We refer to simple analyses as analyses that are used to examine the relationship between two variables, a one-to-one relationship.
Examples come before illustrating the different simple analyses and introducing some terminologies..
Example 1: IRS Study
Lewith & Machin (1981) reported a randomized, controlled study of an infra-red gun called IRS in reducing the pain of subjects with cervical osteoarthrosis. A total of 25 subjects were studied with 12 of them receiving IRS and 13 of them receiving a placebo gun (an infra-red gun with no anticipated therapeutic effect).
There were 75% (9/12) and 31% (4/13) subjects who had pain improvement in the IRS and the placebo groups respectively, resulting in a difference of 44%. The question is whether the difference is genuine or by chance.
The table is often called a contingency table and each combination of a level of the two variables is called a cell. So, there are 4 cells in the above contingency table, which constitute 2 rows and 2 columns of cell frequencies. The above contingency table may also be called a 2x2 table, which signifies the numbers of rows and columns.
Example 2: An IQ Study
Willerman et al. (1991) reported a study that measured the Full Scale IQ (FSIQ) score, Verbal IQ (VIQ) score, Performance IQ (PIQ) score, height (in inches), and weight (in lbs) in a sample of 40 right-handed students. Moreover, Magnetic Resonance Imaging (MRI) was also used to determine the brain size (MRI_C) of the students. Note all measurements are or are approximately continuous. Of interest are the associations among different IQ scores and if a large brain size has any bearings on the IQ scores.