Precision issues with Computing Sum and Average PROC MEANS

[rajclin]

Dear Members,

I have encountered a problem while computing sum and mean in SAS for particularly a set of four numbers (0.3, -0.2, -0.1, 0). While I pass these numbers to Proc means the output gives sum as -2.77556E-17 and mean as -6.93889E-18. While actually the sum should be zero and hence the mean should be zero.

I have also tested with different order combination of above 4 numbers (there are 24 combination of arranging different order) where for some of the combination I am getting sum as -5.55112E-17 and mean as -1.38778E-17. The same problem occurs in Proc Summary, even tested with Proc GLM, PROC mixed, which gives different answers in LSmeans.

But Proc Univariate gives the correct result with mean and sum as zero.

If any one can give some insight what is happening with this four magic numbers. Also I have cross checked with Excel and R and facing the same problem for different order combination of above 4 numbers.

PS Attached PROC MEANS and PROC UNIVARIATE output for reference.

Kind Regards,

Rajesh kumar  

[RW9 · Accepted solution]

I expect your hitting floating point storage issues as the resulting number is very small:

See Numerical Accuracy in SAS Numbers.

Just make sure you round values.

[rajclin]

Many thanks for your quick response!!!

[rajclin]

This link gives detailed information Thank you!!!

[Kurt_Bremser]

This is the typical artifact of the conversion of decimal fractions to binary. Do a google search for "SAS numerical precision", and you'll find ample information about what happens behind the scenes, and why it does.

Whenever you work with fractions in SAS, and you need to get a "clean" value for comparisons or such, use the round() function to get rid of the artifacts. Some procedures to that automatically (using "fuzz" factors), others need "manual" intervention.

Note that this is not specific to SAS, but happens in all software that uses real formats for numbers.

[rajclin]

Thank you for your detailed response!!!