Determining the sample size required to compare vegetation and soil characteristics in two independent groups using effect size

Extended Abstract Background and objectives: One of the important steps in assessing rangeland vegetation is determining the sample size. Adequacy of sample size and its determination is always one of the main concerns of rangeland vegetation analyzer. There are two general methods for determining the sample size in rangeland science: graphic and statistical methods. In this study, the sample size required studying the percentage of vegetation and soil in under grazing and enclosure area, in addition to the Cochran method, the analysis of power and effect size has also been used. Methodology: This study was conducted on the habitat of Ammodendron persicum in the rangelands of Zirkouh, South Khorasan province. For sampling, initial sampling was performed with 3 transects and 30 plots of 16 m2. In each plot, the percentage of vegetation was estimated; also 18 samples were taken from the soil depth of 0-30 cm. In this study, in order to perform pre-test and post-test power analysis (80% and 60%) in both groups, parametric and non-parametric statistical tests were performed. For this purpose, to compare the percentage of vegetation and sand in the two areas (under grazing and enclosure), if the data is normal, independent samples t-test and if isn't normal, Wilcoxon test were used. The normality of the data was assessed using the Shapiro-Wilk test and the homogeneity of the variances was assessed using the ratio of variance test. In this study, based on the Cochran's formula, the number of plots required for sampling was determined. To determine the sample size, and the validity of the test from the initial data, power analysis and effect size statistics were used. All statistical tests were performed by R software and psych, lsr, pwr and effectsize packages.  Results: The results showed that, despite the absence of outliers, vegetation data did not have a normal distribution. Even after the second root conversion, the results of the Shapiro-Wilk normality test still showed that the data in this study was not normal. Therefore, in this study, non-parametric tests were used. The results showed that about 502 plots are needed to measure vegetation by the Cochran method. The Cohen effect size for the student's t test with independent samples was calculated to be about 0.23, which is a small difference between the percentages of vegetation between the two areas. The results of the present study showed that 30 pre-test samples at the levels of 0.01 and 0.05 with test power of 4.31% and 13.95%, respectively, and type II errors in the test were 95.69% and 86.05%, respectively. It indicates that the test power for this number of samples is really low. At the power level of 60% and 80%, with an "average" effect size between 46 to 73 plots for each region was calculated and the number seemed more economical. The results of the soil sampling power analysis showed that the test power was 27.21% and 52.04% at the level of 0.01 and 0.05, respectively, and type II the errors in the test were 72.79% and 47.96%, respectively. Conclusion:  Finally, it can be said that at least 46 plots and 22 soil samples were required to study this rangeland to an acceptable level. It is suggested that if the null hypothesis is rejected, in addition to the P value, the effect size and test power be reported. According to the results of this study, in this region, the statistical test of the t-test on 30 vegetation samples had an error of about 86 to 96%. Therefore, in areas with high vegetation changes, the use of the Cochrane method and 30 plots is not recommended at all.  Keywords: power analysis, effect size, number of plots, vegetation, rangeland