RAW DATA:
REP TMT pH Plant Fish 1 A 7.3 -2.61 Alive 1 B 7.55 • Dead 1 C 2.91 -3.7 Dead 1 D 2.78 -5 Dead 1 E 2.56 -7 Dead 2 A 7.34 5.1 Dead 2 B 6.68 • Dead 2 C 6.5 -4.3 Dead 2 D 2.16 -7.3 Dead 2 E 2.71 -5.4 Dead 3 A 7.6 2.6 Dead 3 B 6.77 3.6 Dead 3 C 2.86 -3.4 Dead 3 D 2.7 -5.3 Dead 3 E 2.5 -4.6 Dead 4 A 7.15 5.2 Alive 4 B 4.77 -6.7 Dead 4 C 7.02 8.8 Dead 4 D 2.96 • Dead 4 E 2.47 -6.4 Dead 5 A 7.58 3.4 Dead 5 B 6.04 -5.3 Dead 5 C 2.45 -8.2 Dead 5 D 2.99 • Dead 5 E 3.37 -4.4 Dead 6 A 6.83 8.4 Dead 6 B 6.72 -.3 Alive 6 C 6.99 -4.8 Dead 6 D 3.34 -5 Dead 6 E 2.45 -4 Dead 1 F 3.15 • Dead 2 F 2.82 -3.2 Dead 3 F 2.7 -6.9 Dead 4 F 5.97 -6 Dead 5 F 2.67 -4.3 Dead 6 F 2.82 -3.6 Dead
STATISTICAL ANALYSIS:
ANOVA's (Analysis of Variation)
Anytime you have means from a series of experiments, the numbers will be different from each other. The questions is are those numbers statistically different from each other given all the data that was used to calculate them. The variation seen between means can be due to either experimental error (Within groups Source) or from the differences in the treatments we applied (Between groups Source). If it is the former it means that how we did it caused the differences. If it is the latter it means that what we did caused the differences.
Evidence for differences due to treatments occurs if the calculated F-value is greater than the tabular F-value. For this experiment, the tabular F-value for 95% confidence level is 2.53. If the F-test listed in the ANOVA table is greater than this, there is a statistically significance difference between the treatments regarding that factor.
To tell which treatments were statistically different from each other, examine the "Comparison" tables. Here each comparison (A vs B, C vs. D) is listed and, if there is an asterisk by the numbers, those treatments are different from each other. If there is no asterisk, it means that those treatments were not different from each other.
Tmt vs. Final pH:
Analysis of Variance Table
Source: DF: Sum Squares: Mean Square: F-test:
Between groups 5 114.278 22.856 17.12
Within groups 30 40.051 1.335 p = .0001
Total 35 154.329
Model II estimate of between component variance = 3.587
Comparison: Mean Diff.: Fisher PLSD: Scheffe F-test: Dunnett t:
A vs. B .878 1.362 .347 1.317
A vs. C 2.512 1.362 2.835 3.765
A vs. D 4.478 1.362 9.013 6.713
A vs. E 4.623 1.362 9.607 6.931
A vs. F 3.945 1.362 6.994 5.914
B vs. C 1.633 1.362 1.199 2.448
B vs. D 3.6 1.362 5.825 5.397
B vs. E 3.745 1.362 6.303 5.614
B vs. F 3.067 1.362 4.227 4.597
C vs. D 1.967 1.362 1.738 2.948
C vs. E 2.112 1.362 2.004 3.165
C vs. F 1.433 1.362 .923 2.149
D vs. E .145 1.362 .009 .217
D vs. F -.533 1.362 .128 .799
E vs. F -.678 1.362 .207 1.017
Statistically significant differences exist between treatments.
Tmts A and B are different from C, D, E and F.
Tmt C is also different from D, E, and F.
