Wow. If I discovered this page earlier this year, my understanding of statistics would have been so much better. I'm learning a ton even though it's 1AM and I'm not thinking straight. Unbelievable.

*bookmarked*

 

As I wrote, the difference between display and internal data is clear to me.

If you are receiving tank mpg data as x.y, then I should ask: has the additional precision of the mpg been rounded or truncated ? And was the original mpg calc done with three significant digit gallon data, or something rounded or truncated ? We will never know, and can safely assume a mixture of both. Heck, who even knows if a person is consistent in truncating or rounding from calc to calc ??
Ughh

I'll have to think about this some more .. In the meantime, I bid you goodnight with this thought: my car is off by 0.2 in the GH DB. I verified the miles as only off by two (too few) but could not check the tank filling data since it is not relisted (only the mpg/tank is). I input miles, and gallons to 3 significant digits. My total fuel is actually 223.451, and not 222.6 as listed.

 

It's interesting that apparently mileage is only being stored to one decimal place in tanks. I thought it was more. I guess I'll look into exactly how this is being stored in the first place.

Am I right about using standard error instead of standard deviation? Deviation only shows distribution, while error shows accuracy?

 

*gasp*
I found the culprit: $mileage = round($mileage,1);
This code appeared before the system inserted the mileage figure into the database for storage. I took it out, so everything should be more accurate from now on. I wonder what I was thinking! My apologies.

On the optimistic side, I think you're in the minority -- most people just add the mileage in as it is displayed. So, tenths accuracy is all they'd get, anyway. For those who have been using the gallons conversion, I believe the farthest their average could possibly be off is .1 MPG.

 

Hah .. for me it is mostly just a haze.

I believe you are talking about the S.E.M - - standard error of the mean.
The SEM does not replace the SD. You can think of the SEM as telling you the likely range that the "true" mean may lie from your calculated mean, reached as the sample size increases.

I did come across the additional stats, btw. I LIKE IT !

5/06: I have edited out comments regarding change of SD as the sample size increases, since I am not sure they are correct. Sorry for the confusion.

 

Okay. Now we've got:

Median
Middle 50%
Mean
Standard Deviatoin
Standard Error
Sample Size

 

Is the standard error/margin of error in MPG or %?

[edit] Nevermind. Figured it out. I swear I'm learning more statistics after the course than I did during it.

 

I've found some very useful websites in figuring out how to best use statistics in the database:
http://www.isixsigma.com/library/content/c030506a.asp
http://helios.bto.ed.ac.uk/bto/statistics/tress3.html

One thing I still need to look into is sample size at which the data starts becoming "reliable." I keep seeing n=30 pop up, but I'll have to reference my statistics textbook to determine exactly what all these requirements actually mean. I'm also having a tough time determining how everything should be calculated, as the sample size in cars kind of forgets the fact that each individual car is based on a different amount of tanks and miles! Gee, whizz. I need a statistician.

Does population size also change calculations or reliability in any way?

 

A few weeks ago I went through the Prius II DB, and calculated the mean for the subset of cars that had posted at least 5K miles. The result was not much different than the whole group (I cannot remember exactly, but surely less than 1 mpg) -- which surprised me, but there you have it.

I do not understand what you are asking in your last question. I had mentioned n=30 in an earlier post, but culled it out after I remembered that the sample size is pretty explicit ..

 

Yes, I know about this. A while ago I calculated without all cars <3k miles and the averages were about the same.

As far as the n: right now, there are a couple models with a sample of just 23 cars. I'm asking if this means that model's calculations are inaccurate for the time being? I need to look up the assumptions for t-tests, as I believe the data falls in that category for testing?

I think I'm going to approach my statistics teacher to see if she can help me figure out what the true error in the database is, as first there's a small error we'd have to guess at for the actual calculation of fuel economy per tank. So there's error in each tank, and then each car, and finally the whole model. To make matters more complicated, each car is the result of either many tanks or a single lifetime mileage override. *confusing*

I have plans to make a page that explains exactly how the database works.