 0.0253

upper x W 1.968 0.0357

upper x M 2.002 0.0253

All Pairwise Multiple Comparison Procedures (Tukey Test):

Comparisons for factor: Stratum within lower

ComparisonDiff of MeanspqPP<0.05

M vs. W 0.186 2 6.384 <0.001 Yes

Comparisons for factor: Stratum within middl

ComparisonDiff of MeanspqPP<0.05

M vs. W 0.173 2 6.343 <0.001 Yes

Comparisons for factor: Stratum within upper

ComparisonDiff of MeanspqPP<0.05

M vs. W 0.0336 2 1.086 0.443 No

Comparisons for factor: section within W

ComparisonDiff of MeanspqPP<0.05

upper vs. lower 0.0301 3 0.841 0.823 No

upper vs. middl 0.0157 3 0.481 0.938 Do Not Test

middl vs. lower 0.0144 3 0.440 0.948 Do Not Test

Comparisons for factor: section within M

ComparisonDiff of MeanspqPP<0.05

middl vs. upper 0.124 3 4.900 0.002 Yes

middl vs. lower 0.00122 3 0.0531 0.999 No

lower vs. upper 0.123 3 5.315 <0.001 Yes

A result of "Do Not Test" occurs for a comparison when no significant difference is found between two means that enclose that comparison. For example, if you had four means sorted in order, and found no difference between means 4 vs. 2, then you would not test 4 vs. 3 and 3 vs. 2, but still test 4 vs. 1 and 3 vs. 1 (4 vs. 3 and 3 vs. 2 are enclosed by 4 vs. 2: 4 3 2 1). Note that not testing the enclosed means is a procedural rule, and a result of Do Not Test should be treated as if there is no significant difference between the means, even though one may appear to exist.