> TIPsters....
>
> Here is a question I have not seen addressed before....
>
> My stats class typically draws some students from Chemistry and
> Biology. Recently, one of the chemistry students was having a lot of
> trouble getting the correct answers in her computations. I went
> through her work, and discovered that she was applying the rules for
> "significant figures" to her statistical calculations. In other
> words, she was rounding her calculations so that the result of the
> calculation never had a degree of precision greater than the degree of
> precision in the original data.
>
> I have not thought this through, but it looks like application of
> "significant figures" to statistical calculations will virtually
> always result in an "incorrect" calculation.
>
> For example, if our original data are expressed only in whole numbers,
> it seems like a Pearson r could only take on three values: -1.00,
> 0.00, and 1.00.
>
> For now, I have simply told my students to "forget about everything
> you have ever learned about significant figures..." I would prefer a
> better answer. Any suggestions?
>
> -- Jim
>
> P.S. My analysis may be completely incorrect - as I said, I have not
> thought through this completely....
I use Pagano's (1998) text, Understanding Statistics in the Behavioral Sciences (5th ed.) from Brooks/Cole. He addresses this very issue.
"In the physical sciences, we usually follow the practice of carrying the same number of significant figures as are in the raw data. . . . For various reasons, this procedure has not been followed in the behavioral sciences. Instead, a tradition has evolved in which most final values are reported to two or three decimal places, regardless of the number of significant figures in the raw data. . . . Occasionally there will be exceptions. For example, correlation and regression coefficients have three decimal places, and probability values are often given to four places, as is consistent with tradition. It is standard practice to carry all intermediate calculations to two or more decimal places than will be reported in the final answer. [italics in original]. Thus, when the final answer is required to have two decimal places, you should carry intermediate calculations to at least four decimal places and round the final answer to two places." (pp. 29-30)
By probability, he doesn't mean probabilities associated with inferential statistics (p-values) which are usually, due to the alpha = .05 convention, carried to only two decimal places, although they are sometimes carried to three or four if there are a number of zeros after the decimal.
I hope this is helpful.
Rick
Dr. Rick Froman Psychology Department Box 3055 John Brown University Siloam Springs, AR 72761 [EMAIL PROTECTED] http://www.jbu.edu/sbs/psych Office: (501)524-7295 Fax: (501)524-9548
