37
- undetected, involuntary change of part of the measurement procedure during the measurement series;
- undetected change in standards;
- temporal change in an unidentified relevant variable, i.e., a source of ‘noise’.
Examples
We can gain insight into the statistical techniques described above by considering their application to a few datasets of different types. Our examples come from a variety of original sources, but I got almost all of them from the World Almanac [Hoffman, 1990]. The exceptions are the examples of random normal numbers and of the hare and tortoise. I have deliberately chosen familiar examples rather than artificial data or real scientific data, because the explanation for observed statistical behavior is easier to comprehend with familiar examples. The examples are:
- reexamination of the random normal numbers of Figures 1 and 2;
- race between the hare and the tortoise;
- percentage of high school students that graduate, by state;
- state population (1990 census);
- state taxes, per capita, by state;
Table 6 summarizes the statistical results for these examples, as well as some examples introduced in the next chapter.
| Dataset | N | X | σ | α95 | skew | σx | med | range | α95 | Ch? |
| rand100 | 100 | 0.02 | 0.95 | 0.19 | -0.1 | 0.1 | 0.11 | -2.4/2.2 | -0.28/0.39 | N |
| rand50a | 50 | 0.05 | 0.98 | 0.28 | -0.4 | 0.14 | 0.16 | -2.4/1.9 | -0.28/0.39 | N |
| rand50b | 50 | -0.01 | 0.94 | 0.27 | 0.1 | 0.13 | 0.03 | -1.9/2.2 | -0.4/0.4 | N |
| rand20a | 20 | 0.03 | 0.9 | 0.42 | -1 | 0.2 | 0.19 | -2.4/1.3 | -0.11/0.39 | Y |
| rand20b | 20 | 0.39 | 0.95 | 0.42 | -0.1 | 0.21 | 0.53 | -0.9/1.9 | -0.55/1.23 | N |
| pop | 50 | 4.9 | 5.38 | 1.53 | 2.4 | 0.76 | 3.34 | .4/29.3 | 2.3/4.8 | Y |
| pop -1 | 49 | 4.41 | 4.11 | 1.18 | 1.5 | 0.59 | 3.27 | .4/17.6 | 2.3/4.7 | Y |
| ln(pop) | 50 | 1.11 | 1.01 | 0.29 | 0 | 0.14 | 1.21 | -0.8/3.4 | 0.8/1.6 | N |
| taxes | 50 | 1140 | 343 | 97 | 2 | 48 | 1056 | 553/2674 | 993/1161 | Y |
| tax -1 | 49 | 1109 | 265 | 76 | 0.8 | 38 | 1055 | 553/1993 | 993/1141 | Y |
| deficit | 30 | 10.6 | 7.5 | 2.8 | 0.2 | 1.4 | 11.3 | -1.8/25.7 | 5.5/14.1 | N |
| HS grad | 50 | 75.1 | 7.4 | 2.1 | -0.1 | 1.1 | 76.2 | 58/90 | 72.9/78.0 | N |
| smoked | 10 | 69.6 | 31.2 | 22.3 | 0.5 | 9.8 | 69.2 | 65.7/75.3 | 66.4/73.6 | N |
| Anch T | 12 | 35.2 | 16.8 | 10.7 | 0 | 4.9 | 35 | 13/58 | 18/54 | N |
| bat avg | 90 | 352 | 21 | 4.5 | 0.9 | 2.3 | 350 | 313/424 | 342/354 | Y |
| bat -30 | 60 | 347 | 15 | 3.9 | 0.2 | 1.9 | 346 | 313/385 | 341/353 | N |
