On the Mathematical Theory of Errors of Judgment, With Special Reference to the Personal Equation
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Lee and myself can well be described by a normal curve (see 2-1) ; the constants differing by less or by very little more from their normal values than the probable errors. On the other hand, Mr. Yule's and Dr. Lee's (see 1-3) relative judgments differ from normality on the score both of asymmetry and of flat-toppedness, by odds of more than 10 to 1 in each case, or of 100 (or at least 50) to 1 in the combination. Lastly, the odds against Mr. Yule's and my relative judgments (see 3-2) on the ba...sis of a random dis- tribution are only about 4 to 1 on the more unfavourable way of considering them, so that 3-2 might pass as a normal distribution.
We thus conclude that while two out of the six distributions in the bisection series are very improbably random selections from normal material, two others are capitally represented by normal curves, while the remaining two are not very favourable cases.
Taking these results in connection with those for the bright-line distributions we must conclude : That the distribution of errors of judgment can diverge in a very sensible way, both on account of asymmetry and of flat-toppedness, from the Gaussian curve of errors ; but that cases can be found which approximate with all probability to random sampling from normal material.
What to read after On the Mathematical Theory of Errors of Judgment, With Special Reference to the Personal Equation?
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To quickly assess the difficulty of the text, read a short excerpt:
Lee and myself can well be described by a normal curve (see 2-1) ; the constants differing by less or by very little more from their normal values than the probable errors. On the other hand, Mr. Yule's and Dr. Lee's (see 1-3) relative judgments differ from normality on the score both of asymmetry and of flat-toppedness, by odds of more than 10 to 1 in each case, or of 100 (or at least 50) to 1 in the combination. Lastly, the odds against Mr. Yule's and my relative judgments (see 3-2) on the ba...sis of a random dis- tribution are only about 4 to 1 on the more unfavourable way of considering them, so that 3-2 might pass as a normal distribution.
We thus conclude that while two out of the six distributions in the bisection series are very improbably random selections from normal material, two others are capitally represented by normal curves, while the remaining two are not very favourable cases.
Taking these results in connection with those for the bright-line distributions we must conclude : That the distribution of errors of judgment can diverge in a very sensible way, both on account of asymmetry and of flat-toppedness, from the Gaussian curve of errors ; but that cases can be found which approximate with all probability to random sampling from normal material.
What to read after On the Mathematical Theory of Errors of Judgment, With Special Reference to the Personal Equation?
You can find similar books in the "Read Also" column, or choose other free books by Karl Pearson to read onlineMoreLess
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