Unexpected failures of recommended tests in basic statistical analyses of ecological data

Accepted 21 May 2008 Copyright © EEF ISSN 1399-1183 Statistical analysis is an important and responsible stage in ecological research, often posing a challenge. One of the main problems is that the statistical samples typical of ecological research frequently include data that violate the original assumptions of standard analytical tools. A large array of tests has been designed for data of different characteristics (non-normal distribution, unequal variance). Yet, recommendations found in textbooks (Snedecor and Cochran 1980, Sokal and Rohlf 1995, Zar 1999) and handbooks of statistical software (e.g. Statistix 8, Analytical Software, Tallahassee, FL) are not always consistent. For example, ANOVA can compare two or more means, and, when applied to two samples, produces exactly the same p-values as t-test for equal variance. Therefore, ANOVA can replace t-tests for two samples, yet habitually we still use t-tests, and employ ANOVA only when we have more than two means. Why this redundancy? The advantage of t-tests may be that it has a special version adjusted to unequal variance. As far as we know, ANOVA does not provide any widely used procedure for correcting p-values for unequal variance, although tests for equality of variance, such as Bartlett’s test or Levene’s test, are routinely calculated for testing departures from ANOVA assumptions. In these situations, the user is left in a position of Unexpected failures of recommended tests in basic statistical analyses of ecological data