Originally Posted by KevinP
Originally Posted by dnewton3
What I can tell is that you have fallen victim to the typical noob approach to mathematical statistics. This is a perfect example of the perfect storm; too little understanding of statistics combined with too little data causing one to draw inaccurate conclusions.
To know how your fuel mileage would truly track with oil brand, you'll need 30 samples of your full-tank fill ups with brand X, then another 30 with brand Y. You have to know not only the average, but the variation with each product. You only have 9 sets (2017), 6 sets (2018), and 9 sets (2019). That's well short of the 30 needed for each. Without accurate knowledge of the standard deviation (variation) you cannot understand how much overlap there is. This is not unlike the concept I try to educate folks about in the UOA normalcy study I wrote.
Your data shows many things that would cause concern to a person practicing good statistics:
- there is far too little data to understand variation properly; a prime violation of any statistical process analysis
- there's a large amount of disparity in how many miles are exhibited between the max and min data collection points (2018 shows only 12 mile spread in total miles per sample, but 2017 and 2019 are up near 100; this means you didn't drive near-identical cycles per fill-up for all tests)
- your resolution of stated values violates the mantra of reporting within your gauge accuracy; a magnitude of 10:1 (one decimal place) is acceptable (if you measure to the tenth of a value, then you can only report to the whole number ... etc)
- you have no calorimeter data for the fuel loads; this is paramount to knowing an input that should be corrected for. while you cannot control it, you have to correct for it and without knowing it's value, your assumptions are based on false presumptions. If you use E10 gas, it does not mean it always has 10% ethanol. It only means it has a max limit of 10% ethanol. Therefore the fuel can vary from 0% to 10% ethanol and you have no idea of the true BTU energy in the fuel.
- you don't show any data for accounting for tire wear. A tire's circumference will wear away, altering the true distance for any measured cycle relative to the indicated miles driven; up to 4% of tire circumference can be easily accounted for with only 1/2" of tread wear.
In fact, that last point is critical in knowing. Do the math ...
Using a tire that starts out at 27" in diameter, and degrades 1" in circumference (1/2" wear in depth is radius; 2x for diameter), you'll loose about 4% in tire circumference. (I am ignoring the compression of weight on the tire radius). Doesn't seem like a lot, does it? OK, then take your average miles per fill up and subtract 4% of miles. In this case, we'll presume your fill up shows 470 miles traveled. But the REAL miles traveled will vary greatly. Examples:
1) new tire indicates 470.00 miles traveled; actual driven is 470.00 miles divided by 13.00 gallons = 36.2 mpg
2) worn tire indicates 470.00 miles traveled; actual driven is 451.00 miles divided by that same 13.00 gallons = 34.7 mpg
This represents the variation of using a tire from new condition down to 1/2" tread depth worn away. IF NOTHING ELSE CHANGED, YOUR MILEAGE WOULD VARY BY 1.5 MPG OVER TIME !!! Your indicated distance covered would make your mpg shift over time. Because your data is spread out over three years, we have zero idea of what condition the tires were in for any given fill-up.
My point is that there are so many inputs that you cannot accurately define your mpg down to a whole number, let alone hundredths; you've got too much missing info in terms of both magnitude and resolution. You cannot claim that you know what your true economy is using one brand of motor oil relative to another. Your data is incomplete and your methodology ignores very important key inputs that need to be understood.
It says on the bottle "Make your fuel economy Great Again". All your statistical mumbo jumbo is fake news!
Disagree, not statistical mumbo jumbo, it is reality. I have done something similar and tried to limit or eliminate as many variables as I could. Although the results are compelling to me in my situation, there are variables outside of my control, that could realistically influence the outcome. I will post it soon.