Point and Interval Estimates
On average you are not OK when your head is in the oven and your feet are in the fridge. But management’s fixation on averages or point estimates to approximate performance is equally ambiguous.
Most often management want certainty and yet as researchers the tools we apply do not allow us to provide such certainty. The question for our fraternity is, in the face of such expectations, are we sufficiently clear in our communication about the limitations of point estimates?
A point estimate is a value calculated from a sample to estimate the unknown population characteristic of interest, such as the mean or proportion.
Inherent Variability
As researchers we know that it is not enough to simply look at the absolute value of a mean or proportion. Since it is an estimate calculated from one of many possible samples, it has inherent variability or margin of error (or standard deviation-SD) associated with it.
Suppose a researcher reports a market share of 20%; 3% down on the previous period. Many important decisions may flow from this information but they may be incorrect if this proportion is considered in isolation of its associated margin of error. Let’s say the error margin on this estimate was 5%. This tells us that the true but unknown population market share of this company falls somewhere between 15% - 25%.
In addition to considering the margin of error (SD) associated with point estimates, it is also important to take into account the size of the sample from which the estimate was made.
Incorporating Sample Size
Generally, the larger the sample the more accurate the estimate will be. It would be a folly to assume two point estimates to be equally precise when one was drawn from a sample of say, 50 respondents and the other from a sample of 1,000.
We can incorporate the sample size consideration into the previously discussed margin of error by using the standard error (SE) rather than the standard deviation.
For the mean estimate, the standard error is calculated as:
SE = SD/√n when sampling without replacement from infinite populations
Thus, the ‘point estimate ± SE’ gives us an interval range that takes into account the variability in the data from which the estimate was made AND the size of the sample.
Our Managerial Challenge
As researchers we need to lead the way in educating management to look at results in terms of interval estimates and not simply point estimates. While we are at it, let’s get them to expect tests of significance as well!
