173 Determination of optimal sample size for understanding the distribution of fecal starch in a fattening cattle herd using numerical simulations.

Abstract Fecal starch (FS) concentration is a critical indicator of starch digestibility in fattening cattle. Accurately understanding its distribution is essential for effective herd management. However, precise assessment requires substantial effort, necessitating efficient and representative sampling methods. This study aimed to determine the optimal sample size for understanding the distribution of FS concentration using the bootstrap method, which does not assume a distribution, and the Monte Carlo simulation, which requires a distributional assumption. An FS dataset obtained from chemical analysis (81 samples from 43 cattle) was analyzed. First, the most appropriate reference distribution was identified from six candidate distributions based on five goodness-of-fit statistics and criteria. Subsequently, the optimal sample size was determined by setting sample sizes ranging from 5 to 150 and applying the bootstrap method and Monte Carlo simulations. In the bootstrap method, the median was calculated for each sample size across 100,000 iterations, and the 2.5th and 97.5th percentiles were used to construct the interval. The change rate of the interval, representing the reduction in width as sample size increased, was calculated. The optimal sample size was defined as the point at which this change rate dropped below 5%. In the Monte Carlo method, reference distributions were fitted to subsets of each sample size (10,000 iterations per size), and the median and intersection-over-union (IoU) were calculated. The optimal sample size was determined when the change rate of the interval (2.5th–97.5th percentile for the median, 5th percentile for IoU) dropped below 5%. The original FS dataset (N = 81) had a median FS concentration of 2.8%DM, ranging from 0.3%DM to 9.4%DM. The results indicated that the gamma distribution was the most suitable reference distribution for the FS dataset. When using the bootstrap method, the variability of the median decreased as the sample size increased, and the optimal sample size was determined to be 40, at which point the 2.5th and 97.5th percentile range was 1.84%DM to 3.32%DM. When using the Monte Carlo simulation, the optimal sample size was approximately 25. At this sample size, the median interval ranged from 1.85%DM to 3.36%DM, and the IoU interval was 0.70. Although the bootstrap method required a larger sample size, its interval was comparable to that of the Monte Carlo simulation with a smaller sample size. Furthermore, with a sample size of 25, a distribution could be obtained in which over 70% of the area matched the reference distribution. In conclusion, this study identified gamma distribution as the most appropriate reference distribution for understanding the distribution of FS concentration in a fattening cattle herd and determined the optimal sample sizes. The Monte Carlo simulation required fewer samples to determine the optimal sample size.