Page 22 - Coincidences in the Bible and in Biblical Hebrew

INTRODUCTION

Introduction: About Coincidences,

About This Book

What are coincidences, and how do they differ from other observations that
appear to be random, meaningless, and yet, because they have been subjected

to adequate scientific scrutiny, we treat them as conveying properly established
information?
Science deals with observations that most often are random by nature. Given
this quality of most observed phenomena, a certain approach developed within
the science of statistics, and applied, throughout all disciplines of science and
engineering, to observations where randomness, or noise, is integral and cannot be
ignored. This approach has been realized in a methodology denoted “hypothesis
testing.” The major objective of the latter is to help the researcher separate, in a
collection of noisy observations, the signal from the noise. What is implied by
this is that if one has two competing hypotheses about the true State of Nature
(namely, both hypotheses cannot be simultaneously true), then the decision as
to which hypothesis is true cannot be taken with absolute certainty. Given the
randomness of most observations of nature, all we can do is accept the hypothesis
that is more likely to be true in light of the available evidence. Formulated in a
more formal fashion, one assumes that there are two hypotheses about the true
state of nature: the null hypothesis (H 0), which expresses the current state of our
knowledge, and the alternative hypothesis (H a), which expresses the claim that
one wishes to examine for its validity, given the available data.
Since many observations of nature are random, performing hypothesis testing
requires calculating the plausibility of H 0, given the data, and the plausibility of
H a, given the same data. Most commonly, these “plausibilities” are expressed in
terms of probabilities to err, given the decision that has been selected and the data.
In fact, the testing procedure is constructed in such a way that the error probabili-

ties are minimal and specified prior to conducting the test. Thus, we commonly
denote by α the probability of rejecting wrongly H 0 (this is also called an error of

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