# A Glimpse into History and Statistical Tests

Find historical information on the statisticians who developed statistical tests, such as the normal distribution, Student t distribution, Chi-Square distribution, F distribution, Mann-Whitney test, Pearson product-moment correlation, Spearman rank correlation, Wilcoxon nonparametric tests, Kruskal-Wallis test, Levene test, Ryan-Joiner test, Fisher exact test, and McNamar test. Tell us who these people are and how they happened to make their discoveries and subsequent creations. Identify your Internet sources with an active link.

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#### Solution Preview

One approach to help you with an assignment like this one is to look at the concepts individually, which you can then consider for your final copy. This is the approach this repsonse takes.

RESPONSE:

a)

Normal distribution was developed by de Moivre as an approximation to the binomial distribution, and it was subsequently used by Laplace in 1783 to study measurement and distributions errors and by Gauss in 1809 in the analysis of astronomical data (Havil 2003, p. 157, cited in http://mathworld.wolfram.com/NormalDistribution.html). Subsequently, Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. The term bell-shaped curve is often used in everyday usage. De Moivre's paper, however, was not discovered until 1924 by Karl Pearson. (http://www.stat.wvu.edu/SRS/Modules/Normal/normal.html)

b)

Student t distribution to also called the t-distribution was published by an Englishman named William Gossett in 1908. Specifically, Gosset went to work as a mathematician/chemist for a brewery in Dublin called Guinness. Gosset saw a need for scientific analysis of many factors in the brewing process, such as barley types, hop varieties, yeast activity, cooking temperature/duration, etc. To improve the quality of the beer, he experimented with the different factors, typically using small sample sizes. Realizing that does not follow the normal distribution, he developed a new distribution that is more appropriate for small sample sizes (http://www.bobabernethy.com/bios_stats.htm). The t distribution is very similar to the normal, but it depends on the sample size, and is more appropriate when we must estimate σ with s. There is a different t distribution for every sample size. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student" due to an earlier paper containing trade secrets and consequently the distribution was named "Student's t-distribution".[2] Student's -distribution is defined as the distribution of the random variable which is (very loosely) the "best" that we can do not knowing ( http://mathworld.wolfram.com/Studentst-Distribution.html).

c)

Chi-Square distribution's properties were first investigated by Karl Pearson. Pearson proposed the Chi Square for situations where it is important to make a distinction between the test statistic and its distribution, and siimilar to Pearson Χ-squared test or statistic are used. It is used both in probability theory and statistics. Specifically, the chi-square distribution (also chi-squared or χÂ²-distribution) and developed to use k degrees of freedom and the distribution is of a sum of the squares of k independent standard normal random variables. This test is a widely used probability distributions in inferential statistics and Pearson proposed it to use in hypothesis ...

#### Solution Summary

Discuses the history leading to the development and the developers of various statistic tests, inclduing the Student t distribution, Chi-Square distribution, F distribution, Mann-Whitney test, Pearson product-moment correlation, Spearman rank correlation, Wilcoxon nonparametric tests, Kruskal-Wallis test, Levene test, Ryan-Joiner test, Fisher exact test, and McNamar test..