Summu~y.-Formula are derived for the reliability of a composite in the case of ranked data, making use of the special formulas for the mean, variance, and correlation coefficient that are available in this case. The formulas derived are actually identities, differing not in the answers they give but in certain satistics which the investigator may prefer to use. Some years ago, Tryon (1957) demonstrated that four different "methods" of determining the reliability of a composite (rtt) are actually alternative formulas which differ not in the answers they give but in certain scatistics which the investigator may prefer to use. He pointed out that in the case of dichotomous data, there are special formulas for stt, just as there are for the mean (P), variance (pq), and correlation coefficient (4). The purpose of the present note was to derive formulas for 4tt in the case of ranked data, making use of the special formulas for the mean, variance, and correlation coefficient that are also available in this case. To illustrate the problem, consider the data of Table 1, which shows the rankings of N = 5 individuals (objects or persons) by n = 3 judges. Also shown are the mean (M,) and variance (V' = of each judge's ranking, the mean (Mt) and variance (V, = at2) of the pooled rankings, and certain other statistics which will be used subsequently. Note that M4 = MI = (N + 1)/2, the mean of the first N consecutive ranks and that Vi = Vj = (N" 11/12, the corresponding variance. Table 2 shows the correlation (rU) between each pair of judges' rankings and the corresponding covariance (C4, = rilui~,). Note that rij = pp = 1 - 6bED2/N(N2 - I), Spearman's rank correlation coefficient.

http://prx.sagepub.com/content/26/1/67.full.pdf

Reliability of a Composite in the Case of Ranked Data

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Reliability of a Composite in the Case of Ranked Data