# we do not reject the null hypothesis.

The critical value approach involves determining "likely" or "unlikely" by determining whether or not the observed test statistic is more extreme than would be expected if the null hypothesis were true. That is, it entails comparing the observed test statistic to some cutoff value, called the "**critical value**." If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected.

## otherwise we do not reject the null hypothesis

### if we reject the null hypothesis, we conclude that: ..

There are different ways of doing statistics. The technique used by the vast majority of biologists, and the technique that most of this handbook describes, is sometimes called "frequentist" or "classical" statistics. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis. You estimate what the probability would be of obtaining the observed results, or something more extreme, if the null hypothesis were true. If this estimated probability (the *P* value) is small enough (below the significance value), then you conclude that it is unlikely that the null hypothesis is true; you reject the null hypothesis and accept an alternative hypothesis.

### Dec 12, 2008 · If we conclude "Do not reject ..

There is one more point we haven't stressed yet in our discussion about the correlation coefficient *r* and the coefficient of determination *r*^{2} — namely, the two measures summarize the strength of a linear relationship *in samples only*. If we obtained a different sample, we would obtain different correlations, different *r*^{2} values, and therefore potentially different conclusions. As always, we want to *draw conclusions about populations*, not just samples. To do so, we either have to conduct a hypothesis test or calculate a confidence interval. In this section, we learn how to conduct a hypothesis test for the population correlation coefficient *ρ* (the greek letter "rho").