OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 In Table 2, the observed and critical values of the Pearson’s chi-squared test statistic satisfying the condition χ2 obs < χ 2 crit are highlighted in bold. This indicates that the sample data conforms to the distribution model under consideration. The grain length distribution in nine out of ten fractions aligns with the gamma distribution (90 %) and the law of maximum value (90%). The lognormal distribution provides a better fit for the grain length distributions resulting from rotary grinding (in four out of five fractions). The grain length of the roller-ground material does not conform to the lognormal distribution. Grain width in all considered fractions follows a normal distribution (Table 3). The observed values of the Pearson’s chi-squared test statistic in these fractions are less than the critical values. The grain shape factor in nine out of ten fractions adheres to both the gamma distribution and the law of maximum value (90 %). Based on these findings, the following distribution models were adopted: grain width follows a normal distribution, while grain length and shape factor adhere to the law of maximum value. The Pearson correlation coefficient is a widely used statistical measure that quantifies the strength of the linear relationship between two variables. Its application requires that both variables are normally distributed and derived from the same sample. Given that the grain width follows a normal distribution, while grain length and shape factor adhere to the law of maximum value, any selected pair of geometric grain parameters will not satisfy the condition of the normal distribution law. Therefore, Spearman’s rank criterion was used to estimate the strength of the relationship between the parameters [25]. This involved converting the natural values of the geometric parameters into ranks. Specifically, the numerical values of the geometric parameters were ranked in ascending order, and each value was assigned an ordinal number (rank) accordingly. Fig. 4 presents a graphical representation of the correlations between the geometric parameters of grains obtained through roller press and rotary grinding. The x-axis displays the arithmetic mean of the nominal a b Fig. 2. Experimental distribution of grain length l for fractions after roller-press (a) and rotary (b) milling methods a b Fig. 3. Experimental distribution of the aspect ratio l/b for fractions after roller-press (a) and rotary (b) milling methods
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