Kendall’s Tau

Kendall’s tau (τ) represents a means of providing a correlation for rank order level data, which can be important when analyzing data in a quantitative communication research study. Rank order data represents a measurement in which the evaluation of some stimuli is provided in terms of a relative ordering among the elements (1st, 2nd, 3rd, 4th, etc.). The measurement consideration is that the distance between the various evaluations may not be the same. The Kendall’s tau rank order coefficient compares the relationship of rank ordering between two different approaches to measuring the variables. Essentially, a variable becomes rank ordered using two different systems. Take, for example, a ranking of National Collegiate Athletic Association (NCAA) football teams by a computer system and a ranking by sportswriters. The statistic could provide an examination of the level of agreement between the two methods of rank ordering. When different means of rank ordering a set of stimuli are used, the question of whether the same outcomes are produced can become very important. Arguments in collegiate football often involve the issues of how best to rank order teams and compare the various methods of determining the relative value of the teams.

The statistical test involved in Kendall’s tau is considered a nonparametric test. A nonparametric test is one in which no assumption is made about the distribution of the variables (a parametric test by contrast assumes that the variables reflect a bell-shaped or normal curve distribution). The test can range from 1.00 (indicating a perfect agreement in ranking) to a −1.00 (indicating a perfect ranking where one variable is the inverse of the other). A zero Kendall’s tau correlation indicates no correspondence between the two rankings. Like all correlations, the statistic can be thought of as a means of prediction. Knowing the value of one variable, how predictable is the value of the other variable? A perfect set of predictions is indicated by a 1.00 (−1.00) correlation, and a zero correlation indicates no information or predictability exists (i.e., knowing the value of one variable gives no information about the other variable). The greater or smaller the correlation, the greater the departure from zero, the more correspondence between the two rankings, and the greater the accuracy of prediction of the second system if the value in the first ranking system is known. A perfect correlation indicates that the value of the first ranking perfectly predicts the value of the ranking in the second system. A zero correlation indicates that knowing the value of the first system provides no information about the value in the second system.

The statistic is useful for comparing whether or not the two methods of ranking are statistically independent. Alternatively, the statistic could establish the degree that alternative means of rank ordering units produce the same results. When considering whether alternatives produce the same outcome, the researcher should establish a priori what standards should be employed to consider the methods of evaluation as capable of substitution. The remainder of this entry focuses on basic [Page 830]terminology and various versions of Kendall’s tau, a significance test for Kendall’s tau, and some of the uses and applications.

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