Doing research is testing theories by means of experiments. However, all experiments are impacted by chance variation such as the (in-)accuracy and the (limited) number of measurements. So, we need statistical techniques to test how big a part chance plays in the outcome.

Here are two issues to consider:

• Is a sample's mean of 6 within the range of means expected for a population whose mean is 7?

• Can two samples with a mean of 6 and of 8 be drawn from the same population with a mean of 7?

In practice, we usually have two hypotheses:

• Null hypothesis: All variation is due to random sampling variation.

• Alternative hypothesis: All variation is due to some hypothetical factor

Next we need to set a limit (usually 95%):

• Inside the limit: We accept the null hypothesis and declare the results random.

• Outside the limit: We accept the alternative hypothesis and declare the results significant (one-tailed: 5%; two-tailed: 2*2.5%) or highly significant (2*1%).

The limit we set here depends on how much of a risk we are willing to take that our null rejection may be wrong. At a 5% significance level, we accept a 5% risk of rejecting a true null hypothesis. This risk can be at both the low end (2.5%) and the high end (2.5%) or at one end only (5%).