PSYC 480 -- A TUTORIAL ON ROUNDING!

Here are a few simple rules that will help you not be graded down for improper rounding.

Let's say the instructions ask for rounding to two nonzero decimal places. Then the following would be examples of correct rounding.

  • Degrees of freedom would not be rounded as they are (usually) whole numbers: df = 15 would be written as 15, df = 10 would be written as 10. Writing them as 15.00 or 10.00 would be wrong.
    • When calculating a mean square, SS/df, the df is considered an exact value. Rules for significant figures don't apply to it. Thus, the correctly rounded answer to 293.78236/15 would depend entirely on how the numerator should be rounded. (This is true when df is a whole number. We'll see later, this is not always the case.)
  • The same rules apply to all integer values (positive and negative whole numbers). If you have 12 subjects, that number is considered to be exact. Don't write it as a decimal number. The rounded value of a mean, sum/N, depends entirely on how many significant figures are in the sum (the numerator), as N is considered exact.
  • Let's say you get an F-value that turns out to be exactly 15. F-values are not whole numbers (integers), so an F-value of 15 rounded to two nonzero decimal places would be written 15.00. That indicates that the value is exactly 15 to two decimal places. If it's written as F = 15, all that tells us is that it is 15 to the nearest whole number, which is not what was asked for.
  • Leading zeros (i.e., zeros on the left) are not significant figures. Therefore:
    • 0.0125437 rounds to 0.013
    • 0.000683457 rounds to 0.00068
  • Zeros in the midst of other nonzero digits are significant. Therefore:
    • 128.704378 could be rounded to 128.70 (although 128.704 would also be accepted)
    • 8.001967 could be rounded to 8.00 (although 8.0020 and 8.00197 would slide by)
  • Trailing zeros are often significant figures. The leading zeros in 0.0011 are just place holders and do not give information about the accuracy of the value. This value contains two significant figures. The trailing zeros (zeros at the end) of 0.001100 do, or at least should, give information about the accuracy of the value. (The correct word is "precision" but "accuracy" will do for our purposes. Just in case you know the difference.) Thus, 0.001100 should be considered to have four significant figures. If it doesn't, if the trailing zeros are spurious, get rid of them.
  • When calculating things by hand, don't round until the very end. Thus, when taking the ratio of two variances, 109.128997/25.03001 is the correct division, not 109.13/25.03, although in this case the rounded answer comes out the same. (It won't always.)
  • p-values that are less that 1/1000 should be written as <.001. STOP WRITING THEM IN SCIENTIFIC NOTATION!
  • R will do your rounding for you (usually correctly). The function is round( , digits=). Thus, round(123.780123, digits=2) will round that number to two decimal places. round(109.128997/25.03001, 2) will round the result of that calculation to two decimal places. R has a tendency to drop trailing zeros (zeros on the right) that should be retained, so be careful about that.
  • As a general note, in statistics we often play a little fast and loose with significant figures because nonsignificant figures are just random error (noise), and in statistics we eat random error for breakfast!
    • However, it is generally considered correct that we are allowed an additional significant figure over what would be allowed in, say, chemistry. Thus, it is considered proper to express the mean of whole numbers to one decimal place, for example.
    • In general, you should follow the rules set by the editor you are writing for (APA Style has rules about how many decimal places to use in published results) or by your COURSE INSTRUCTOR!