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V Statistics

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The term “V statistic” could refer any one of several statistics. Which one you’re using depends on what type of analysis you’re performing. For example:

  1. Correlation analysis: Cramer’s V
  2. Discriminant analysis: Rao’s V
  3. MANOVA: Pillai’s V

These statistics are usually called “Cramer’s V, Rao’s V and Pillai’s trace respectively, which avoids the terminology confusion. However, some authors will use the terms “V statistic” without clarification, which can get confusing unless you can decipher the author’s intent and analysis method.

Another type of “V statistic” you might come across is Von Mises’ V-statistic,. Von Mises U and V stats are used in estimation theory, asymptotic theory, and advanced probability theory.

Less common V’s include Bhapkar’s V, used in a distribution-free test for the hypothesis of homogeneity of c populations (Bhapkar & Schwarz, 1977).

1. Cramer’s V Statistic

The term “V statistic” could refer to the statistic associated with Cramer’s V correlation. V used in this sense is a correlation statistic. It tells you if two variables covary (does one variable change when the other changes) and by how much; A V-value of 0 indicates no correlation while 1 indicates perfect correlation.

2. Rao’s V

Rao’s V is a measure of the distance between group centroids, which tells you a little about total group separation. This particular statistic doesn’t tell you anything about within group behavior—just the behavior of the centroid for each group.

Formula for Rao’s V (Klecka, 1980).


3. Pillai’s V

Pillai’s V (also called Pillai-Bartlett trace or just Pillai’s trace) is a general use MANOVA statistic. Compared to similar measures (Like Wilks’ Lambda or Hotelling’s Trace), it is robust to variance heterogeneity and can also handle violations of the assumption of normality (Barnes, 1993).

References

Barnes, M. (1993). Oceanography and Marine Biology, An Annual Review. CRC Press.
Bhapkar, V. & Schwarz, J. (1977). Efficient computation of bhapkar’s V and significance points for its use in small samples. Journal of Statistical Computation and Simulation. Volume 10, 1979-Issue 1.
Frey, V. (2018). The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. SAGE Publications.
IBM. Using Rao’s V as criteria in stepwise Discriminant Analysis in SPSS Statistics.
Klecka, W. Discriminant Analysis, Volume 19; Volume 1980. SAGE, 1980.

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