I have emphasized numerous times how important a thorough understanding of the t-test is. A t-test is also the simplest form of linear contrasts. The Least Significant Difference is just one application of the basic t-test. Now is the time to show that you understand the concept. Assume that you have a CRD experiment with 2 treatments, each replicated 4 times; the homogeneity of variance assumption holds. The means for T1 and T2 are 2 and 5, respectively. The residual variance is 2.0. The critical t-value for this experiment at a 5% Type I error rate is 2.5.

a. Use a t-test to determine whether the difference between T1 and T2 is statistically significant at the stated Type I error rate.

b. Determine the Least Significant Difference for this experiment. Although the numbers are easy to calculate, I will be satisfied if you put each numeric part in its proper place.

c. Now use algebra to relate the LSD to the t-test. This will show whether or not you truly understand what an LSD is. You can check your work by plugging actual values into the equation.