What type of test should I use on my data?

I am testing gas mileage between three brands of gasoline. I am testing on a small population of 10 cars.

• Hypothesis: Cars using higher grade gasoline will have a significant higher gas mileage than cars using regular grade gasoline.

• Null Hypothesis: There will be no significant difference in gas mileage between cars using regular grade gasoline and higher grade gasoline.

The cars first fill up with regular gasoline and record the mileage. Then they fill up with super gasoline and record the mileage. Lastly, they fill up with ultra gasoline and record the mileage.

I am doing tests between:

1. Regular and super
2. Regular and ultra
3. Super and ultra

I am not sure of which test I should use on my data. I was thinking maybe Levene's test or an independent t-test, but I'm not sure.

• Perhaps you could edit your question to tell us what your hypothesis about the different fuel choices is? – mdewey Sep 14 '17 at 13:26
• Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. – gung - Reinstate Monica Sep 14 '17 at 13:55

What you want to do is sum up everything that is relevant in choice for statistical test.

1) amount of dependent variables (from you description: '1' (i.e. mileage))
2) type of this dependent variable (from you description: 'continuous')
3) amount of predictor variables (from you description: '1' (i.e. 'fuel')
4) type of this predictor variable (from you description: 'categorical')
4.b) categorical predictor -> 2 categories or more (from you description: 'more' (3))
4.c) categorical predictor -> between or within? (from you description: between (since each car only drives on one type of gas, instead of having each individual car do the distance on each of the three gastypes))

This all summed up leaves you with 2 options:
(One Way independent samples) ANOVA and Kruskal-Wallis Test.

You should choose the ANOVA if your data meets the 'assumptions for parametric tests' (there are standard tests to check this). If these assumptions are not met, go for Kruskall-Wallis Test.

Later edit: If you designed it like testdriving 3 types of gas per each car, it is slightly different. In this case you would want to use one way repeated measures ANOVA (unless your data don't meet the ussumptions for parametric tests, in which case you should use Friedman's ANOVA)

Later later edit: You can use an in-browser tool for deciding which significance test is the correct one for your research design and type of data; 7questionsorless to find the correct statistical test for any research design.

• My reading of the question, "first they fill up, ...then they fill up, ...", etc., suggests that this is a within car study, not a between car study. – gung - Reinstate Monica Sep 15 '17 at 0:42
• Ah thank you, (i thought that using different types of gas in a car would damage the engine, haha I am not a car person :p) If you indeed designed it like testdriving 3 types of gas per each car, you would want to use one way repeated measures ANOVA (unless your data don't meet the ussumptions for parametric tests, in which case you should use Friedman's ANOVA) – Steven B. Peutz Sep 16 '17 at 9:40