3.2 Null hypothesis

The chi-squared test : this was copied from nature’s scitable

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http://www.nature.com/scitable/buildbook/preview/open-genetics-129407306/129407486#headerAndCitation

Forming and testing a hypothesis

This needs to The first thing any scientist does before performing an experiment is to form a hypothesis about the experiment's outcome. This often takes the form of a null hypothesis, which is a statistical hypothesis that provides the expected values for an experiment. The null hypothesis is proposed by a scientist before completing an experiment, and it can be supported by data or disproved in favor of an alternate hypothesis.

Let's consider some examples of the use of the null hypothesis in a genetics experiment. Remember that Mendelian inheritance deals with traits that show discontinuous variation, which means that the phenotypes fall into distinct categories. As a consequence, in a Mendelian genetic cross, the null hypothesis is usually an extrinsic hypothesis; in other words, the expected proportions can be predicted and calculated before the experiment starts. Then an experiment can be designed to determine whether the data confirm or reject the hypothesis. On the other hand, in another experiment, you might hypothesize that two genes are linked. This is called an intrinsic hypothesis, which is a hypothesis in which the expected proportions are calculated after the experiment is done using some information from the experimental data (McDonald, 2008).

How math merged with biology

But how did mathematics and genetics come to be linked through the use of hypotheses and statistical analysis? The key figure in this process was Karl Pearson, a turn-of-the-century mathematician who was fascinated with biology. When asked what his first memory was, Pearson responded by saying, "Well, I do not know how old I was, but I was sitting in a high chair and I was sucking my thumb. Someone told me to stop sucking it and said that if I did so, the thumb would wither away. I put my two thumbs together and looked at them a long time. ‘They look alike to me,' I said to myself, ‘I can't see that the thumb I suck is any smaller than the other. I wonder if she could be lying to me'" (Walker, 1958). As this anecdote illustrates, Pearson was perhaps born to be a scientist. He was a sharp observer and intent on interpreting his own data. During his career, Pearson developed statistical theories and applied them to the exploration of biological data. His innovations were not well received, however, and he faced an arduous struggle in convincing other scientists to accept the idea that mathematics should be applied to biology. For instance, during Pearson's time, the Royal Society, which is the United Kingdom's academy of science, would accept papers that concerned  either  mathematics  or  biology, but it refused to accept papers than concerned  both  subjects (Walker, 1958). In response, Pearson, along with Francis Galton and W. F. R. Weldon, founded a new journal called  Biometrika  in 1901 to promote the statistical analysis of data on heredity. Pearson's persistence paid off. Today, statistical tests are essential for examining biological data.