Accuracy versus precision

“You’re on the bus and running a little late for work.  In your hurry, you forgot your watch and your cell phone is at the bottom of your briefcase, so you ask the woman next to you what time it is.  She glances at her watch, which reads 8:33:46, and replies ‘Eight-thirty.’

Did she lie?  Why didn’t she say, ‘Eight thirty-three and forty-six seconds A.M.?’ ”

–    How Many Licks?: Or, How to Estimate Damn Near Anything
by Aaron Santos.

Santos’ scenario is a great example of the difference between accuracy and precision.  The woman gave an accurate yet imprecise answer.  But why do that?  She had the more precise data yet she chose not to use it.

The woman would  probably determine that you didn’t need that level of precision.  Knowing the exact minute or second wasn’t going to change anything.  Santos also suggests that she realized that by the time she gave you the more precise answer, it no longer would have been correct.  So, she chose a response that provided the best answer to your question based on her assessment of your need.

Often we think of accuracy and precision together.  In reality they are quite different attributes of data. They should be treated that way.

Accuracy is the degree to which your data reflect reality.  Saying that the time is eight-thirty was accurate.  Saying eight o’clock or nine o’clock would be less accurate.

Precision is the level of granularity to which the data are reported.  Eight thirty-three is more precise than eight-thirty because it is reporting down to the minute (as opposed to five-minute intervals).  Eight thirty-three and forty-six seconds is even more precise.

Accuracy and precision are separate issues.  Greater precision does not guarantee greater accuracy.  For example, if the woman forgot to adjust her watch for Daylight Savings Time, her statement of eight thirty-three and forty-six seconds would still be precise yet it would be very inaccurate. 

Confusing precision with accuracy can be dangerous, yet many leaders fall into this trap.  Of course, it’s usually more subtle than a time change.  For example, if you asked two people for a report on your quarterly sales and one came back with $150,000 and the other came back with $132,431.53 who would you be more likely to believe?  Many people would believe the second person. Our brains tend to have an unwarranted bias toward specificity.

So which is more important – accuracy or precision?  Both are important but in different ways.  Accuracy is an absolute requirement.  You should not be using data that do not reflect reality. 

Precision is a bit more complicated. Greater precision isn’t always better.  In fact, greater precision can create problems.

Your data should only be as precise as your decision-making.  In other words, if changes at the smallest increment in the data don’t change your decision or actions, you don’t need that level of precision.  For example, consider the earlier example of the woman on the bus.  Changes to the individual minute or second aren’t going to change the man’s behavior.  However, suppose that the two weren’t on the bus but were waiting at the bus stop.  In that case, knowing the time to the exact minute is more important as that could be the difference between catching the bus and missing the bus.

I often encounter reports whose data are too precise.  For many of the decisions that leaders have to make, changes in the tens, ones, tenths, or hundredths place don’t make a difference.  That’s not to say that such a level of precision is bad.  It just depends on context.  For an engineer, a scientist, or a surgeon, changes at those levels (or even smaller changes) can have catastrophic results.  There is no arbitrary cut-off point at which there is too much precision, it is solely dependent on the types of decisions being made.  The right level of precision is the one that informs actions.  Too much can cause over-reactions, too little can cause missed opportunities.  Of the two ends of the continuum, having too much precision is a more common problem.

Too much precision creates distractions.  As measurements become more precise, they become more sensitive to change.  The hundredths place is more sensitive than the tenths place, which is more sensitive than the numbers to the left of the decimal point.  When numbers change, we have a natural tendency to want to understand the cause of the change.  I once spent forty-five minutes with a group of leaders who were trying to explain a .07 change in one of the questions on an employee satisfaction survey.  In the end, the discussion was pointless as the change itself didn’t matter and therefore didn’t require any new or different action.  Despite that, the team still felt a need to explain the change.

Misaligned levels of precision can cause you to spend a lot of time trying to make sense of changes that don’t matter.  That slows down and possible hinders decision-making.

Take a look at your data.  Is it accurate in the sense that it truly answers your question?  Or, have you possibly fallen into the trap of using highly precise measures that may not actually reflect what is going on.  Then, look at the level of precision.  Will you alter your decision or actions if the last digit changes?  If not, you may want to think about decreasing the level of precision at which you are reporting.

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Brad Kolar is the President of Kolar Associates, a leadership consulting and workforce productivity consulting firm.  He can be reached at brad.kolar@kolarassociates.com.

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