Four soldering techniques are to be compared at each of five different factories

Question

Four soldering techniques are to be compared at each of five different factories. Four technicians are chosen at random from each factory to participate, and each is randomly assigned one soldering technique, so that each technique is applied at each factory. The technicians then apply their assigned technique to solder ten joints. Each joint is then subjected to a stress test, and the time until the electric current flow is disrupted for the first time is recorded. Would it be appropriate to apply the ANOVA F-test to evaluate whether there is a difference in mean disruption time across the four soldering techniques? Explain.

Explanation / Answer

Assumptions of ANOVA:
(i) All populations involved follow a normal distribution.
(ii) All populations have the same variance (or standard deviation) across the treatments.
(iii) The samples are randomly selected and independent of one another.

It is given that four technicians are chosen at random from each factory to participate, and each is randomly assigned one soldering technique. So, the assumption (iii) is satisfied.

If the disruption time data follows a normal distribution and the variances of the disruption time are almost equal for four soldering techniques then ANOVA F-test can be applied to test whether there is a difference in mean disruption time across the four soldering techniques.

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