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.
Working, Null and Alternative Hypotheses
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.