## 1 Tailed vs 2 Tailed Test and Null vs Alternative Hypothesis

### Hypothesis testing - Handbook of Biological Statistics

One of the main goals of statistical hypothesis testing is to estimate the P value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals.

### Statistical hypothesis testing - Wikipedia

The statistical is that the number of observations in each category is equal to that predicted by a biological theory, and the alternative hypothesis is that the observed numbers are different from the expected. The null hypothesis is usually an extrinsic hypothesis, where you know the expected proportions before doing the experiment. Examples include a 1:1 sex ratio or a 1:2:1 ratio in a genetic cross. Another example would be looking at an area of shore that had 59% of the area covered in sand, 28% mud and 13% rocks; if you were investigating where seagulls like to stand, your null hypothesis would be that 59% of the seagulls were standing on sand, 28% on mud and 13% on rocks.

Usually, the null hypothesis is boring and the alternative hypothesis is interesting. For example, let's say you feed chocolate to a bunch of chickens, then look at the sex ratio in their offspring. If you get more females than males, it would be a tremendously exciting discovery: it would be a fundamental discovery about the mechanism of sex determination, female chickens are more valuable than male chickens in egg-laying breeds, and you'd be able to publish your result in Science or Nature. Lots of people have spent a lot of time and money trying to change the sex ratio in chickens, and if you're successful, you'll be rich and famous. But if the chocolate doesn't change the sex ratio, it would be an extremely boring result, and you'd have a hard time getting it published in the Eastern Delaware Journal of Chickenology. It's therefore tempting to look for patterns in your data that support the exciting alternative hypothesis. For example, you might look at 48 offspring of chocolate-fed chickens and see 31 females and only 17 males. This looks promising, but before you get all happy and start buying formal wear for the Nobel Prize ceremony, you need to ask "What's the probability of getting a deviation from the null expectation that large, just by chance, if the boring null hypothesis is really true?" Only when that probability is low can you reject the null hypothesis. The goal of statistical hypothesis testing is to estimate the probability of getting your observed results under the null hypothesis.