# Rounding options

Many scrutiny functions have a rounding argument that controls how numbers are rounded. Specify rounding as any of the strings below.

## In scrutiny

These options return two rounded numbers for each input number. In consistency tests, this means counting a value set as consistent if the reported number matches either of the two rounded reconstructed numbers.

• "up_or_down" (the default): one number rounded up from 5, one down from 5; in this order.
• "up_from_or_down_from": one number rounded up, one down — but not from 5. Instead, specify threshold as the number from which the input should be rounded.
• "ceiling_or_floor": one number ceiled, one floored.

By contrast, these options only return one rounded number per input:

• "even" rounds to the next even number, using base R’s own round(). See note below.
• "up" or "down" rounds in the specified direction, starting at 5.
• "up_from" or "down_from" rounds in the specified direction, starting at some number other than 5. Specify this number via the threshold argument.
• "ceiling" or "floor" always rounds to the next higher or lower decimal place, respectively.
• "trunc" and "anti_trunc" always round towards zero or away from it.

## Rounding at 5 in other software

If the decimal portion to be cut off by rounding is 5, how do these technologies round?

• Python’s standard rounding function rounds to even.

• SPSS rounds to even by default, but users may choose to round up instead.

• Matlab rounds away from zero by default (i.e., it rounds up if the input is positive). However, other rounding procedures can be chosen.

• In SAS, ROUND() rounds up, and ROUNDE() rounds to even. Both have a small tolerance. ROUNDZ() rounds to even without a tolerance.

• Stata seemingly rounds to even, but the documentation is not very explicit.

• In Excel, ROUND() rounds up from 5, ROUNDUP() ceils the number, and ROUNDDOWN() floors it.1

## Note on rounding to even

Rounding to the next even number is not reliable. The fundamental facts of floating-point computation imply that results may vary in unpredictable ways. See this explanation of base::round(), or a more general article about the limits of floating-point arithmetic.

1. Excel’s naming is inconsistent with scrutiny’s usage. For instance, ROUNDUP() always rounds to the higher number, which is called ceiling in scrutiny (and in more common parlance). However, scrutiny’s notion of "up" relies on a shared understanding with the user that numbers will only be rounded up from 5, not from any lower value; likewise with "down". This is arguably suboptimal: compare scrutiny::round_up() to the more explicit naming of janitor::round_half_up().↩︎