Aquatic Toxicology Lab 10 Pimephales promelas Larval Survival and Growth Test Data Analysis 1. Complete test initiated last week 1. make day 7 observations 2. prepare fish for drying 3. weigh aluminum fish drying boats 4. begin 24 hour drying process 5. data will be emailed to you 2. Data Analysis 1. Hypothesis testing for statistical differences between control and treatments for growth and survival 2. We will use the same program, Toxstat, that was used for the C. dubia chronic data analysis 3. Please refer to the flowcharts on pages 70 and 83 in the handout for lab 9 as we proceed 1. These should look somewhat familiar to you 1. Normality test 1. Shapiro-Wilk s 2. Homogeneity of Variance test 1. Bartlett s 3. Parametric ANOVA multiple range tests 1. Dunnett s 2. t-test with Bonferroni adjustment 4. Non-Parametric ANOVA multiple range tests 1. Steel s Many-One Rank test 2. WilcoxonRank Sum test with Bonferroni adjustment 4. Survival analysis (p. 70) 1. Hypothesis testing to determine NOEC/LOEC 2. Analysis is performed on proportion surviving in each replicate 1. due to the replicated design, appropriate hypothesis testing procedure is Analysis of Variance 1. data must be transformed using arc sine square root transform 1. data are entered like the reproduction data from a C. dubia test 1. remember we are not using Fisher s test for survival 2. done in an attempt to meet normality assumption for parametric ANOVA 2. test for normality and equality of variances on transformed data 3. based on the distribution of data select the appropriate ANOVA technique using the flow chart on page 70 4. concentrations above the NOEC for survival are not included in the NOEC/LOEC test for growth differences 5. Growth analysis (p.83) 1. Again, hypothesis testing is used to determine the NOEC/LOEC for growth. 1. Analysis performed on the mean weight of surviving individuals in each replicate 2. due to the replicated design, appropriate hypothesis testing procedure is Analysis of Variance 1. No data transformation
2. exclude concentrations above the NOEC for survival 3. test for normality and equality of variances on transformed data 4. based on the distribution of data select the appropriate ANOVA technique using the flow chart on page 70 5. concentrations above the NOEC for survival are not included in the NOEC/LOEC test for growth differences 6. Perform data analysis 1. data set from page 68 in laboratory 9 handout 2. 2 included practice data sets Fathead Minnow Practice Set 1 Pimephales promelas Survival n=10 % Effluent Replicates Control 100 100 100 100 6.25 100 100 100 100 12.5 100 100 100 100 25 100 90 100 100 50 50 50 50 70 100 20 40 30 30 Pimephales promelas Dry Weight %Effluent Replicates 1 2 3 4 Control.725.737.767.705 6.25.598.645.569.637 12.5.599.578.569.589 25.518.508.524.525 50.404.414.438.442 100.315.274.298.301
Fathead Minnow Practice Set 2 Pimephales promelas Survival n=10 % Effluent Replicates Control 100 100 100 100 6.25 100 100 100 100 12.5 90 100 100 100 25 90 90 100 100 50 90 90 100 90 100 50 40 50 30 Pimephales promelas Dry Weight %Effluent Replicates 1 2 3 4 Control.625.637.567.605 6.25.598.645.589.637 12.5.601.589.599.604 25.598.578.534.555 50.504.514.498.472 100.345.354.298.301
Example Set 1 Output Fish Example Set 1 Survival File: ex1surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) Chi-square test for normality: actual and expected frequencies INTERVAL <-1.5-1.5 to <-0.5-0.5 to 0.5 >0.5 to 1.5 >1.5 EXPECTED 1.608 5.808 9.168 5.808 1.608 OBSERVED 0 2 20 2 0 Calculated Chi-Square goodness of fit test statistic = 21.0074 Table Chi-Square value (alpha = 0.01) = 13.277 Data FAIL normality test. Try another transformation. Warning - The first three homogeneity tests are sensitive to non-normal data and should not be performed. Fish Example Set 1 Survival File: ex1surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) Shapiro - Wilk s test for normality D = 0.076 W = 0.844 Critical W (P = 0.05) (n = 24) = 0.916 Critical W (P = 0.01) (n = 24) = 0.884 Data FAIL normality test. Try another transformation. Warning - The first three homogeneity tests are sensitive to non-normal data and should not be performed. Fish Example Set 1 Survival File: ex1surv.txt Transform: ARC SINE(SQUARE ROOT(Y))
Hartley s test for homogeneity of variance Bartlett s test for homogeneity of variance These two tests can not be performed because at least one group has zero variance. Data FAIL to meet homogeneity of variance assumption. Additional transformations are useless. Fish Example Set 1 Survival File: ex1surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) STEEL S MANY-ONE RANK TEST - Ho:Control<Treatment TRANSFORMED RANK CRIT. GROUP IDENTIFICATION MEAN SUM VALUE df SIG ----- -------------------- ----------- ------- ------ ----- --- 1 Control 1.412 2 6.25% 1.412 18.00 10.00 4.00 3 12.5% 1.412 18.00 10.00 4.00 4 25% 1.371 16.00 10.00 4.00 5 50% 0.837 10.00 10.00 4.00 * 6 100% 0.577 10.00 10.00 4.00 * Critical values use k = 5, are 1 tailed, and alpha = 0.05 Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Chi-square test for normality: actual and expected frequencies INTERVAL <-1.5-1.5 to <-0.5-0.5 to 0.5 >0.5 to 1.5 >1.5 EXPECTED 1.072 3.872 6.112 3.872 1.072 OBSERVED 0 4 6 6 0 Calculated Chi-Square goodness of fit test statistic = 3.3198 Table Chi-Square value (alpha = 0.01) = 13.277 Data PASS normality test. Continue analysis.
Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Shapiro - Wilk s test for normality D = 0.006 W = 0.970 Critical W (P = 0.05) (n = 16) = 0.887 Critical W (P = 0.01) (n = 16) = 0.844 Data PASS normality test at P=0.01 level. Continue analysis. Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Hartley s test for homogeneity of variance Calculated H statistic (max Var/min Var) = 20.57 Closest, conservative, Table H statistic = 120.0 (alpha = 0.01) Used for Table H ==> R (# groups) = 4, df (# reps-1) = 3 Actual values ==> R (# groups) = 4, df (# avg reps-1) = 3.00 Data PASS homogeneity test. Continue analysis. NOTE: This test requires equal replicate sizes. If they are unequal but do not differ greatly, Hartley s test may still be used as an approximate test (average df are used). Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION
Bartlett s test for homogeneity of variance Calculated B1 statistic = 5.98 Table Chi-square value = 11.34 (alpha = 0.01, df = 3) Table Chi-square value = 7.81 (alpha = 0.05, df = 3) Data PASS B1 homogeneity test at 0.01 level. Continue analysis. Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Cochran s test for homogeneity of variance Calculated G statistic = 0.5808 Table value = 0.78 (alpha = 0.01, df = 4, 4) Table value = 0.68 (alpha = 0.05, df = 4, 4) Data PASS homogeneity test at 0.01 level. Continue analysis. NOTE: Cochran s test is most powerful for detecting one large deviant variance. Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Levene s test for homogeneity of variance ANOVA TABLE SOURCE DF SS MS F Between 3 0.001 0.000 3.508 Within (Error) 12 0.001 0.000 Total 15 0.003
Critical F value = 3.49 (0.05,3,12) Since F > Critical F REJECT Ho: All equal Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION STEEL S MANY-ONE RANK TEST - Ho:Control<Treatment TRANSFORMED RANK CRIT. GROUP IDENTIFICATION MEAN SUM VALUE df SIG ----- -------------------- ----------- ------- ------ ----- --- 1 Control 0.734 2 6.25% 0.612 10.00 10.00 4.00 * 3 12.5% 0.584 10.00 10.00 4.00 * 4 25% 0.519 10.00 10.00 4.00 * Critical values use k = 3, are 1 tailed, and alpha = 0.05
Example Set 2 Output Fish Example Set 2 Survival File: ex2surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) Chi-square test for normality: actual and expected frequencies INTERVAL <-1.5-1.5 to <-0.5-0.5 to 0.5 >0.5 to 1.5 >1.5 EXPECTED 1.608 5.808 9.168 5.808 1.608 OBSERVED 0 4 15 5 0 Calculated Chi-Square goodness of fit test statistic = 7.6011 Table Chi-Square value (alpha = 0.01) = 13.277 Data PASS normality test. Continue analysis. Fish Example Set 2 Survival File: ex2surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) Shapiro - Wilk s test for normality D = 0.095 W = 0.954 Critical W (P = 0.05) (n = 24) = 0.916 Critical W (P = 0.01) (n = 24) = 0.884 Data PASS normality test at P=0.01 level. Continue analysis. Fish Example Set 2 Survival File: ex2surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) Hartley s test for homogeneity of variance Bartlett s test for homogeneity of variance
These two tests can not be performed because at least one group has zero variance. Data FAIL to meet homogeneity of variance assumption. Additional transformations are useless. Fish Example Set 2 Survival File: ex2surv.txt Transform: ARC SINE(SQUARE ROOT(Y)) STEEL S MANY-ONE RANK TEST - Ho:Control<Treatment TRANSFORMED RANK CRIT. GROUP IDENTIFICATION MEAN SUM VALUE df SIG ----- -------------------- ----------- ------- ------ ----- --- 1 Control 1.412 2 6.25% 1.412 18.00 10.00 4.00 3 12.5% 1.371 16.00 10.00 4.00 4 25% 1.331 14.00 10.00 4.00 5 50% 1.290 12.00 10.00 4.00 6 100% 0.709 10.00 10.00 4.00 * Critical values use k = 5, are 1 tailed, and alpha = 0.05 Chi-square test for normality: actual and expected frequencies INTERVAL <-1.5-1.5 to <-0.5-0.5 to 0.5 >0.5 to 1.5 >1.5 EXPECTED 1.340 4.840 7.640 4.840 1.340 OBSERVED 0 6 7 7 0 Calculated Chi-Square goodness of fit test statistic = 3.9756 Table Chi-Square value (alpha = 0.01) = 13.277 Data PASS normality test. Continue analysis.
