Some comments on design and analysis of comparative silage experiments
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1 Statistics and experimental design in silage research: Some comments on design and analysis of comparative silage experiments Bärbel Kroschewski 1, Kirsten Weiß 1 & Horst Auerbach 2 1 Humboldt Universität zu Berlin 2 ISC Wettin-Löbejün
2 1. Introduction Reproducible results define the very core of scientific integrity in modern research... but across all scientific disciplines only too a little number of trials generate reproducible results. improper scope of inference failure in understanding data generation process unclear distinction between experimental and observational units insufficient number of experimental replication inferential misinterpretations associated with use of P-values... error inflation due to multiple comparisons... selective reporting Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
3 1. Introduction Aim: Critical findings on design, analysis, and interpretation of results will be addressed based on comparative silage experiments. Scientific papers on silage trials during the last 8 years published in Journal of Dairy Science Grass and Forage Science Agricultural and Food Science - Experiments with 1 up to 3 factors (sometimes even more), - 3 to 6 replicates per treatment, - Statistical analyses: frequently performed by parametric analysis of variance, followed by pairwise comparisons (LSD, Tukey, Bonferroni, Sidak, Duncan,...), sometimes by non-parametric procedures (Wilcoxon and others). Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
4 1. Introduction Aim: Critical findings on design, analysis, and interpretation of results will be addressed based on comparative silage experiments. Lab-scale ensiling trial on biostatistical questions in 2017 (1) What can the scope of inference for one ensiling experiment with mini-silos be? - material taken from different field locations versus a composite sample, - impact of location and fermentation process on silage traits. (2) Is the frequently used (low) number of replications sufficient regarding significance and relevance of results? Do the traits meet the assumptions of normal distribution and variance homogeneity? - three treatments: untreated control, biological, and chemical silage additive, - ten mini-silos as replicates (composite sample = restricting experimental input), - samples of smaller size (n=3, n=6) extracted: to contrast the results of statistical analyses for different sample sizes. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
5 2. Description of the grassland trial Lab-scale ensiling trial (1) with respect to field sampling locations material taken from three randomly selected sampling points (P1, P2, P3) of natural grassland P2 23%DM P1 24%DM per sampling point: ten 1.5-L jars (=mini-silos) filled with grass material without silage additives (= CON) P3 20%DM Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
6 2. Description of the grassland trial Lab-scale ensiling trial (2) with grass mixture composite grassland sample, mixing identical quantities from three sampling points three treatments (silage additive) ten 1.5-L jars per treatment CON P1+P2+P3 = MIX CHEM LAB biological additive Lactobacillus buchneri CNCM-I 4323 and Pediococcus acidilactici DSM without silage additive chemical additive sodium nitrite, hexamethylene tetramine and potassium sorbate Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
7 2. Description of the grassland trial Lab-scale ensiling trial Traits fresh forage per sampling point (P1, P2, P3) n=5 Traits silage (after 121 days of storage at 22⁰C) per sampling point (P1, P2, P3) mixture (MIX): per treatment (CON, CHEM, LAB) n=10 -> total sample size N=60 DM WSC NO 3 - BC Yeasts Lactobac dry matter water-soluble carbohydates nitrate buffering capacity yeast count lactic acid bacteria known to have an influence on the fermentation process ph LA lactic acid AA acetic acid 1,2-PD 1,2-propanediol WSC water-soluble carbohydates ETOH ethanol PROP n-propanol ASTA aerobic stability DML anaerobic DM losses butyric acid, counts of yeasts and moulds: small values Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
8 3.1 Results field sampling locations (CON) Scope of inference Population, to which the results from a research study are applicable. Ideally, this population is sampled at random. What can the scope of inference for one ensiling experiment with mini-silos be? Where can I reasonably expect results to reproduce? = Degree of generalization. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
9 3.1 Results field sampling locations (CON) Scope of inference (1) One field sampling point Forage material represents exactly this field location. Variability of measurements reflects only the different fermentation processes in the replicated mini-silos per treatment for one material P1 different location farm silo Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
10 3.1 Results field sampling locations (CON) Scope of inference (2) Mixture of field sampling points Composite sample of forage material represents an average field situation. P2 P1 Variability of measurements reflects only the different fermentation processes in the replicated mini-silos per treatment for one composed material P1+P2+P3 = MIX different location farm silo P3 Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
