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The likelihood ratio P[en | hj·b·cn] / P[en | hi·b·cn] itself measures the extent to which the outcome sequence distinguishes between hi and hj.
In Phase II (qualitative), interview protocols were developed based on the outcome sequence of items in Phase I. Nine teachers were interviewed and have their teaching sessions video-recorded.
This leads us to the idea that finite random sequences, like their infinite cousins, are not able to be generated by an algorithm which exploits patterns in the outcome sequence.
Because of the modal aspect of RCT, for most processes there will possibly be a long enough sequence of outcomes to overcome any 'accidental' randomness due to actual brevity of the outcome sequence.
But a related contrast does exist between those algorithms which are simply crude lists of outcomes, and those which produce outcomes which involve patterns and regularities in the outcome sequence.
The theorem says that when these conditions are met, according to hypothesis hi (taken together with b·cn), the likelihood is near 1 that that one of the outcome sequence en will occur for which the likelihood ratio is smaller than ε (for any value of ε you may choose).
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The theory of randomness for the outcome sequences of such a simple process can be extended to more complicated sets of outcomes.
Thus, the true hypothesis hi probabilistically implies that as the amount of evidence, n, increases, it becomes highly likely (as close to 1 as you please) that one of the outcome sequences en will occur that yields a likelihood ratio P[en | hj·b·cn] / P[en | hi·b·cn] less than ε; and this holds for any specific value of ε you may choose.
In particular, RCT does not propose to analyse chance in terms of these hypothetical sequences, so we can rely on the law of large numbers to guide our expectation that chance processes produce certain outcome frequencies, in the limit, with probability 1; this at least may provide some reason for thinking that the outcome sequences will behave as needed for RCT to turn out true.
The outcome sequences of each assay for the JAK2 V617F and MPL W515L/K detection were aligned with the reference sequence of JAK2 (NG_009904.1) and MPL (NG_007525.1), respectively.
That is (on the standard, though not uncontroversial, Lewis-Stalnaker semantics for counterfactuals: Lewis 1973), though the all-heads outcome sequence is possible, it does not occur at any of the nearest possibilities in which a fair coin is tossed infinitely many times.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com