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)
Refresher:
- Geologists have a "hardness" scale for rocks 1-10
- Three cubes were measures with a ruler and found to have volumes of 40, 65, and 75 cubic inches
- Three different highways are identified by their numbers: 95, 76, 476
- Republicans, Democrats, Independents, Libertatians
- The pages of a book 1-150.
Statistics with Scales:
Nominal: ModeOrdinal: Median or Mode
Interval/Ratio: Mean Median or Mode
Descriptive Statistics
Mean= averageMedian= point at which 1/2 scores fall above, 1/2 below
ex:
12, 11, 10, 9, 8
45, 44, 43, 42, 41, 40
10, 9, 8, 8, 8, 7, 7
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?
| Frequency distribution of Lot Elevations at SARH | ||
| Elevation on feet | Number of lots | Fx |
| 348-352 | 20 | 7000 |
| 13-17 | 30 | 450 |
| 8-12 | 30 | 300 |
| 3-7 | 20 | 100 |
| Sum: | 100 | 7850 |
| 7850/100=78.5 | ||
Mean elevation = 78.5 (20 lots above water)
Median Elevation = 12.5
Mean larger than median = "skew"