Determining the Minimum Sample Size Required to Create Regression Model in Plant Ecology (Case Study: Cover-Production Relationship)

Document Type : Original Research

Authors
M. Rostampour 1
M. Yousefian 2
R. Yari 3
1 Department of Rangeland and Watershed Management and Research Group of Drought and Climate Change, Faculty of Natural Resources and Environment, University of Birjand, Birjand, Iran
2 Forest and Rangelands Research Department, Mazandaran Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization (AREEO), Sari, Iran.
3 Khorasan Razavi Agricultural and Natural Resources Research and Education Center, Agricultural Research, Education and Extension Organization (AREEO), Mashhad, Iran.
10.22034/ecopersia.12.1.39
Abstract
Regression analysis is one of the most widely used statistical tests in vegetation evaluation. Indirect methods of estimating forage yield always require regression analysis. The basic question in such research is that at least a few pairs of samples are required to achieve a valid regression equation. Therefore, this study determines the sample size required to estimate the yield of Haloxylon persicum Bunge, Artemisia sieberi Besser and Stipagrostis pennata (Trin.) De Winter using plant dimensions including cover percentage, plant area, height and volume. After correlation and regression analyzes, power analysis and effect size were calculated. The results showed that for regression analysis and the statistical importance of the equation and regression coefficients between the cover and yield for these species, about 26, 14 and 18 pairs (respectively) were proposed. By comparing the method used in this study with other rules of thumb, it can be deduced that the use of Green's rule (N≥ 50 + 8M and N ≥104 + M) is not recommended, because with at least one independent variable (M) About 58 to 105 pairs of samples are required. In the studies within Iran, double sampling methods are generally used, in which between 7 and 30 pairs (an average of 15 pairs) are recommended, which is closer to the number of pairs of the present study (14 to 26) than the rules of thumb.
Keywords
Cover
Power analysis
Rangeland
Regression
Sample size

Subjects

1. Motamedi J, Afradi J, Sheidai Karkaj E, Alijanpour A, Emadodin I, Banej Shafiei S et al. Environmental Factors Affecting the Structural Trials and Biomass of Onobrychis aurea Bioss. ECOPERSIA 2020; 8 (4):247-259. https://ecopersia.modares.ac.ir/article-24-27458-en.html
2. Bonham C.D. Measurements for Terrestrial Vegetation, 2nd Edition. John Wiley Sons, New York, NY. 2013; 260 p. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118534540
3. Olsoy P. J., Glenn N. F., Clark P. E. Estimating sagebrush biomass using terrestrial laser scanning. Rangel. Ecol. Manag. 2014; 67(2): 224–228. https://www.sciencedirect.com/science/article/abs/pii/S1550742414500279
4. Yao X., Yang G., Wu B., Jiang L., Wang F. Biomass Estimation Models for Six Shrub Species in Hunshandake Sandy Land in Inner Mongolia, Northern China. Forests. 2021; 12(2): 167. https://www.mdpi.com/1999-4907/12/2/167
5. Attaeian B. Estimation of Aboveground Biomass Carbon Sequestration Potential in Rangeland Ecosystems of Iran. ECOPERSIA 2016; 4 (1):1283-1294. https://ecopersia.modares.ac.ir/browse.php?a_id=534&slc_lang=en&sid=24&printcase=1&hbnr=1&hmb=1
6. Paruelo J. M., Lauenroth W. K., Roset P. A. Technical note: Estimating aboveground plant biomass using a photographic technique. J. Range. Manage. 2000; 53(2): 190-193. https://rangelandsgateway.org/dlio/19852
