Mann–Whitney U test when variances are unequal

Kasuya, Eiiti

doi:10.1006/anbe.2001.1691

Cited by 128 publications

(70 citation statements)

References 2 publications

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“…New sexuals were removed after eclosion. As the data were not normally distributed (Shapiro-Wilks test, p!0.05) and variances were not homogeneous (Levene test, p!0.05), we used nonparametric median and sign tests (Kasuya 2001).…”

Section: Methodsmentioning

confidence: 99%

Queen number influences the timing of the sexual production in colonies of Cardiocondyla ants

et al. 2008

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Wingless males of the ant genus Cardiocondyla engage in fatal fighting for access to female sexual nestmates. Older, heavily sclerotized males are usually capable of eliminating all younger rivals, whose cuticle is still soft. In Cardiocondyla sp. A, this type of local mate competition (LMC) has turned the standard pattern of brood production of social insects upside down, in that mother queens in multi-queen colonies produce extremely long-lived sons very early in the life cycle of the colony. Here, we investigated the emergence pattern of sexuals in two species with LMC, in which males are much less long-lived. Queens of Cardiocondyla obscurior and Cardiocondyla minutior reared their first sons significantly earlier in multi-queen than in single-queen societies. In addition, first female sexuals also emerged earlier in multi-queen colonies, so that early males had mating opportunities. Hence, the timing of sexual production appears to be well predicted by evolutionary theory, in particular by local mate and queen–queen competition.

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Section: Methodsmentioning

confidence: 99%

Queen number influences the timing of the sexual production in colonies of Cardiocondyla ants

et al. 2008

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“…The differences between copepod toxin concentrations and differences between the ELISA and PP1 inhibition assays were tested with non-parametric tests, because the assumptions for the parametric tests were not met. The Mann-Whitney U-test was used because the variances were not different (Kasuya 2001). Statistical analyses were done with the Systat 8.0 version for Windows.…”

Section: Methodsmentioning

confidence: 99%

Fate of cyanobacterial toxins in the pelagic food web: transfer to copepods or to faecal pellets?

Lehtiniemi¹,

Engström‐Öst²,

Karjalainen³

et al. 2002

Mar. Ecol. Prog. Ser.

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Toxic cyanobacterial blooms are a common phenomenon in the Baltic Sea. The fate of the toxin in the food web is largely unknown. We studied the effect of algal diets on production of pellets and toxin content of the calanoid copepod Eurytemora affinis in the northern Baltic Sea. Fieldcollected copepods were fed with (1) cultured toxic cyanobacteria Nodularia spumigena; (2) cultured non-toxic flagellates Brachiomonas submarina; and (3) a natural phytoplankton assemblage. Natural phytoplankton was dominated by non-toxic cyanobacteria Aphanizomenon flos-aquae, but also remnants of toxic N. spumigena were found. Pellet production was highest on cultured B. submarina, second highest on N. spumigena and lowest on natural phytoplankton. Because pellets were produced on cultured N. spumigena, this shows that toxic cyanobacteria are consumed if no other food is available. The toxin content of E. affinis was highest in copepods fed with cultured N. spumigena, but toxin was also found in lower concentrations in animals fed with natural phytoplankton. Results indicate that an accumulation of toxins mainly occurs during a growing phase of cyanobacterial blooms. The toxin concentration in the pellets was approximately 6 to 12 times lower than in the copepods. We suggest that a large part of the ingested toxin accumulates in copepod tissues, although some is egested with pellets. This may lead to transport and, possibly, accumulation of cyanobacterial toxin in higher pelagic trophic levels in the Baltic Sea. KEY WORDS: Cyanobacterial toxin · Nodularia spumigena · Toxin transfer · Copepods · Faecal pelletsResale or republication not permitted without written consent of the publisher

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“…Argument 4 relies on the central limit theorem and would require a combined sample size of at least 30 (Sokal and Rohlf 1987, p. 107); however, in my survey, the majority (47 out of 61) of tests for which sample sizes were provided had a combined sample size below 30. The fallacy of argument 3 has been demonstrated previously on several occasions (e.g., Kasuya 2001;Neuhauser 2002 …”

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confidence: 92%

The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test

2006

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Often in the study of behavioral ecology, and more widely in science, we require to statistically test whether the central tendencies (mean or median) of 2 groups are different from each other on the basis of samples of the 2 groups. In surveying recent issues of Behavioral Ecology (Volume 16, issues 1-5), I found that, of the 130 papers, 33 (25%) used at least one statistical comparison of this sort. Three different tests were used to make this comparison: Student's t-test (67 occasions; 26 papers), Mann-Whitney U test (43 occasions; 21 papers), and the t-test for unequal variances (9 occasions; 4 papers). My aim in this forum article is to argue for the greater use of the last of these tests. The numbers just related suggest that this test is not commonly used. In my survey, I was able to identify tests described simply as ''t-tests'' with confidence as either a Student's t-test or an unequal variance t-test because the calculation of degrees of freedom from the 2 sample sizes is different for the 2 tests (see below). Hence, the neglect of the unequal variance t-test illustrated above is a real phenomenon and can be explained in several (nonexclusive ways) ways:1. Authors are unaware that Student's t-test is unreliable when variances differ between underlying populations. 2. Authors are aware of this but consider their samples to have similar variances. 3. Authors believe than the Mann-Whitney U test can effectively substitute for Student's t-test when variances are unequal. 4. Because the t distribution tends to the normal distribution for large sample sizes, authors may consider that their sample sizes are sufficiently large for concerns about unequal variance and nonnormality of the samples to be ignored. Argument 4 relies on the central limit theorem and would require a combined sample size of at least 30 (Sokal and Rohlf 1987, p. 107); however, in my survey, the majority (47 out of 61) of tests for which sample sizes were provided had a combined sample size below 30. The variances of the 2 samples are pooled in order to achieve the best estimate of the (assumed equal) variances of the 2 populations. Hence, we can see the need for the underlying assumption of equal population variances in this test. The Student's t-test performs badly when these variances are actually unequal, both in terms of Type I and Type II errors (Zar 1996). Figure 1 suggests that unequal sample variances are common in behavioral ecology. Although it is true that unequal variances are less problematic if sample sizes are similar, in practice, we often have quite unequal sample sizes (Figure 2). Hence, I suggest that the Student's t-test is frequently used in behavioral ecology when one of its important underlying assumptions is violated, and consequently, its performance is unreliable.The unequal variance t-test does not make the assumption of equal variances. Coombs et al. (1996) presented measured Type I errors obtained by simulated sampling from normal distributions for the Student's t-test and the unequal variance t-test (their r...

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Mann–Whitney U test when variances are unequal

Cited by 128 publications

References 2 publications

Queen number influences the timing of the sexual production in colonies of Cardiocondyla ants

Queen number influences the timing of the sexual production in colonies of Cardiocondyla ants

Fate of cyanobacterial toxins in the pelagic food web: transfer to copepods or to faecal pellets?

The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test

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