File: ex2grow.txt Transform: NO TRANSFORMATION Shapiro - Wilk s test for normality D = 0.009 W = 0.964 Critical W (P = 0.05) (n = 20) = 0.905 Critical W (P = 0.01) (n = 20) = 0.868 Data PASS normality test at P=0.01 level. Continue analysis. Hartley s test for homogeneity of variance Calculated H statistic (max Var/min Var) = 22.24 Closest, conservative, Table H statistic = 151.0 (alpha = 0.01) Used for Table H ==> R (# groups) = 5, df (# reps-1) = 3 Actual values ==> R (# groups) = 5, df (# avg reps-1) = 3.00 Data PASS homogeneity test. Continue analysis. NOTE: This test requires equal replicate sizes. If they are unequal but do not differ greatly, Hartley s test may still be used as an approximate test (average df are used). Bartlett s test for homogeneity of variance Calculated B1 statistic = 5.47
Table Chi-square value = 13.28 (alpha = 0.01, df = 4) Table Chi-square value = 9.49 (alpha = 0.05, df = 4) Data PASS B1 homogeneity test at 0.01 level. Continue analysis. Cochran s test for homogeneity of variance Calculated G statistic = 0.3297 Table value = 0.70 (alpha = 0.01, df = 5, 4) Table value = 0.60 (alpha = 0.05, df = 5, 4) Data PASS homogeneity test at 0.01 level. Continue analysis. NOTE: Cochran s test is most powerful for detecting one large deviant variance. Levene s test for homogeneity of variance ANOVA TABLE SOURCE DF SS MS F Between 4 0.001 0.000 2.171 Within (Error) 15 0.002 0.000 Total 19 0.003 Critical F value = 3.06 (0.05,4,15) Since F < Critical F FAIL TO REJECT Ho: All equal
ANOVA TABLE SOURCE DF SS MS F Between 4 0.038 0.010 16.802 Within (Error) 15 0.009 0.001 Total 19 0.047 Critical F value = 3.06 (0.05,4,15) Since F > Critical F REJECT Ho: All equal DUNNETT S TEST - TABLE 1 OF 2 Ho:Control<Treatment TRANSFORMED MEAN CALCULATED IN GROUP IDENTIFICATION MEAN ORIGINAL UNITS T STAT SIG ----- -------------------- ----------- ------------------ ------ --- 1 Control 0.609 0.609 2 6.25% 0.617 0.617-0.518 3 12.5% 0.598 0.598 0.607 4 25% 0.566 0.566 2.502 * 5 50% 0.497 0.497 6.604 * Dunnett table value = 2.36 (1 Tailed Value, P=0.05, df=15,4) DUNNETT S TEST - TABLE 2 OF 2 Ho:Control<Treatment NUM OF Minimum Sig Diff % of DIFFERENCE GROUP IDENTIFICATION REPS (IN ORIG. UNITS) CONTROL FROM CONTROL ----- -------------------- ------- ---------------- ------- ------------ 1 Control 4
2 6.25% 4 0.040 6.5-0.009 3 12.5% 4 0.040 6.5 0.010 4 25% 4 0.040 6.5 0.042 5 50% 4 0.040 6.5 0.112