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When samples are extracted from a population with a normal distribution, the distribution of the average of the samples also becomes a normal distribution, and the standard deviation of samples becomes [8].
What lognormal distribution means is that it becomes a normal distribution when the variables are converted by taking logarithmic transformation.
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Much more importantly, even if the distribution of HRQoL data is not Normal, as is frequently the case, that of the sample mean will become closer to a Normal distribution as the sample size gets larger.
Thus, our analytic results are valid only for the initial growth of the trait variance where unimodal distribution (approximated by a normal distribution) becomes broader at the singular point.
Consequently, it has become common practice to fit a normal distribution to log transformed faecal egg counts (FEC) of the form log FEC+ c) for some constant c [ 4, 24] or to Box-Cox transform faecal egg counts [ 25].
Central limit theorem, which states that given a statistically large sample (n >30), the shape of the sampling distribution will become more and more like a normal distribution, irrespective of the parent population [ 18] was applied in analysis and hence parametric statistics were used.
The data for time from PZQ addition until miracidial inactivity and the proportion that became inactive were normally distributed, whereas the time for miracidia to become dumbbell was log-transformed to a normal distribution.
The dataset follows a normal distribution when (K = 1) and gradually changes to uniform distribution when (K) becomes large.
The trait distributions approximately followed a normal distribution except for family EAW78 for which the distribution at BM2 and BM3 became bimodal.
For a normal distribution, only one in 31,574 times will you get an upward statistical fluctuation of 4-sigma or greater.
But very few – if any – online phenomena follow a normal distribution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com