The randomized complete block design is used in the experiment when there are two factors affecting its outcome. It is inappropriate to consider only one factor to explain the outcome of the experiment. If only one factor is considered, then it will lead to the wrong results of the experiment (Groebner, Shannon, & Fry, 2011). For example, if a company has several products and it could only introduce one product into the new market, then its products are considered as the first factor.
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The success of the company’s products in the new market also depends on the size of the market. The size of the market is the second factor that also affects the decision of the company regarding the product that it could introduce in the new market. Therefore, the company’s expected revenue (outcome) depends on both factors (blocks), and it is not suitable to consider just one of them. In this case, the use of the randomized complete block design is suitable.
The t-test is applicable when there are two samples and the pooled variance is calculated based on the variances of the two samples. However, if there are more than two samples, then the t-test is not useful. It is the discrepancy of the t-test. The following example could be considered to understand this discrepancy.
If there are three populations, then a two-sample t-test can be used to compare only two populations. The third population is left out which affects the calculation of pooled variance within three sample populations. In such cases, Turkey-Kramer or LSD tests are useful to estimate pooled variance by considering sample variance of all three populations (Groebner, Shannon, & Fry, 2011).
Groebner, D. F., Shannon, P. W., & Fry, P. C. (2011). Business Statistics (8th ed.). New Jersey, NY: Pearson.