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

Aims: Regression analysis is one of the most widely used statistical tests in vegetation evaluation. However, determining more than the sample size for the model validation is required in the plant ecology literature. Indirect methods of estimating forage production always require regression analysis. The fundamental 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 production of Haloxylon persicum Bunge, Artemisia sieberi Besser, and Stipagrostis pennata (Trin.) De Winter uses plant dimensions, including cover percentage, plant area, height, and volume. Materials Methods: The study was conducted in Shahrakht Plain, Zirkouh in South Khorasan province. The research focused on three indicator species in the study area: Haloxylon persicum, Artemisia sieberi, and Stipagrostis pennata. The study utilized the relationship between plant cover and dimensions to estimate forage production. In each habitat, 25 plots were established. After computing the power of the correlation and regression tests, the minimum data pair required for the study was estimated, aiming for a power of 80% at the significance level of 0.05. The effect size and power analysis methods were employed to determine the sample size and were then compared with the coefficient of determination (R2) and thumb rules methods. Findings: The results of correlation analysis between cover percentage and production show that in Haloxylon persicum, Artemisia sieberi, and Stipagrostis pennata species, the correlation coefficients are 0.54 (p ≤ 0.01), 0.76 (p ≤ 0.001) and 0.40 (p ≤ 0.05) respectively. The correlation power analysis results indicate that with a sample size of 25 pairs of numbers, the effect size of the correlation coefficient is large, and the power ranges between 52% and 99%. The regression power analysis results indicate that with a sample size of 25 pairs of numbers, the effect size of the regression coefficient is significant for some species and medium for others, with power ranging from 78% to 97%. To achieve a test power of 80%, the recommended number of pairs for regression analysis in the three species would be around 30, 12, and 56, respectively. Conclusion: The results showed that for regression analysis and the statistical importance of the equation and regression coefficients between the cover and production for Haloxylon persicum, Artemisia sieberi, and Stipagrostis pennata, about 30, 12, and 56 pairs were proposed, respectively. This study did not examine the relationship between all plant species and production dimensions, but only the relationship between cover and production. Although the correlation test results showed significant relationships between plant dimensions and production, it is not necessarily a good predictor of production (valid regression equations were not obtained).