Table 1. Obtained frequencies of leading digits in textbooks and testbank.
Benford dist. | Knight 3rd ed. end-of-chapter answers | Young 10th ed. end-of-chapter answers | Skoog 7th ed. end-of-chapter answers | Knight testbank answers | Knight testbank distractors | combined data | ||
---|---|---|---|---|---|---|---|---|
# entries | 1644 | 2155 | 294 | 1485 | 5671 | 11249 | ||
1 | 0.3010 | 0.2889 | 0.2858 | 0.3129 | 0.2774 | 0.2906 | 0.2883 | |
2 | 0.1760 | 0.1673 | 0.1689 | 0.1667 | 0.1872 | 0.1816 | 0.1774 | |
3 | 0.1249 | 0.1247 | 0.1128 | 0.1224 | 0.1428 | 0.1259 | 0.1253 | |
4 | 0.0969 | 0.0991 | 0.1104 | 0.1122 | 0.0875 | 0.1010 | 0.1011 | |
i | 5 | 0.0791 | 0.0803 | 0.0891 | 0.0714 | 0.0714 | 0.0890 | 0.0850 |
6 | 0.0669 | 0.0803 | 0.0733 | 0.0646 | 0.0835 | 0.0615 | 0.0695 | |
7 | 0.0579 | 0.0566 | 0.0617 | 0.0510 | 0.0606 | 0.0531 | 0.0562 | |
8 | 0.0511 | 0.0535 | 0.0599 | 0.0340 | 0.0505 | 0.0474 | 0.0508 | |
9 | 0.0457 | 0.0493 | 0.0381 | 0.0646 | 0.0391 | 0.0497 | 0.0464 | |
MAD 1 | 0.0050 | 0.0094 | 0.010 | 0.011 | 0.0054 | 0.0033 | ||
close conform | accept. conform | accept. conform | accept. conform | close conform | close conform | |||
SSD 2 | 4 | 9 | 12 | 15 | 3 | 2 | ||
accept. conform | accept. conform | accept. conform | accept. conform | accept. conform | perfect conform |
1 MAD = Mean Absolute Deviation (see text for definition)
2 SSD = Sum of Square Differences (see text for definition)
Obtained distributions of leading digits and measures of conformation to Benford’s Law for three textbooks, a multiple-choice testbank, and aggregate data