Aquatic Toxicology Lab 10 Pimephales promelas Larval Survival and Growth Test Data Analysis 1. Complete test initiated last week 1.

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1 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 ed 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 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 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 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 Pimephales promelas Dry Weight %Effluent Replicates Control

3 Fathead Minnow Practice Set 2 Pimephales promelas Survival n=10 % Effluent Replicates Control Pimephales promelas Dry Weight %Effluent Replicates Control

4 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 < to < to 0.5 >0.5 to 1.5 >1.5 EXPECTED OBSERVED Calculated Chi-Square goodness of fit test statistic = Table Chi-Square value (alpha = 0.01) = 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 = W = Critical W (P = 0.05) (n = 24) = Critical W (P = 0.01) (n = 24) = 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))

5 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 Control % % % % * 6 100% * 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 < to < to 0.5 >0.5 to 1.5 >1.5 EXPECTED OBSERVED Calculated Chi-Square goodness of fit test statistic = Table Chi-Square value (alpha = 0.01) = Data PASS normality test. Continue analysis.

6 Fish Example Set 1 Growth File: ex1gow.txt Transform: NO TRANSFORMATION Shapiro - Wilk s test for normality D = W = Critical W (P = 0.05) (n = 16) = Critical W (P = 0.01) (n = 16) = 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) = Closest, conservative, Table H statistic = (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

7 Bartlett s test for homogeneity of variance Calculated B1 statistic = 5.98 Table Chi-square value = (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 = 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 Within (Error) Total

8 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 Control % * % * 4 25% * Critical values use k = 3, are 1 tailed, and alpha = 0.05

9 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 < to < to 0.5 >0.5 to 1.5 >1.5 EXPECTED OBSERVED Calculated Chi-Square goodness of fit test statistic = Table Chi-Square value (alpha = 0.01) = 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 = W = Critical W (P = 0.05) (n = 24) = Critical W (P = 0.01) (n = 24) = 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

10 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 Control % % % % % * Critical values use k = 5, are 1 tailed, and alpha = 0.05 Chi-square test for normality: actual and expected frequencies INTERVAL < to < to 0.5 >0.5 to 1.5 >1.5 EXPECTED OBSERVED Calculated Chi-Square goodness of fit test statistic = Table Chi-Square value (alpha = 0.01) = Data PASS normality test. Continue analysis.

11 File: ex2grow.txt Transform: NO TRANSFORMATION Shapiro - Wilk s test for normality D = W = Critical W (P = 0.05) (n = 20) = Critical W (P = 0.01) (n = 20) = 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) = Closest, conservative, Table H statistic = (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

12 Table Chi-square value = (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 = 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 Within (Error) Total Critical F value = 3.06 (0.05,4,15) Since F < Critical F FAIL TO REJECT Ho: All equal

13 ANOVA TABLE SOURCE DF SS MS F Between Within (Error) Total 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 Control % % % * 5 50% * 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 Control 4

14 2 6.25% % % %