A biological perspective on interpreting interaction effect

Factorial experiments are commonly employed in agricultural research as in other branches of applied sciences. In these experiments, inferences related to the interaction are essential. However, many researchers are still unable to analyze this type of experiment and interpret the results in the correct way. This is because researchers focus on interpreting the main effects although there is a significant interaction effect. Of course, meaningful main effects can exist even in the presence of an interaction, especially if interactions do not affect the main effects. Therefore, it is extremely important to understand thoroughly in which situations only the interaction effect(s), in which cases only the main effect(s), and in which cases the interpretation of the main effects will be meaningful although the interaction effect is significant. In this study, evaluating factorial experiments has been discussed in detail, especially in studies related to animal science. It has also been focused on the importance of considering both statistical and practical significance while interpreting the statistical analysis results.

PDF

___

1. Yassin N, Morais AR, Muniz JA. Analysis of variance of factorial experiments with two factors and additional treatments. Ciência e Agrotecnologia 2002; 26 (7): 1541-1547.
2. Rocha F, do Vale NM, Barili JLOC, Guidolin AF, Bertoldo JG. An approach to the decomposition of interaction in a factorial experiment with five factors. Acta Scientiarum Agronomy 2012; 34 (1). doi: 10.4025/actasciagron.v34i1.12104
3. Mendeş M. Statistical Methods and Experimental Design. Kriter Publication. İstanbul 2019 (in Turkish).
4. Bezerra NF, Nunes GHS, Negreiros MZ. Assessment of multiple-comparison procedures of published articles in the journal Horticultura Brasileira from 1.983 to 2.000. Horticultura Brasileira 2002; 20 (1): 5-9. doi: 10.1590/S0102- 05362002000100001
5. Bertoldo JG, Coimbra JLM, Guidolin AF, Mantovani A, Vale NM. Difficulties related to the use of tests of comparison of averages in scientifi c articles. Biotemas 2008; 21 (2): 145-153. doi: 10.5007/2175-7925.2008v21n2p145
6. Bertoldo JG, Coimbra JLM, Guidolin AF, Miqueloto A, Toaldo D. Use or abuse in mean comparison tests: scientific or empiric knowledge?. Ciência Rural 2008; 38 (4): 1145-1148. doi: 10.1590/ S0103-84782008000400039
7. Mendeş M, Yigit S. Type I error and test power of different tests for testing interaction effects in factorial experiments. Statistica Neelandica 2013; 67: 1-26. doi: 10.1111/j.1467-9574.2012.00528.x
8. Siemiatycki J, Thomas DC. Biological models and statistical interactions: An example from multistage carcinogenesis. International Journal of Epidemiology 1981; 10: 383-387. doi: 10.1093/ije/10.4.383
9. Cardellino RA, Siewerdt F. Use and misuse of statistical tests for comparison of means. Revista Brasileira de Zootecnia 1992; 21 (6): 985-995.
10. Wechsler FS. Unbalanced factorials: a misunderstood analysis. Pesquisa Agropecuária Brasileira 1998; 33(3): 231-26.
11. Nogueira MCS, Corrente JE. Triple interaction fractioning using PROC GLM CONTRAST/SAS applied to a three-way layout for balanced data. Bragantia 2000; 59 (1): 109-115. doi: 10.1590/ S0006-87052000000100017
12. Starmer CF, Lastra AA, Nesterenko VV, Grant AO. A proarrhythmic response to sodium channel blockade: Theoretical model and numerical experiments. Circulation 1991; 84:1364- 1377.
13. Nickerson RS. Null hypothesis significance testing: a review of an old and continuing controversy. Psychol Methods 2000; 5: 241- 301.
14. Fan X. Statistical significance and effect size in education research: two sides of a coin. The Journal of Educational Research 2001; 94: 275-282. doi: 10.1080/00220670109598763
15. Yiğit S, Mendeş M. Which effect size measure is appropriate for one-way and two-way anova models? A monte carlo simulation. Revstat Statistical Journal 2016; 16 (3): 295-313.
16. Yiğit S, Mendeş M. ANOM technique for evaluating practical significance of observed difference among treatment groups. International Journal of Agricultural Science Research 2017; 6 (1): 001-007.
17. Cohen J. Eta-squared and partial eta-squared in fixed factor anova designs. Educational and Psychological Measurement 1973; 33: 107-112. doi: 10.1177/001316447303300111
18. Carroll RM, Nordholm, LA. Sampling characteristics of Kelley’s and Hays’. Educational and Psychological Measurement 1975; 35: 541-554. doi: 10.1177/001316447503500304
19. Keselman HJ. A Monte Carlo investigation of three estimates of treatment magnitude: Epsilon squared, eta squared, and omega squared. Canadian Psychological Review 1975; 16: 44-48. doi: 10.1037/h0081789
20. Fritz CO, Morris PE, Richler JJ. Effect size estimates: current use, calculations, and interpretation. Journal of Experimental Psychology: General 2012; 141 (1): 2-18. doi: 10.1037/a0024338
21. Okada K. Is omega squared less biased? A comparison of three major effect size indices in one-way ANOVA. Behaviormetrika 2013; 40: 129-147. doi: 10.2333/bhmk.40.129
22. Skidmore ST, Thompson B. Bias and precision of some classical ANOVA effect sizes when assumptions are violated. Behavior Research Methods 2012; 45 (2): 536-546. doi: 10.3758/s13428- 012-0257-2
23. Wu C, Hamada M. Experiments: Planning, Analysis, and Parameter Design Optimization. New York: Wiley 2000.
24. Lewis SM, Dean AM. Detection of interactions in experiments on large number of factors. Journal of the Royal Statistical Society Series B 2001; 63 (4): 633-672. doi: 10.1111/1467- 9868.00304
25. Collins LM, Dziak JJ, Li R. Design of experiments with multiple ındependent variables: a resource management perspective on complete and reduced factorial designs. Psychol Methods 2010; 14 (3): 202-224. doi: 10.1037/a0015826
26. De Gonzalez AB, Cox RD. Interpretation of interaction: a review. The Annals of Applied Statistics 2007; 1 (2): 371-385. doi: 10.1214/07-AOAS124
27. Chew V. Comparing treatment means: a compendium. Hort Science 1976; 11(4): 348-335.
28. Silva JGC. The consideration of the unit structure in ınferences from the experiment. Pesquisa Agropecuária Brasileira 1999; 34 (6): 911-925. doi: 10.1590/S0100-204X1999000600001
29. Perecin D, Cargnelutti Filho A. Comparisonwise and experimentwise effects in factorial experiments interactions. Ciência e Agrotecnologia 2008; 32 (1): 68-72. doi: 10.1590/ S1413-70542008000100010
30. Rothman KJ, Greenland S, Walker AM. Concepts of interaction. American Journal of Epidemiology 1980; 112: 467-470. doi: 10.1093/oxfordjournals.aje.a113015