The Student’s t-test

The famous t-test was initially illustrated by “Student” in a paper published in 1908 (available at: http://biomet.oxfordjournals.org/ cgi/reprint/6/1/1). In the paper, Student used several examples to illustrate the process. One example (Illustration 3) discussed the yield of barley of seeding plots with two different kinds of seed. Each type of seed (kiln-dried and not kiln-dried) was planted in adjacent plots in two different years, accounting for 11 pairs of “split” plots. The data listed below are from the table on page 24 of the 1908 paper.

The statistical method used in Student (1908) is very different from the ones we use now. On page 24, Student concluded that the odds that kiln-dried seeds have a higher yield is 14:1. Conduct the t-test using the “head corn” yield data shown above. Can you guess where the 14:1 odds come from?

The Everglades wetland ecosystems are phosphorus limited. After the Everglades Agriculture Areas (EAA) were established (enabled by a series of federal government constructed water diversion systems for draining part of the Everglades wetland), phosphorus-rich agriculture runoff reached the Everglades wetland and resulted in dramatic changes in parts of the Everglades wetlands. To better protect the Everglades, many studies were conducted in the late 1980s and the 1990s to learn about the effects of phosphorus enrichment in the Everglades. One study focused on estimating the background level of phosphorus concentration. To identify which site is not affected by the agriculture runoff, researchers measured phosphatase activity (APA) in sites known to be affected (TP > 30 µg/L) and sites that are unaffected by agriculture runoff. Phosphatase is an enzyme produced by organisms in low P environment. Because producing this enzyme costs energy, organisms do not produce them when bio-available phosphorus are present. As a result, high APA is an indicator of P limitation. The data file apa.s contains both APA and TP concentrations. It can be imported into R using function source.

(a) Compare the distributions of APA from sites with  and APA from sites with  using graphical tools we learned in Chapter 3.

(b) What is the nature of difference between the two populations of APA?

(c) Use an appropriate test to determine whether the difference is statistically significant and describe the result in non-technical terms.