Rishabh -

If you are asking how many digits should have been published, with regard to accuracy, then I think most would assume that there is a reasonable chance that the last digit to the right should be off by no more than 1 or 2, such that, for example, 71.026 should have at least a 50% chance of really being somewhere between 71.024 and 71.028, inclusive. Ideally one would expect substantially better than that, but in reality, data you see may be much more misleading, if anything like many of the official statistics from US government statistical and related agencies.  Before deciding how many digits may be reasonably considered valid for you to 'trust' from data you are given, or data you are to report, you should find out what you can about sampling and nonsampling error, about variance and bias.  If you have a confidence interval for a number, the actual accuracy is liable to be worse.  (Note that for a census, there is no sampling error, but there may be a great deal of measurement error.)  So, if you had an estimate of 71.026, and a standard error of 0.673, then you know too many digits were reported (perhaps 71 would have been somewhat reasonable to report).  If you wanted to know if such a number had changed from a previously reported value of 71.389 to 71.026 here, then the answer would be that you can not say with any reasonable certainty, and that in fact those numbers appear to be virtually identical. 

I assume that you may have similar challenges with pharmaceutical statistics.

Cheers - Jim

Rishabh -

If you are asking how many digits should have been published, with regard to accuracy, then I think most would assume that there is a reasonable chance that the last digit to the right should be off by no more than 1 or 2, such that, for example, 71.026 should have at least a 50% chance of really being somewhere between 71.024 and 71.028, inclusive. Ideally one would expect substantially better than that, but in reality, data you see may be much more misleading, if anything like many of the official statistics from US government statistical and related agencies.  Before deciding how many digits may be reasonably considered valid for you to 'trust' from data you are given, or data you are to report, you should find out what you can about sampling and nonsampling error, about variance and bias.  If you have a confidence interval for a number, the actual accuracy is liable to be worse.  (Note that for a census, there is no sampling error, but there may be a great deal of measurement error.)  So, if you had an estimate of 71.026, and a standard error of 0.673, then you know too many digits were reported (perhaps 71 would have been somewhat reasonable to report).  If you wanted to know if such a number had changed from a previously reported value of 71.389 to 71.026 here, then the answer would be that you can not say with any reasonable certainty, and that in fact those numbers appear to be virtually identical. 

I assume that you may have similar challenges with pharmaceutical statistics.

Cheers - Jim

 Significant Figures

Significant figures (or significant digits) are used to express, in an approximate way, the

precision or uncertainty associated with a reported numerical result. In a sense, this is the most

general way to express “how well” a number is known. The correct use of significant figures is

important in today’s world, where spreadsheets, handheld calculators, and instrumental digital

readouts are capable of generating numbers to almost any degree of apparent precision, whichmay be much different than the actual precision associated with a measurement. A few simple

rules will allow us to express results with the correct number of significant figures or digits. The

aim of these rules is to ensure that the final result should never contain any more significant

figures than the least precise data used to calculate it. This makes intuitive as well as scientific

sense: a result is only as good as the data that is used to calculate it (or more popularly, “garbage

in, garbage out”).

Definitions and Rules for Significant Figures

• All non-zero digits are significant.

• The most significant digit in a reported result is the left-most non-zero digit: 359.741

(3 is the most significant digit).

• If there is a decimal point, the least significant digit in a reported result is the rightmost

digit (whether zero or not): 359.741 (1 is the least significant digit). If there is

no decimal point present, the right-most non-zero digit is the least significant digit.

• The number of digits between and including the most and least significant digit is the

number of significant digits in the result: 359.741 (there are six significant digits).

The following table gives examples of these definitions:

Number Sig.

Digits

A 1.2345 g 5

B 12.3456 g 6

C 012.3 mg 3

D 12.3 mg 3

E 12.30 mg 4

F 12.030 mg 5

G 99.97 % 4

H 100.02 % 5

Significant Figures in Calculated Results

Most analytical results in ORA laboratories are obtained by arithmetic combinations of numbers:

addition, subtraction, multiplication, and division. The proper number of digits used to express

the result can be easily obtained in all cases by remembering the principle stated above:

numerical results are reported with a precision near that of the least precise numerical

measurement used to generate the number

Addition and Subtraction

The general guideline when adding and subtracting numbers is that the answer should have

decimal places equal to that of the component with the least number of decimal places:

21.1

2.037

6.13

________

29.267 = 29.3, since component 21.1 has the least number of decimal places

Multiplication and Division

The general guideline is that the answer has the same number of significant figures as the

number with the fewest significant figures:

56 X 0.003462 X 43.72

1.684

A calculator yields an answer of 4.975740998 = 5.0, since one of the measurements has only two

significant figures.

www.fda.gov/downloads/ScienceResearch/FieldScience/UCM092179.pdf

www.fda.gov/downloads/drugs/.../guidances/ucm386366.pdf

www.ivtnetwork.com/.../statistical-analysis-analytical-method-validation

www.fao.org/docrep/w7295e/w7295e0a.htm