Tmts D, E, F, are not different from each other
Tmt vs. Plant Weight:
Analysis of Variance Table
Source: DF: Sum Squares: Mean Square: F-test:
Between groups 5 342.629 68.526 5.25
Within groups 25 326.312 13.052 p = .002
Total 30 668.94
Model II estimate of between component variance = 10.802
Comparison: Mean Diff.: Fisher PLSD: Scheffe F-test: Dunnett t:
A vs. B 5.857 4.803 1.261 2.511
A vs. C 6.282 4.296 1.814 3.012
A vs. D 9.332 4.803 3.202 4.001
A vs. E 8.982 4.296 3.708 4.306
A vs. F 8.482 4.506 3.006 3.877
B vs. C .425 4.803 .007 .182
B vs. D 3.475 5.261 .37 1.36
B vs. E 3.125 4.803 .359 1.34
B vs. F 2.625 4.991 .235 1.083
C vs. D 3.05 4.803 .342 1.308
C vs. E 2.7 4.296 .335 1.294
C vs. F 2.2 4.506 .202 1.006
D vs. E -.35 4.803 .005 .15
D vs. F -.85 4.991 .025 .351
E vs. F -.5 4.506 .01 .229
Statistically significant differences exist between treatments.
Tmt A is different from B, C, D, E, and F
Tmts B, C, D, E, and F are not different from each other
Tmt vs. Fish Survival:
Analysis of Variance Table
Source: DF: Sum Squares: Mean Square: F-test:
Between groups 5 .583 .117 1.615
Within groups 30 2.167 .072 p = .1863
Total 35 2.75
Model II estimate of between component variance = .007
Statistically significant differences DO NOT exist between treatments.
I cannot explain why there are asterisks showing differences between Tmt A and C, D, E, and F. Ignore them.
REGRESSION CORRELATION
Regressions are an attempt to show how closely related (correlated) two factors are to each other. For example, if the final pH increases is there a direct correlation in the weight of the plant. This is best shown by simply looking at the regression and studying the R-squared value. If this value is close to 1.0 there is a high correlation between the two things being compared. If it is close to 0.0 there is a low correlation between the two things being compared.
Such regression correlations also create nice graphs showing the relationships and compute a regression line (shown graphically and in the calculated Y-intercept and slopes given). This allows you to extrapolate beyond the data points used to compute the line.
Final pH vs. Plant Weight:
Count: R: R-squared: Adj. R-squared: RMS Residual: 31 .71 .504 .487 3.381
Analysis of Variance Table
Source DF: Sum Squares: Mean Square: F-test: REGRESSION 1 337.38 337.38 29.509 RESIDUAL 29 331.56 11.433 p = .0001 TOTAL 30 668.94
R-squared = .5044 indicates a weak correlation as shown in the line on
the graph. Data points around the 6.0 and 7.0 pH's are all over the place
whereas the ones by the low pH's are close to the line.
Final pH vs. Fish Survival:
Count: R: R-squared: Adj. R-squared: RMS Residual: 36 .363 .132 .107 .265
Analysis of Variance Table
Source DF: Sum Squares: Mean Square: F-test: REGRESSION 1 .363 .363 5.176 RESIDUAL 34 2.387 .07 p = .0293 TOTAL 35 2.75
R-squared = .1321 indicates no real correlation as can be seen by the graph.
CONCLUSIONS:
The ANOVA's indicate that adding the different amounts of acid did affect the final pH and the plant weight.
Regarding the final pH, adding the different amounts did lower the pH in treatments C,D,E, and F so that the pH was significantly different from the control and B.
Regarding the final plant weight, the control was significantly better than the other treatments but no difference existed between any of the treatments.
The addition of acid did not affect the survival of the fish as can be seen in the low F-value and the fact that even fish in the control group died.
The Regression correlations indicate, however, that the changes in plant weight had to do with something other than the final pH. There was a slight correlation (.5) but that is not very strong and seemed, according to the graph, to be due primarily to the high correlation between low pH and very low plant weight.
NOW- EXPLAIN ALL THIS, ESPECIALLY IN LIGHT OF WHAT YOU FOUND/PUT IN YOUR INTRODUCTION!!