Figure 4 is a flowchart that shows one possible way of approaching analysis of a variable. Rarely does anyone evaluate a variable as systematically as is shown in Figure 4; indeed, I have never seen such a flowchart or list of steps. This flowchart demonstrates why different examples, such as those in the following section, require different treatments.
A useful first step in analyzing a variable is to ask oneself whether the individual observations, measurements, or data are independent. Two events are independent if they are no more likely to be similar than any two randomly selected members of the population. Independence is implicit in the idea of random errors; with random errors we expect that adjacent measurements in our dataset will be no more similar to each other than distant measurements (e.g., first and last measurements) will be. Independence is an often-violated assumption of the single-variable statistical techniques. Relaxation of this assumption sometimes is necessary and permissible, as long as we are aware of the possible complications introduced by this violation (note that most scientists would accept this statement pragmatically, although to a statistician this statement is as absurd as saying A≠A). Except for the random-number example, none of the example datasets to follow has truly independent samples. We will see that lack of independence is more obvious for some datasets than for others, both in a priori expectation and in data analysis.
Actual scientific data have the same problem: sometimes we expect our measurements to be unavoidably nonindependent, whereas at other times we expect independence but our analysis reveals non-independence. Thus, regardless of expectations, one should plot every dataset as a function of measurement sequence, for visual detection of any unexpected secular trends. Examination of the data table itself often is an inadequate substitute. No statistical test detects secular trends as consistently as simple examination of a plot of variable vs. measurement order. Examples of such unexpected secular trends are:
- instrumental drift;
- measurement error during part of the data acquisition;
