Truth and Central Tendency ◾ 31
2. Geometric mean: central tendency for skewed positive data
3. Harmonic mean: central tendency for skewed positive data
In the second category, we obtain participation from only strategically selected
data points. We have seen seven such measures.
Category 2
1. Mode: a better indicator of central tendency in human performance
2. Median: a better indicator of central tendency in nonnormal data
3. Trimmed mean: straight removal of extreme values
4. Winsorized mean: robust calculation
5. Trimean: a weighted average of quartiles
6. Midhinge: an average of the first and the third quartiles
7. Midrange: average of lowest and largest values
We can estimate a pertinent set of means before judging the central tendency. e
choice would depend on the skew, the presence of outliers, and the degree of protec-
tion we need from outliers. Such a choice would make analysis robust and safe.
Truth
Truth, expressed as central tendency, has many variants. We can narrow down our
options depending on the type of data and depending on what we wish to do with
the finding. e message is not in the mean, nor in the median. e message is to
be seen in the many expressions. To the mathematically inclined, geometric mean
and harmonic mean are alternatives to the arithmetic mean. e differences must
be reconciled with practical reasoning.
Statistical judgment is never the ultimate end.
Further reasoning alone can discover truth.
Statistical calculations need not be the ultimate truth. At best, they can guide
us toward truth. e moment of truth occurs only with reasoning.
To the empirical researchers, there is a series of trimmed means to bestow alter-
natives to the median.
e impact of multiple definitions of central tendency is rather heavy while
evaluating shifts in process means. It is safer to work out all the definitions, obtain
multiple numbers for central tendency, and treat them as a small universe of values.
We will have to compare one universe of central tendency values with
another. We can no longer pitch one mean against another or engage in
such misleading exercises.