11 3.1 Results field sampling locations (CON) Scope of inference (3) Several field sampling points, n=1 Forage material represents the field. P1 1 P2 1 Variability of measurements reflects arbitrary field locations and the different fermentation processes in the replicated mini-silos per treatment. 1 P3 P4 1 Both effects are confounded (no separation possible). arbitrary location farm silo P5 1 1 P6 Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
12 3.1 Results field sampling locations (CON) Scope of inference (4) Several field sampling points, n>1 Forage material represents the field. P2 23%DM P1 24%DM Variability of measurements reflects arbitrary field locations and the different fermentation processes in the replicated mini-silos per treatment Both effects are not confounded (separation is possible). arbitrary location farm silo P3 20%DM Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
13 3.1 Results field sampling locations (CON) Box-Whisker-Plot for three sampling points and grass mixture (MIX), n=10 Ethanol (g kg -1 DM) ASTA (days) except ASTA: observations more or less different between sampling points (e.g. ethanol) all traits: values from grassland mixture reflect average situation Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
14 3.1 Results field sampling locations (CON) Variation between field sampling points and within sampling points for Ethanol 6.6 total mean = observation 11.9 mean per field sampling point Ethanol (g kg -1 DM) Decomposition of total variability (random effects model) Source of variation Variance component percentage % Field sampling point Residual (Fermentation process) Total Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
15 3.1 Results field sampling locations (CON) Decomposition of total variability of observed values All traits (except ASTA): largest fraction of variation was caused by field sampling point, remaining residual variation was related to effects of fermentation process of the ten replicates per sampling point. ASTA: was affected almost completely by the fermentation process. Note: But: How far the efficacy of silage additives will be affected by sampling points cannot be shown in our study. Final evaluation of silage additive effects should request more than one trial (EFSA). Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
16 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments fixed effects model, Anova + Tukey s test procedure, assuming normally distributed data, variance homogeneity, scope of inference: one composed material, mini-silos. Table of LSMeans, n=10 Treatment Ethanol ASTA CON 11.4 b 5.7 a LAB 17.1 c 8.7 a CHEM 2.0 a 8.4 a HSD (α=5%) s% Residual duration of air exposure Ethanol (g kg -1 DM) ASTA (days) Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
17 3.2 Results grass mixture (CON, LAB, CHEM) Observations come from populations with normally distributed data? Ethanol Shapiro-Wilk-Test W=0.975 P=0.689 ASTA Shapiro-Wilk-Test W=0.921 P=0.030* Here: 3 treatments x (n=10) 30 residuals But if: 3 treatments x (n= 3) 9 residuals How reliable are test and graphs? Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
18 3.2 Results grass mixture (CON, LAB, CHEM) Observations come from populations with homogeneous variances? Trait Residual variance AIC (fit criteria) smaller is better CON LAB CHEM Average Var.hom. Var.het. Acetic acid Ethanol ASTA DM losses Here: treatment variances estimated from n=10 (as basis for inferences). With n=3/6 also reliable estimations? Anova approach, assuming variance homogeneity, average residual variance used ANOVA approach, assuming variance heterogeneity,! individual residual variances used Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
19 3.2 Results grass mixture (CON, LAB, CHEM) Extraction of subsets from the whole sample (n=10) e.g. Ethanol n=3 Treatment Replication CON LAB CHEM subset subset 120 n=6 Treatment Replication CON LAB CHEM subset subset 210 separate data analyses for all subsamples Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
20 3.2 Results grass mixture (CON, LAB, CHEM) LSMeans for total sample and subsets Ethanol Ethanol (g kg -1 DM) Compared to CON, LAB increases ethanol content, whereas CHEM decreases... Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
21 3.2 Results grass mixture (CON, LAB, CHEM) Residual variances for total sample and subsets Ethanol average variances far too large for CHEM; too small for CON, LAB Ethanol (g kg -1 DM) Compared to CON, LAB increases ethanol content, whereas CHEM decreases... CHEM reduces the variability dramatically! Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
22 3.2 Results grass mixture (CON, LAB, CHEM) LSMeans for total sample and subsets ASTA ASTA (days) Compared to CON, LAB and CHEM show slightly higher aerobic stability... Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
23 3.2 Results grass mixture (CON, LAB, CHEM) Residual variances for total sample and subsets ASTA ASTA (days) Compared to CON, LAB and CHEM show slightly higher stability... variability similar. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
24 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments Significance versus Relevance ASTA (days, n=10) Comparison Difference P-value assuming variance homogeneity HSD (α=5%) Confidence limits LAB CON [-0.1 ; +6.1] CHEM CON [-0.4 ; +5.9] No relevance??? No significance!!! EFSA (2008):... additive shall be stable two days longer than untreated control. Effect size of interest Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
25 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments Significance versus Relevance Scenario Significance Relevance (+) (+) Effect size of interest EFSA (2008):... additive shall be stable two days longer than untreated control. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
