Example Problem

Random-Effect Model One-Way ANOVA

Video 4 provides the step by step analysis for this data using both MS Excel and Minitab.

Video 4. Fixed vs Random Effect Model Design of Experiments Explained with Examples Using Excel and Minitab

Three computers are randomly selected from a computer lab, and the computing times for a task are collected 30 times for all three computers. The data is provided Table 2.

Table 2. Computing Time of 30 replications for Three Randomly Selected Computers

Four Steps

Random Effect Model Design of Experiments

In any design of experiment or any research study, regardless of the discipline, the following four steps are generally followed.

Step #1. Research question (hypothesis)

The variability associated with the random treatment part (τi) of the random effect model in Equation 5 are tested as follows.

Step #2. Appropriate Method

The random effect model in Equation 5 is appropriate for this research question of “whether there is a significant variability between computers.” Analysis can be performed either using MS Excel or Minitab.

Step #3. Analysis & Results with Statistical Explanations

Video 4 provides analysis procedure for a random effect model using MS Excel and Minitab.

The analysis output is provided in Figure 7.

Figure 7. Analysis of Variance ANOVA results from One-Way Random Effect Model Analysis

Statistical Explanation of the Result

We accept (do not reject or fail to reject is the statistical jargon for the word “accept”) the null hypothesis as the p-value (0.925) is larger than the level of significance alpha (=0.05). In fact, any p-value over 0.5 is considered a “no evidence” case, which is very strong in accepting the null hypothesis.

It can also be noted that the variance component for the experimental random error is much higher as compared to the between-computers variability. The variance component for the random factor effect is estimated using Equation 6. Therefore, for the factor variance (treatment variance) smaller than the experimental error variance, the estimated variance component is negative.

Equation 6

Step #4. Contextual Conclusion: Results Explanation in the Context of the Problem

Statistically, there is no significant variability between computers with respect to the computing power. [Simply, rewrite the accepted hypothesis in the context of the problem. The null hypothesis is accepted in this case.] In fact, the within variation (experimental error) is observed to be very high in this case.

Note. As the randomly selected computers are used for the study, the conclusion is drawn for the entire computer population. In this example problem, the population would be the specific computer lab from when the computers were randomly selected.