7. Ebrahimi M. Effects of semi-circular bunds on plant vegetation and soil properties of Naroon and Neron rangelands- Sistan and Baloochestan. ECOPERSIA 2022; 10 (1):1-11. https://ecopersia.modares.ac.ir/article-24-45557-en.html
8. Ghorbani A, Moameri M, Dadjou F, Seyedi Kaleybar S, Pournemati A, Asghari S. Determinization of Environmental Factors Effects on Plants Production in QezelOzan-Kosar Rangelands, Ardabil Province Factors Effect on Rangelands Production. ECOPERSIA 2020; 8 (1):47-56. https://ecopersia.modares.ac.ir/article-24-36698-en.html
9. Arzani H., Abedi M. Rangeland Assessment Survey and Monitoring. University of Tehran Press. 2013; 305p. https://www.researchgate.net/publication/277813219_Rangeland_Assessment_Survey_and_Monitoring
10. Clark P. E., Hardegree S. P., Moffet C. A., Pierson F. B.. Point sampling to stratify biomass variability in sagebrush steppe vegetation. Rangel. Ecol. Manag. 2008; 61(6): 614-622. https://www.sciencedirect.com/science/article/abs/pii/S1550742408500728
11. Zarekia S, Jafari A A, Mirhaji T. Assessment of Planting Season Effects on Vegetation Parameters of Astragalus effusus and Astragalus brachyodontus Accessions. ECOPERSIA 2016; 4 (1):1225-1237. https://ecopersia.modares.ac.ir/browse.php?a_code=A-24-1000-5431&slc_lang=en&sid=24
12. Motaharfard E, Mahdavi A, Iranmanesh Y, Jafarzadeh A. Effect of Land Uses on Aboveground Biomass and Carbon Pools in Zagros Forests, Iran. ECOPERSIA 2019; 7 (2):105-114. https://ecopersia.modares.ac.ir/browse.php?a_id=28777&sid=24&slc_lang=fa
13. Bados R., Esteban L. S., Esteban J., Fernández-Landa A., Sánchez T., Tolosana, E. Biomass equations for rockrose (Cistus laurifolius L.) shrublands in North-central Spain. For. Syst. 2021; 30(3): e015. https://fs.revistas.csic.es/index.php/fs/article/view/17997
14. Gholinejad, B., PourBabaei, H., Farajollahi, A. and Parvane, E. Assessment and Comparison of Different Methods for Estimating Forage Production (Case Study: Rangeland of Kurdistan Province). J. Rangel. Sci. 2012; 2(2): 483-489. https://journals.iau.ir/article_513028.html
15. Grinath J.B. Comparing predictive measures and model functions for estimating plant biomass: lessons from a sagebrush–rabbitbrush community. J. Plant. Ecol. 2019; 220: 619-632. https://link.springer.com/article/10.1007/s11258-019-00940-1
16. Liu H., Dahlgren R.A., Larsen R.E., Devine S.M., Roche L.M., O’ Geen A.T., Wong A.J.Y., Covello, S., Jin Y. Estimating Rangeland Forage Production Using Remote Sensing Data from a Small Unmanned Aerial System (sUAS) and PlanetScope Satellite. Remote Sens-Basel. 2019; 11(5):595. https://www.mdpi.com/2072-4292/11/5/595
17. Rojo V., Arzamendia Y., Pérez C., Baldo J.L., Vilá B. Double Sampling Methods in Biomass Estimates of Andean Shrubs and Tussocks. Rangel. Ecol. Manag. 2017; 70: 718 - 722. https://www.sciencedirect.com/science/article/abs/pii/S1550742417300593
18. Tsutsumi M., Itano S., and Shiyomi M. Number of samples required for estimating herbaceous biomass. Rangel. Ecol. Manag. 2007; 60(4): 447-452. https://www.sciencedirect.com/science/article/abs/pii/S155074240750059X
19. Coulloudon B., Eshelman K., Gianola J., Habich N., Hughes L., Johnson C., Pellant M., Podborny P., Rasmussen A., Robles B. Sampling vegetation attributes: interagency technical reference. Technical Reference 1734-4, USDI Bureau of Land Management. Second Revision. Denver, CO, USA: National Applied Resource Sciences Center.1999, 163 pp. https://www.blm.gov/noc/blm-library/technical-reference/sampling-vegetation-attributes
