Analysis of Ranks

One method of providing an evaluation is the rank ordering of some unit. For example, the ranking of college football teams provides an annual exercise in comparison of units. Rank ordering provides a relative placement of units to each other without regard to the relative distance between the evaluations. For example, if teams were rated on a 1–100 basis, it is possible that two teams could receive a ranking of 95, a tie for first place. However, such an evaluation does not mean that the next team will receive a 94; the next team could be evaluated and given a score of 85, for example. We could say that there are two great college football teams and the rest simply not nearly as good.

Rank ordering is to place the teams relative to each other without regard to how much better one team is than another. For example, the first place team may be considered much better than the second place team but the rankings would still be 1 and 2. The third place team may be considered only slightly less skilled than the second place team but would still receive a ranking of 3. The rank order indicates only the relative evaluation, the distance between the evaluations that exists as an exact same interval, in terms of the mathematical or numerical distance but fails to represent the true level of comparison between units.

Special statistics are used to evaluate data generated in these circumstances, permitting the analysis of data collected in this fashion. The analysis of ranks can provide the same kinds of outcomes as when the desire is to compare means, calculate correlations, or even perform more complicated statistical analyses (ordinal multiple regression or ordinal analysis of variance) under this set of conditions.

The question is how to generate the underlying tests that can be used to perform an analysis of ranks. Like all statistics, the issue is the ability to generate an expectation of what the distribution should look like if the ranks were randomly distributed. Suppose we take a simple example of a comparison of whether or not two systems of ranking produce the same or different results. Consider the issue of football rankings; we have two groups do the rankings: (a) coaches and (b) fans. The question is whether the two groups largely agree or not on the rank order of the teams.

[Page 31]A central and simple question considers whether or not the outcome of the two rankings produces the same results. One possibility involves the use of Spearman’s rank correlation coefficient. The goal is the consideration of to what degree the two systems of ranking provide a correspondence with each other. Similar to Pearson’s correlation (used on interval or ratio data), the values run from the perfect levels of 1.00 (as one value increases, the value on the other ranking also increases) to −1.00 (as one value increases, the other decreases). A correlation of 0.00 indicates no predictability or correspondence between the ranking methods. The generated value expresses the degree of accuracy of the value of the second ranking when the value of the first ranking is known. With a perfect correlation, knowing that a team was rated first by the fans would correspond to a ranking of first by the coaches. The higher the correlation, the more accurate the prediction.

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