• Story Name: Student t-distribution
  • Story Topics: Biology,
  • Datafile Name: Student t-distribution
  • Methods: Paired T-Test, T-test,
  • Abstract:

    Charles Darwin (1809-1882), author of The Origin of Species (1859) later investi-
    gated the effect of cross-fertilization on the size of plants. Pairs of plants, one cross- 
    and one self-fertilized at the same time and whose parents were grown from the same
    seed, were planted and grown in the same pot.  The numbers of pairs of plants were
    not large because the time and care needed to carry out the experiments were sub-
    stantial. Darwin's experiments had taken 11 years. Darwin had sent the data for 
    several species to his cousin, Francis Galton. Galton (1822-1911), an eminent statis-
    tician, was unaware of any rigorous method for making an inference about  the 
    mean of a population when its standard deviation was unknown. Certainly that was
    the case for Darwin's differences in sizes of pairs of plants. The results of one of
    Darwin's experiments (given by R.A. Fisher) are presented in the datafile.
    W.S. Gosset (1876-1937) was employed by the Guniess Brewing Company of Dublin.
    Sample sizes available for experimentation in brewing were necessarily small, and 
    Gosset knew that a correct way of dealing with small samples was needed. He con-
    sulted Karl Pearson (1857-1936) of Universiy College in London about the problem.
    Pearson told him the current state of knowledge was unsatisfactory. The following 
    year Gosset undertook a course of study under Pearson. An outcome of his study
    was the publication in 1908 of Gosset's paper on "The Probable Error of a Mean,"
    which introduced a form of what later became known as Student's t-distribution. 
    Gosset's paper was published under the pseudonym "Student." The modern form
    of Student's t-distribution was derived by  R.A. Fisher and first published in 1925.

    The datafile Student includes a set of data given by Gosset as an example in his
    1908 paper. Today's student will benefit from applying the Student t-distribution
    to obtain a confidence interval or test a null hypothesis using Darwin's paired
    plant sizes data as well as the sleep differences data given by Gosset. Given the
    modest sample sizes, it is instructive as well to apply single sample non-parametric
    methods for the median to the same sets of data.

Contact Us

© 2017 Data Description, inc. All rights reserved.