TY - JOUR

T1 - Is the t test really conservative when the parent distribution is long-tailed?

AU - Benjamini, Y.

N1 - cited By 34

PY - 1983

Y1 - 1983

N2 - It is generally believed that the t test is conservative for a sample from a long-tailed symmetric distribution. Yet the probability inequalities expressing this property have not been proved. The inequalities are explored here using various criteria for long-tailedness and leaning on the geometrical interpretation of the t test. It is proved that the t test is conservative but only for large enough critical values. Examples of a liberal t test for lower values are given. The results are used to explain some curiosities in the asymptotic distribution of the t statistic and to study its behavior when the parent distribution is skewed. © 1983 Taylor & Francis Group, LLC.

AB - It is generally believed that the t test is conservative for a sample from a long-tailed symmetric distribution. Yet the probability inequalities expressing this property have not been proved. The inequalities are explored here using various criteria for long-tailedness and leaning on the geometrical interpretation of the t test. It is proved that the t test is conservative but only for large enough critical values. Examples of a liberal t test for lower values are given. The results are used to explain some curiosities in the asymptotic distribution of the t statistic and to study its behavior when the parent distribution is skewed. © 1983 Taylor & Francis Group, LLC.

KW - Conservatism

KW - Long-tailed distributions

KW - Probability inequality

KW - Scale mixture of normals

KW - T test

UR - http://www.scopus.com/inward/record.url?scp=0013340926&partnerID=8YFLogxK

U2 - 10.1080/01621459.1983.10478024

DO - 10.1080/01621459.1983.10478024

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SN - 0162-1459

VL - 78

SP - 645

EP - 654

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

IS - 383

ER -