Testing biological hypotheses using statistics is a matter of searching for systematic patterns of signal against the background noise of natural variation.  Our goal is to quantify some measure of the signal-to-noise ratio.  Such measures are known as test statistics, which are defined as calculated measures whose distribution is known when the null hypothesis is true.  Values such as t, F, and X² are commonly-used test statistics.  Since its distribution under the null hypothesis is known, once we have estimated the value of the test statistic, we can calculate the probability that we would generate a value of that magnitude if the null hypothesis were true.  This is equivalent to asking whether there is evidence of significant systematic signal in the data.
 
 

As a review, a working hypothesis is a tentative, causal explanation for a set of observations.  In order to test the working hypothesis, we must actually develop and test a null hypothesis.  The null hypothesis (H₀) is an hypothesis of 'no difference' or 'no systematic variation'; typically, under the null hypothesis, we assume the value of the test statistic will be zero.  In fact, the null hypothesis sets an expected value for some population parameter, and the degree of deviation in the data sample from that parameter is what is quantified by the test statistic.  We then determine the probability of getting a value for the test statistic equal to that observed by chance alone (i.e., when the null thpothesis is true).  If this probbaility is low, we reject the null hypothesis and conclude there is NOT 'no difference' in the data.

^{An alternative hypothesis is a converse to the null hypothesis, and is generally a formalization of the working hypothesis.  There may be multiple alternative hypotheses; in this case, it is best when they are mutually exclusive.  In this way, if we are able to reject the null hypothesis, the type of deviation from the null expectation will tend to support one (and only one) of the alternative hypotheses.}

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