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Both normality and homoscedasticity tests and standardized residual diagnostics have confirmed the statistical significance of the results.
Table 5 shows the results of applying both normality tests for the scenarios presented in Table 1 for the UP mechanism9 (for the results related to the OR mechanism, refer to Table 2).
Tables 2 and 3 show the results of applying both normality tests for the scenarios described in Table 1.8 For scenarios where both admission control mechanisms have obtained p value > α, we considered that the samples were normally distributed.
Both normality tests consider the following hypotheses, with a confidence level of 95%% (α = 0.05): left{ begin{array}{ll} mathrm{H}_{0}:& text{the sample is normally distributed;} mathrm{H}_{A}:& text{the sample is not normally distributed.} end{array}right.
Both normality (Shapiro-Wilk test) and homoscedasticity (residue plot) were checked; transformations were applied when necessary to approximate normality.
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It is clear from these plots that there are more long-range jumps than would be expected for a Brownian Motion, but for completeness we also performed a Shapiro Wilk test of normality; both the selenium- and sulfur-pooled data gave p-values below 0.001, and so we can reject the hypothesis that Brownian Motion describes the movement of the Os atoms.
For two continuous variables Pearson Correlation was used, as long as both satisfied normality criteria.
We performed the t-test after square root transforming the raw data and testing both for normality (K-S test) and for equality of variances (Levene's test).
Therefore, we logarithmically transformed the data, which led to the satisfaction of both the normality (i.e. through a p-value of 0.10 from the Shapiro-Wilk's test and visual inspection on the histogram) and equal variance (through a p-value of 0.06 from the Breusch-Pagan/Cook-Weisberg test) assumptions.
The long German march to normality required both the '68 Paris-Berlin challenge to bourgeois conformity and Prague's uprising against the Soviet order.
The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com