20. Flombaum P., Sala O. E. A non-destructive and rapid method to estimate biomass and aboveground net primary production in arid environments. J. Arid. Environ. 2007; 69(2): 352-358. https://www.sciencedirect.com/science/article/abs/pii/S0140196306002886
21. Jan S.L., Shieh G. Sample size calculations for model validation in linear regression analysis. BMC Med. Res. Methodol. 2019: 19, 54. https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-019-0697-9
22. Bonett D. G., Wright T. A. Sample size requirements for multiple regression interval estimation. J. Organ. Behav. 2011; 32(6): 822–830. https://onlinelibrary.wiley.com/doi/abs/10.1002/job.717
23. Mousaei Sanjerehei M. Sample Size Calculations for Vegetation Studies. MJEE. 2021; 23(2): 85–97. https://www.researchgate.net/publication/357468928_Sample_size_calculations_for_vegetation_studies
24. Jenkins D.G., Quintana-Ascencio P.F. A solution to minimum sample size for regressions. PLoS ONE. 2020; 15(2), e0229345. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7034864/
25. Button K.S., Ioannidis J.P., Mokrysz C., Nosek B.A., Flint J., Robinson E.S. Power failure: why small sample size undermines the reliability of neuroscience. Nat. Rev. Neurosci. 2013; 14: 365. https://pubmed.ncbi.nlm.nih.gov/23571845/
26. Bujang M. A., Sa'at N., Sidik T. M. I. T. A. B., Joo L. C. Sample Size Guidelines for Logistic Regression from Observational Studies with Large Population: Emphasis on the Accuracy Between Statistics and Parameters Based on Real Life Clinical Data. Malays. J. Med. Sci. 2018; 25(4): 122–130. https://pubmed.ncbi.nlm.nih.gov/30914854/
27. Cohen J. Statistical power analysis for the behavioral sciences. 3rd ed. Hillsdale: Erlbaum. 2013; 579 p. https://www.taylorfrancis.com/books/mono/10.4324/9780203771587/statistical-power-analysis-behavioral-sciences-jacob-cohen
28. R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2021. URL https://www.R-project.org/
29. Algina J., Olejnik S. Determining sample size for accurate estimation of the squared multiple correlation coefficient. Multivar. Behav. Res. 2000; 35: 119–137. https://pubmed.ncbi.nlm.nih.gov/26777233/
30. Gregory T.K., Daniel M. Sample Sizes When Using Multiple Linear Regression for Prediction. Educ. Psychol. Meas. 2008; 68:431. https://journals.sagepub.com/doi/10.1177/0013164407310131
31. Hair J., Black W.C., Babin B.J., Anderson R.E. Multivariate Data Analysis, 8th edition. United Kingdom: Cengage Learning. 2018; ‎832 p. https://books.google.com/books/about/Multivariate_Data_Analysis.html?id=0R9ZswEACAAJ
32. Harris R. J. A Primer of Multivariate Statistics. 3rd ed. Mahwah, NJ: Lawrence Erlbaum. 2001; 634 p. https://www.taylorfrancis.com/books/mono/10.4324/9781410600455/primer-multivariate-statistics-richard-harris
33. Hemphill, J. F. Interpreting the magnitudes of correlation coefficients. Am. Psychol. 2003, 58; 78–79. https://pubmed.ncbi.nlm.nih.gov/12674822/
34. Franklin J., Miller J. A. Mapping Species Distributions: Spatial Inference and Prediction. Cambridge; New York: Cambridge University Press. 2009; 320 p. https://www.cambridge.org/core/books/mapping-species-distributions/58225AE5693AED8BD812F7CEBE35378A
35. Gotelli N. J., Ellison A. M. A Primer of Ecological Statistics. Sunderland, MA: Sinauer Associates, Inc. 2004; 510 p. https://global.oup.com/academic/product/a-primer-of-ecological-statistics-9781605350646
