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Suppose a out of all s loci belong to the category A. Moreover, we find that our set of highly conserved loci contains z < a loci in A. Under the null hypothesis of sampling x loci from s loci uniformly at random, the random number of sampled loci that are in A, X, follows a hypergeometric distribution with parameters s, a, x.
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Under the null hypothesis of sample equality p ij = p ¯ i the non-centrality parameter is zero.
A resampling procedure was therefore carried out to evaluate the likelihood of observed T statistics under a null hypothesis of random sampling from the genome (see Table 1 caption and Methods).
Under perfect concordance this plot will behave like y = x and under random sampling it will behave like y= x 2. The acceptance region at a given level of significance for the hypothesis of random sampling can be constructed by the hypergeometric distribution [ 12].
The pooled case and control sample means are normallz distributed, and the hypothesis of differing sample mean can be tested by using the t-Test.
So, we find the evidence of endogenous switching and reject the null hypothesis of no sample selection bias (Maddala and Nelson 1975).
The Pearson's linear correlation coefficient (Pearson's r) between the pathology and endoscopic examination of oral leukoplakia was calculated under the null hypothesis of both samples of pairs showing the same correlation strength [ 20].
The null hypothesis of the samples being drawn from the same distribution was rejected with a p-value of 0.011 when a data set composed of 4 10 mm SL fish was used.
Nevertheless, concurrent to the functional hypothesis, analysis of samples with non-random XCI revealed that shorter alleles were preferentially more activated among the PCOS cases than controls, although the relative proportion of the activated alleles were not significantly different between them (OR = 1.443, p = 0.33).
We rejected the null hypothesis (similarity of sample and population) on the basis of p ≤ 0.25 in order to keep the β-error, i.e. false acceptance of the null hypothesis, small.
Thus the hypothesis of the continuous sampling observations is unreasonable since in practice it is obviously impossible to observe a process continuously over any given interval, due, for instance, to the limitations on the precision of the measuring instrument or the unavailability of observations at every point in time.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com