Scales of Measurement:Introductory quotes:
"Attributing to statistics the inherent ability to describe universal laws leads to many prevalent and interesting fallacies. Following G.K. Chesterton, we caution against using statistics as a drunk uses a lamp post: for support rather than illumination." (A. Einstein, 1956)
"There are three kinds of lies: lies, damn lies, and statistics." (Benjamin Disraeli, the prime minister of the British Empire from 1874-1880)
Statistics with Scales:Nominal: Mode
Ordinal: Median or Mode
Interval/Ratio: Mean Median or Mode
Descriptive StatisticsMean= average
Median= point at which 1/2 scores fall above, 1/2 below
Mode= middle point
Standard Deviation variability from Mean
Why is this important?
Even with interval/ratio data, the mean may give inaccurate data.
Example: Swampy Acres Retirement Site
The developer of SARH is attempting to sell lots in a "Southern Paradise" to northern buyers. The "marks" express concern that flooding might occur. The developer reassures them by explaining that the average elevation of the lots is 78.5 feet and that the water has never exceeded 25 feet.
So, would you buy a new lot from this developer?
Mean elevation = 78.5 (20 lots above water)
Mean larger than median = "skew"