36. Schweiger A. H., Irl S. D. H., Steinbauer M. J., Dengler J., Beierkuhnlein C. Optimizing sampling approaches along ecological gradients. Methods. Ecol. Evol. 2016; 7: 463–471. https://cris.fau.de/publications/123610784/
37. Green S.B. How Many Subjects Does It Take to Do a Regression Analysis? Multivar. Behav. Res. 1991; 26 3: 499-510. https://psycnet.apa.org/record/1992-15143-001
38. Kutner M.H., Nachtsheim C.J., Neter J., Li, W. Applied Linear Statistical Models. 5th ed. The McGraw-Hill/Irwin Series Operations and Decision Sciences. Boston: McGraw-Hill Irwin. 2005; 1415 p. https://users.stat.ufl.edu/~winner/sta4211/ALSM_5Ed_Kutner.pdf
39. Tabachnick B.G., Fidell L.S. Using multivariable statistics. 6th ed. Boston: Pearson Education. 2013; 983 p. https://www.amazon.com/Using-Multivariate-Statistics-Barbara-Tabachnick/dp/0205849571
40. Khamis H. J., Kepler M. Sample size in multiple regression: 20+ 5K. J. Appl. Statist. Sci. 2010; 17: 505-517. https://www.researchgate.net/publication/285744052_Sample_size_in_multiple_regression_20_5k
41. Rossi J.S. Statistical power analysis. In J.A. Schinka and W.F. Velicer (Eds.), Handbook of psychology. Volume 2: Research methods in psychology. John Wiley and Sons, Inc. 2013; pp. 71–108. https://psycnet.apa.org/record/2012-27075-003
42. Bujang M. A. Step-by-Step Process on Sample Size Determination for Medical Research. Malays. J. Med. Sci. 2021, 28(2):15-27. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8075593/
43. Cohen J., Cohen P., West S.G., Aiken, L.S. Applied multiple regression/correlation analysis for the behavioral sciences. 3rd ed. Mahwah: Erlbaum. 2003; 734 p. https://www.taylorfrancis.com/books/mono/10.4324/9780203774441/applied-multiple-regression-correlation-analysis-behavioral-sciences-jacob-cohen-patricia-cohen-stephen-west-leona-aiken
44. Arzani H., Dehdari S., King, G. Models for estimating range production by cover measurement. Iranian Journal of Range and Desert Research, 2011;18(1), 1-16. https://ijrdr.areeo.ac.ir/article_101992.html?lang=en
45. Aliloo F., Keyvan behjou F., Moetamedi, J. Study presentation feasibility of statistical models for estimating rangeland plants species of Artemisia aucheri and Agropyron trichophorum (Case Study: Dizaj Batchi and Ghotor Ranglands of Khoy). Iranian Journal of Range and Desert Research, 2016; 22(4), 625-638. https://ijrdr.areeo.ac.ir/article_106035.html
46. Arzani H., Adnani S. M, Bashari H, Azimi M.A.S., Baghri H, Akbarzadeh M., Kaboli S. H. Assessment of vegetation covers and production variation in rangelands of Qum province (2000-2005). Iranian Journal of Range and Desert Research, 2007; 25(4), 296- 313. https://ijrdr.areeo.ac.ir/article_105859.html?lang=en
47. Hoseini S., Mesdaghi M., Pambokhchyan C. Comparing 3 methods of forage estimation in summer rangelands (Case study: Sar-Aliabad rangelands of Golestan province). Iranian Journal of Range and Desert Research, 2012;18(4), 637-651. https://ijrdr.areeo.ac.ir/article_102264.html
48. Sadeghi Nia M., Arzani H., Baghestani, N. Comparison of different production estimation methods for some important shrub plants (the case study in Yazd and Isfahan provinces). J. Pajohesh and Sazandegi, 2001; 61, 28-32. https://www.sid.ir/paper/20112/en
49. Mohammadi Golrang B., Gazanchian G., Ramzani moghadam R., Falahati H., Rouhani H., Mashayekhi M. Estimation of forage productions of some range plant species by plant height and diameter measurements. Iranian Journal of Range and Desert Research, 2008; 15(2), 158-178. https://ijrdr.areeo.ac.ir/article_103683.html?lang=en