26 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments Significance versus Relevance ASTA (days, n=10) Comparison Difference P-value assuming variance homogeneity HSD (α=5%) Confidence limits LAB CON [-0.1 ; +6.1] CHEM CON [-0.4 ; +5.9] LAB CON CHEM CON relevant, but not significant Effect size of interest EFSA (2008):... additive shall be stable two days longer than untreated control. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
27 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments Significance versus Relevance Ethanol (g kg -1 DM, n=10) Comparison Difference P-value assuming variance heterogeneity HSD (α=5%) Confidence limits LAB CON 5.7 < [3.9 ; 7.5] CHEM CON -9.4 < [-10.7 ; -8.0] CHEM CON LAB CON Which effect size of interest is relevant??? Necessary for interpretation! Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
28 3.2 Results grass mixture (CON, LAB, CHEM) Comparison of treatments problem of multiplicity (caused by number of comparisons + numer of response variables) All pairwise comparisons 1 LAB CON 2 CHEM CON 3 CHEM LAB c * 1 (1 ) α* - Experiment-wise Type I error rate α - Comparison-wise Type I error rate Same sample used for several tests results are not independent! number of treatments c (pairwise comparisons) α* (α=0.05) only here: t-test = Tukey s test Error inflation particularly problematic, when large variability + small sample size come together. The more comparisons, the more findings of something in the data! Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
29 3.2 Results grass mixture (CON, LAB, CHEM) ASTA as one of the most important responses (1) assuming normally distributed values parametric data analysis EFSA (2008):... additive shall be stable two days longer than untreated control. all pairwise comparisons, two-sided Comparisons versus control, one-sided n=10 Tukey (HSD 5% = 3.1) Comparison Difference P-value Conf. limits LAB CON [-0.1 ; +6.1] CHEM CON [-0.4 ; +5.9] Dunnett (GD 5% = 2.9) P-value Conf. limits [+0.1 ; +6.0] [-0.2 ; +5.7] LAB CON CHEM CON relevant + significant relevant + not significant Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
30 3.2 Results grass mixture (CON, LAB, CHEM) ASTA as one of the most important responses (2) assuming non-normally distributed values nonparametric data analysis rank procedure with ANOVA-Typ-Statistics (SAS, Proc Mixed) for 1 treatment factor, variance heterogeneity of ranks considered, identical observations no problem,... but: minimal sample size for reliable results about n=10 Treatment LS Mean Rank mean CON LAB CHEM Contrasts (Bonferroni correction) Comparison P-value (1) P-value (2) LAB CON CHEM CON (n=10) all pairwise comparisons, two-sided Tukey comparisons versus Control, one-sided Dunnett Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
31 3.2 Results grass mixture (CON, LAB, CHEM) ASTA as one of the most important responses (3) How to consider identical observations for treatments? grass mixture: duration of air exposure 12.1 days Treatment observations (days), n=10 CON LAB CHEM often situation more extreme (Weiss et. al 2016): duration of air exposure 7 days Treatment observations (days), n=3 CON Additive Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
32 4. Summary Comparative silage experiments are most frequently performed with few replications. The traits of interest for the evaluation of treatments do not meet in each case the assumptions for the chosen statistical analysis procedures. Moreover, checking the assumptions by statistical preliminary tests and performing the analysis on the same data are problematic. Often, the experimenter has information beforehand about treatments which have an impact not only on the magnitude but also on variation. Both, rank procedures in case of non-normality as well as reliable estimations of individual treatment variances in case of variance heterogeneity demand higher sample sizes. Together with well justified effect sizes of interest, the trials should be designed in such a way that significance and relevance of results come together. Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
33 4. Summary Problematic single trials? Don t worry! Put together! Meta - analysis as magic recipe Are aggregated results correct????? Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
34 References Bello, N. M. & Renter, D. G. (2017) Invited review: Reproducible research from noisy data: Revisiting key statistical principals for the animal sciences. Journal of Dairy Science, 101, EFSA (2008) Guidance for the preparation of dossiers for technological additives. The EFSA Journal, 774, 121. Kaiser, E. & Weiss, K. (1997) Zum Gärungsverlauf bei der Silierung von nitratarmem Grünfutter. 2.Mitt.: Gärungsverlauf bei Zusatz von Nitrat, Nitrit, Milchsäurebakterien und Ameisensäure. Archives of Animal Nutrition, 50, Nuzzo, R. (2015) Fooling ourselves. Nature, 526, Udén, P. & Robinson, P. H. (2015) Design and statistical issues in silage experiments. In: Nussio, L. G., de Sousa, D. O., Gritti, V. C., Salvati, G. G., Santos, W. P. & Salvo, P. A. R. (eds.). V International Symposium on Forage Quality and Conservation, Piracicaba, SP, Brazil, 2015, Weiss, K., Kroschewski, B. & Auerbach, H. (2016) Effects of air exposure, temperature and additives on fermentation characteristics, yeast count, aerobic stability and volatile organic compounds in corn silage. Journal of Dairy Science, 99, 1-17 Faculty of Life Science, Thaer-Institute B. Kroschewski ISC
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