Question

We are attempting to see if we can justify the additional expense of premium fuel over economy; i.e., we will only use premium fuel if we are convinced that it actually helps mpg. For each of the 25 cars at our disposal, we randomly picked one fuel to use first, drove the car until nearly empty, and calculated mpg when refilling the tank. We then filled it with the other fuel, repeating the process, obtaining mpg for that fuel, driving over the same roads.  

Explain why it would be important to randomize the order in which we test two gasoline types. Give a specific example of how not randomizing might cause a problem with this design.

Answer 1

It is important to randomize the order because it might be possible that after having used one type of fuel with the car, the car engine system is altered in its mechanical or thermal or material properties and conditions. And therefore, when used with the second type of fuel, the car system may not allow us for a fair and unbiased judgement of the quality of the second fuel. Hence, when we randomize the order of the usage of the fuel types for each of the 25 cars, we are making sure that we provide an unbiased and fair engine environment to both types of fuel. And data thus collected will have sufficiently fair assessment of both types of fuel.

Take for example, the case when using 1 type of fuel, the car's engine looses its heat capacity and thus when used with 2nd type of fuel after usage with 1st type, the car will give lower mpg compared to the case when 2nd fuel was used in the fresh car engine. In this scenario, we will be selecting incorrectly type 1 fuel as the better one, when actually we have not given type 2 fuel a conducive environment to show us its true quality.

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