Statistics deals with uncertainty. When we make a statement; we also need to say how certain we are that this statement is correct. We would like this to be 100%, but realise that this is not possible. It is generally accepted (in medical statistics) that something is ‘proven’ if we are more than 95% certain. This means that there is a probability of 5% that our statement is incorrect. Or p = 5%.
P Value Probability that statement is incorrect
We usually call something ‘proven’ or statistically significant if following a statistical test the p value < 5%.
Statistically significant p < 5%
That something is statistically significant doesn’t necessarily mean it is also clinically significant. It might well be that, although statistically there is a difference, it is of no clinical importance.
Also, if we were unable to demonstrate a statistically significant difference; this doesn’t mean there is no difference. After all, if p = 5% there is a probability of 1 in 20 that our statement is incorrect! It might well be that with more patients in our study, we can demonstrate a significant difference (underpowered study).
If p = 5%, there is a probability of 1 in 20 that our statement is incorrect. However, in 19 out of 20 times our statement is correct. In a lot of cases we would like to be more certain than this (when we cross the road or fly in a plane!). Also when we buy a bottle of wine, we wouldn’t accept it if one in 20 bottles has less than 75 cl of wine!
If p = 1%, our statement is incorrect only 1 out of 100; whilst this is 1 in 1000 if p = 0.1%. The smaller the p value the more certain we are that what we say is true. Consequently, we aim for a low p value.
However, the lower the p value, the more patients would be required to demonstrate a statistically significant difference. Furthermore, in biological systems (unlike man made systems) the variation is large. Therefore, it is very unlikely to get p values much below 5% or 1%. If the p value is considerably lower than 1% it is more likely that we are trying to state the obvious or that the variables are dependent.
In medical statistics we are usually satisfied something is statistically significant if p < 5%. If p < 5%, we feel this is unlikely to be due to chance and the null hypothesis is rejected in favour of the alternate hypothesis.
For example, 29 patients that attended our outpatient department had their biceps skin fold measured. The results are listed in skinfold.rda.
The data are not in order of when the patient attended outpatient clinic, but grouped by diagnosis and increasing thickness of the skin fold. Patients either had ‘No Cancer’ or ‘Cancer’:
Now, we need to decide which statistical test to use.
A parametric test can only be used if the data are Normally distributed. If the data are not Normally distributed, we can not use parametric statistics and we will have to use a non parametric test.