Well, apparantly my attachment did not go through. Here is the text:
RULES FOR THE USE OF SIGNIFICANT DIGITS IN STATISTICS
I. Determining the number of significant digits in the original data
a. Count the number of digits in the original data and look for the datum
with the fewest number of decimal places on the right. Putting all of the
data into scientific notation and the same units (i.e. 3.5 x 105 and 0.069 x
105) is very helpful.
b. Zeros used just to position the decimal point are not significant. For
example, the number 0.0234 g contains only three significant figures; the
two zeros are used to place the decimal point. Similarly, if values were
reported as 300 kg, 200 kg, 500 kg, etc., then the two zeros on the right
are only place holders and this data has only 1 significant digit. Usually
you will have collected the data yourself and will know its accuracy.
c. Zeros that indicate accuracy are significant. For example, the zero in
the number 2.340 g is significant (there is a total of four significant
digits). It tells you the value in the 1/1000th place is 0.
d. When working with count data the number of significant digits is
determined by the largest value reported (some examples of count data are
the number of individuals in a room with a particular hair color or the
number of Fords, Chevys, or Hondas in a parking lot).
e. When data are ranked the number of significant digits is based on the
ranks. The number of significant figures is determined by the largest rank
value/s. A "0.5" due to corrections for ties is not included in the
determination of significant digits. For example, based on the following
ranks -- 1 2 3 4 5.5 7 8 9 10 11 12.5 14 15 -- there are two significant
digits.
II. Going from data to statistics
a. Whenever you are multiplying or dividing, an answer contains no more
significant digits than the least number of significant digits in the
original data. For example, if you multiply the numbers 1.23 and 12.34 on
your calculator you would get the number 15.1782. The correct answer would
be 15.2.
b. When you calculate any statistic from the data that is in the same units
as the original data, the least significant digit is the same decimal place
as the original data. For example, (10.5 cm + 100.2 cm + 1.24 cm + 14.786
cm) / 4 = 31.6815 cm. The correct number of significant digits is 3 or 31.7
cm.
c. When you calculate any statistic that is in different units from the
original data, the statistic has the same number of significant digits as
the original data. For the above example, a t-statistic computed from that
data would have 3 significant digits regardless of the number of digits to
the left or right of the decimal place
III. Reporting
a. Always report one more digit than are significant to account for rounding
error. For example II.b, when reporting the mean, the correct number to
report is 31.68 cm.
b. For statistics in different units from the original data, report the
number of significant digits + 1. Thus for the t-statistic, if you
calculated t = 2.39834, you would report t = 2.398.
c. When reporting critical values from a table, do not use any more digits
to the right of the decimal than are in your calcu�lated statistic. For
example, if a calculated c2=12.24 and the appropriate critical (table) value
is 7.2354 the critical value should be reported as 7.24.
.
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