There is absolutely no point in carrying out an analysis that is more complicated than it needs to be. Occam's razor applies to the choice of statistical model just as strongly as to anything else: simplest is best. The so-called classical tests deal with some of the most frequently used kinds of analysis for single-sample and two-sample problems.
8.1 Single samples
Suppose we have a single sample. The questions we might want to answer are these:
- What is the mean value?
- Is the mean value significantly different from current expectation or theory?
- What is the level of uncertainty associated with our estimate of the mean value?
In order to be reasonably confident that our inferences are correct, we need to establish some facts about the distribution of the data:
- Are the values normally distributed or not?
- Are there outliers in the data?
- If data were collected over a period of time, is there evidence for serial correlation?
Non-normality, outliers and serial correlation can all invalidate inferences made by standard parametric tests like Student's t test. It is much better in cases with non-normality and/or outliers to use a non-parametric technique such as Wilcoxon's signed-rank test. If there is serial correlation in the data, then you need to use time series analysis or mixed-effects models.
8.1.1 Data summary
To see what is involved in summarizing a single sample, read the data called y from the file called classic.txt:
data <- read.table("c:\\temp\\classic.txt",header=T) ...