The null hypothesis is that there is no difference between the data sets, so the test is to see if the mean of the differences between the data deviates significantly from zero or not two-sided test. When two variables move together, they are said to be correlated.
If the analysis covers a longer range, i. Grasping some of the academic theory behind statistics can help ensure that rigor.
The results and inferences are precise only if proper statistical tests are used. If the standard deviations are sufficiently similar they can be "pooled" and the Student t-test can be used. Note in App. Table For example, air temperature and sunlight are correlated when the sun is up, temperatures risebut causation flows in only one direction.
For example, if subjects self-select into a sample group, then the results are no longer externally valid, as the type of person who wants to be in a study is not necessarily similar to the population that we are seeking to draw inference about.
Further investigation of the rapid method would have to include the use of more different samples and then comparison with the one-sided t-test would be justified see 6. We can then apply the more general case of comparing the means of two data sets: the "true" value in Equation 6.