Using bootstrap in MS Excel for small samples with photosynthesis time series data as an example

The problem of the small data sample (with the volume of elements up to 30) and its statistical estimates in the context of expansion to the general population in ecological and biological studies is always relevant and is solved differently depending on the goals and objectives. At the same time, researchers often simply bypass the problem because of unclear application of the required statistics in practice and the mathematical complexity for non-specialists, especially if the data is processed exclusively in MS Excel spreadsheet without the use of macros, VBA routines and add-ins, as well as specialized statistical programs. The goal is to obtain estimates of the statistics of small samples and their general statistical parameters as a result of additional sample generation by means of MS Excel. For this purpose, small samples are multiplied by the classic bootstrap, block bootstrap and selective generation of numbers using formulas in MS Excel and their empirical approximations to the true distribution are estimated using elementary statistical functions (mean, median, standard deviation, percentile, confidence interval). As an example, a comparative assessment of the specified functions of daily plant photosynthesis is given, which is a time series with its inherent nuances compared to the classical case of an array of random and independent variables. All the proposed calculations are not complicated and are presented in the form of combined formulas in MS Excel, usable for both scientific and educational purposes. It is shown that an increase in the number of small samples by the above-mentioned methods testifies in favor of using the block bootstrap for a consistent assessment of the statistical parameters of a time series.