Suppose, we are interested in finding out if there is a difference in nutritional status in patients who present to our outpatient department with cancer as compared to patients who do not have cancer. Our impression is that patients with cancer have a nutritional status that is worse than other patients. We would like to test if this impression is correct.
In order to test this statement, we need to formulate a hypothesis. The null hypothesis states that there is no difference between the two groups of patients.
Null hypothesis: No difference between study groups
As an alternative there is the alternate hypothesis:
Alternate hypothesis: There is a difference between groups
It does seem perhaps a bit strange, but it is common practice in statistical testing to formulate a null hypothesis (ie there is no difference) and then try to refute this hypothesis with a statistical test. The alternative hypothesis becomes true if it can demonstrated our patients have a worse or better nutritional status (two sided testing). A statistical test tries to prove the null hypothesis is incorrect (similar to law; where you are presumed innocent and it should be proven you are guilty).
First, we need to define an outcome measure. We could use several variables for this (such as albumin concentration in peripheral blood, body mass index etc). Here, we use the thickness of the biceps skin fold as our outcome measure. The data is in the skinfold.rda data set.
The variable we use as our outcome measure is the biceps skin fold thickness. We measure this with a special instrument that measures the thickness of the skin fold in millimetres. The data collected is therefore continuous data.
Next, we need to define how certain we would like to be by setting the p value. In first instance one would say 100%! However, nothing is certain (and not even that!). It is generally accepted that the probability the test statistic takes a more extreme value than 5% is unlikely and the null hypothesis is rejected in favour of the alternative hypothesis.