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The CTO (Chief Technical Officer) of a company wants to decide which operating system (OS) to use as standard in the company. In particular, she

The CTO (Chief Technical Officer) of a company wants to decide which operating system (OS) to use as standard in the company. In particular, she wants to compare the OS types Apple, Linux, and Windows. For this, she plans to implement a test strategy that looks at the number of complaints that the employees submit for each OS (response variable). In total, she wants to have 19 observations for each OS. The experimental data has following general structure:

ObservationAppleLinuxWindows
1111
2568
35212
19111215

The CTO and CIO (Chief Information Officer) get into an argument about the type of ANOVA design that should be used. Specifically, the CTO wants to use 57 different employees overall, to get a broad representation of the entire team. The CIO suggests using employees as a blocking variable instead. That is, the CIO wants to select 19 employees who each test all three OS types, Apple, Linux, and Windows.

As they are not able to come to an agreement, they ask you as the resident ANOVA expert. Which approach / design would you recommend? What would be the benefit of your recommended approach, compared to the alternative design?

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