Sinclair ZX81/Timex Sinclair 1000 Statistics: Twelve 16K Programs Including Multifactor Analysis of Variance by A. H. Wolach and M. A. McHale. K.D.V.-H.E. Publishers. $11.00. 6 program tapes, $15; individual program on tape, $1.50.
In the highly variable world in which we live, we use statistics to help us decide whether the small sample of the universe we look at is really representative of the entire universe. In most cases we want to know whether this sample is representative of a process which is better or worse than the rest of the universe.
Some people, highly critical of statistics, say that you can prove anything you want with statistics. Unfortunately, with the misuse of statistics this can be true. People who can be fooled by statistical abuses often confuse mathematical proof with statistical inference. Mathematical proof does not exist outside the theoretical world of mathematics. In the real world we must use more devious reasoning powers. In using statistics we must always be aware of how that reasoning works. Statistics “sneaks in the back door.”
For example, we can never prove that one mouse trap is better than the other by statistics, but we can prove, with 95 percent or so assuredness, that the two mouse traps cannot be equivalent. The default of this circuitous logic is that the trap that catches more mice must be better since we are sure that the differences between mice caught by each trap could be observed by chance alone less than 5 percent of the time. Technically, these mental gymnastics are called rejection of the “null hypothesis.”
The reason for this background argument is that the software package from Wolach and McHale really works.
Many software packages from houses like Microsoft, Sorcim, Ashton-Tate contain long caveats that they do not guarantee the performances of their software in any specific applications, etc. Perhaps Wolach and McHale should have included a similar warning since people seem to abuse the application of statistics more than any other discipline. The programs can be misused if one does not use the proper test in the proper circumstances.
Although the book has 12 programs, it has really only two main types of tests, namely, the t-test and the analysis of variance.
Clearly the t-test, which tests the distribution about the means (averages) of two groups to see if they are different by chance alone, is designed to compare two groups, e.g., to see if Brand A mouse trap catches more mice than Brand B under the same test conditions. In the first t-test in the book, one can test 5 Brand A vs. 10 brand B, and have a valid test. In the second test, the measurements must be equal in number, i.e., paired observations.
The analysis of variance is to be used in such cases where Brand A is compared to brands B, C, D for the number of mice they can catch. This is a one-way problem; two and three way analysis allows for varying such factors as the kind of mouse caught or whether using bread in the trap is better than cheese.
I entered three or four of the listings in the book. The convention of underlining the “tokens” is quite helpful. The tapes all LOADed the first time (3/4 volume) with no problem. Each of the 12 programs worked perfectly as described in the helpful examples.
For comparison to Wolach and McHale I chose a report from “Some Statistical Methods Useful in Circulation Research” by Sylvan Wallenstein, Christine L. Zucker, and Joseph L. Fleiss in Circulation Research, an official journal of the American Heart Association. The editors had requested the authors, all biostatisticians, to study the statistical methods applied in the journal over the years 1970-80 and to comment on the appropriate or inappropriate use of statistics. They found that the t-test and analysis of variance were the most widely used tests and that the t-test was the only test used in most studies reported in the journal to the almost total exclusion of the analysis of variance which in most cases was the more appropriate test. Wolach and McHale must realize this since they present only two approaches to the t-test and 10 to the analysis of variance.
Table 1. Analysis of Mitral Regurgitrant Orifice Areas. Circulation Research, July 1980, p. 8.
Source of variation Sum of squares df Mean squares F Wolach and McHale Dog (row) 1600 4 400 44.7761 Time (column) 852.55 3 284.18333 31.8115 Residual 107.2 12 8.933335 - Total 2559.75 19 - - Wallenstein et al. Dog (row) 1600 4 400 Time (column) 852.6 3 284.2 31.8 Residual 107.2 12 8.93 - Total 2559.8 19 - -
Table 1 describes the results of the data published compared to the results from Wolach and McHale’s program. The test was a randomized block design done by program BMDP2V (Dixon and Brown, Biomedical Computing Programs, P series, Berkeley: Univ. of California Press, 1977) on an IBM 370 in batch mode through IBM VSPC and by #7RBKE (Wolach and McHale) on a kit-built ZX81 in an interactive mode in real time.
The book provides many fine references to experimental design and the proper application of each of the tests in the package. Students of statistics, or anyone wishing to know more on the subject, will find an excellent course of study using the references listed by Wolach and McHale, their trusty TS1000, and the tapes available with the book.