[SmartCat]

But doc, no car is a "zero". Can't you get rid of this anomaly using a 0.1 to 1 scale?

[Dr.AD]

Originally Posted by NutsNBolts

Dr AD, thanks for such a wonderful exercise and explanation. Of course, without the initial spadework by smartcat and echo77, it wouldn't have been achievable. My sincere thanks three of you and a request to mods to make this thread a sticky. This thread doesn't deserve to go un-noticed by people deciding to buy sedans in near future.

Thanks a lot. Yup, it will be great if this thread could be made sticky.

Originally Posted by smartcat

But doc, no car is a "zero". Can't you get rid of this anomaly using a 0.1 to 1 scale?

Smartcat, I completely agree with you. A score of "zero" does not make sense. It is a tempting thought to "alter" the method a bit to take care of the zero problem. However, unless we can find a very intuitive and fair method of doing this, just arbitrary alteration will end up losing the simplicity and logic behind doing this.

I will think about this problem and come up with an improvement in a day or two. But for now, I can say that the score of "zero" can be simply interpreted by the reader as "that car came last in at least one of the categories" (note: there can be cars that come last in more than one categories). We all know that no car is a zero, and we may very well go ahead and not just like but even end up buying a car the scores a zero. In my own case, I am in search for a sedan, and I may end up buying a Linea E+ Petrol, even though all logic says it scores a 0 in this analysis.

[arishi1]

Dr. AD excellent compilation using the correct Statistical model, and as always thanks to the SMART (Smartcat) and Ecko77.

One request to Dr. AD, can you share the excel spreadsheet here.

MODS: Please make this thread sticky, its a wonderful comparison for all future car buyers.

[StarVegabond]

Good cars will remain good irrespective of the statistical method used.

i see the Optras, Manza, City, Vernas, retaining their top dog rating becasue they do not have no real weak links and are all round performers.

where as Fiestas, Lineas, Suzukis have been bit more volatile compared to the above top dogs depending on the statistical method.

So, now we have our T-BHP's (un) official market research and benchmarking team consisting of smartcat, echo77 and Dr.AD.

Great work guys, i have rated this thread 5 star, certainly worth being a sticky thread.

[Dr.AD]

Originally Posted by arishi1

One request to Dr. AD, can you share the excel spreadsheet here.

Yes, certainly. However, I am really bad at Excel and I would be embarrassed to share my current sheet. I did some haphazard and unorganized changes to echo77's sheet to quickly calculate the results table.

I will need to clean up my sheet and do it in a proper way before I can share it with you guys. Please give me a day or two to do this.

Originally Posted by StarVegabond

Good cars will remain good irrespective of the statistical method used.

i see the Optras, Manza, City, Vernas, retaining their top dog rating becasue they do not have no real weak links and are all round performers.

where as Fiestas, Lineas, Suzukis have been bit more volatile compared to the above top dogs depending on the statistical method.

Very good comment, and I completely agree with you. Sometimes, statistics is just a way of convincing ourselves of the obvious. In my own case, I am at pain to see Linea (especially Petrol) languishing at the bottom of the tables regardless of the method used.

However, we all "love" certain cars (which is difficult to capture in any statistical model), and I believe that is finally the deciding factor when we buy a car. If we did not have this unexplainable notion of loving some cars, we all would be driving only a few type of cars ;-)

By the way, let us not forget that factors like "ride and handling" are not even included in any of the methods used here. Is it merely a coincidence that some of the top cars in the table are not recognized on this forum as being good handlers, whereas some of the bottom cars are especially praised for their handling?

Thanks,
-AD

[bhunu AMG]

Smart cat ...hats off to you man ,really great work and thanks a lot for taking this much pain for us and last but not the least thank you DR.AD and ecco77 for the great work
I have rated five star..yup you deserve it.regards

[Dr.AD]

One more interesting example (of significant change in rankings due to different method of calculations) I just noticed is that of Tata Indigo XL 1.4 Diesel. This car gets the best score for "practicality", and hence a normalized score of a perfect 1.0, but unfortunately gets a very poor normalized score (0.0041) for "safety". Hence, the compounded score is very low, and the final ranking of this car is moved down to 20 from 9 (given earlier). The Compounded Score says that you can't compromise on safety and balance that out by better practicality, and hence penalizes this car heavily.

Thanks,
-AD

[StarVegabond]

Best method is the publish a Poll here on degree of importance for each category of benchmarking and assign the relevant weightage to each class of factors and use it as a multiplier.

this way we can include the populist sentiments as well as factors like handling etc.

The weightage so arrived would be from collective buyer (or member) opinion hence more or less democratic

[echo77]

Dr.AD - simply replace the 0 values by 0.01 and see the results.

I was trying a sum based method similar to yours, but it really messes things up! Marina moves up to 4th!

Attaching the sheet in case anyone wants to mess it up more. I think this includes what Dr.AD has done, except that I have replaced zero values by 0.01

[chennai-indian]

Aah..Was waiting to comment until the final rankings were out. I was pretty sure that Tata Manza will end up at the top. A true VFM car. However, it is funny when people comment on the rankings, most of us will talk about all other cars (Dzire, Cedia et al) and completely ignore Manza!!

[ACM]

Dr. AD - Excellent. you did keep your word.

Agree with smartcat and Echo that "0" somehow seems unfair so 0.1 rating for all zero values or a scale of 0.1 to 1 or 0.1 to 1.1 would be ideal.

[pnredkar]

Originally Posted by Dr.AD

Smartcat, I completely agree with you. A score of "zero" does not make sense. It is a tempting thought to "alter" the method a bit to take care of the zero problem. However, unless we can find a very intuitive and fair method of doing this, just arbitrary alteration will end up losing the simplicity and logic behind doing this.

I will think about this problem and come up with an improvement in a day or two. But for now, I can say that the score of "zero" can be simply interpreted by the reader as "that car came last in at least one of the categories" (note: there can be cars that come last in more than one categories). We all know that no car is a zero, and we may very well go ahead and not just like but even end up buying a car the scores a zero. In my own case, I am in search for a sedan, and I may end up buying a Linea E+ Petrol, even though all logic says it scores a 0 in this analysis.

Hi AD,

How about this: We are using '1' the multiplicative identity for the top car. How about using it as the (geometric) mean value. Suppose we decide the penalty factor, say '2' as an example. The best car gets "1 * 2" while the worst car gets "1 / 2" (or 0.5).

Will this satisfy your intuitive constraint

Regards,
Prasad.

[MihirC]

Hey Smartcat, really awesome list you put up there. I dont mean to buttt in but had a suggestion, could we have a column on the high speed manners of these cars, say at speeds above 130km/hr or something.

[SmartCat]

Originally Posted by MihirC

Hey Smartcat, really awesome list you put up there. I dont mean to buttt in but had a suggestion, could we have a column on the high speed manners of these cars, say at speeds above 130km/hr or something.

I have data on top speed of each car. Does that help?

I guess at 130 kmph, a car that has been built for a top speed of 200 km/hr will be more stable, comfortable & confidence inspiring than a car that has been built for a top speed of 160 km/hr.

[Dr.AD]

Originally Posted by echo77

Dr.AD - simply replace the 0 values by 0.01 and see the results.

Somehow I do not like these arbitrary adjustments like replacing 0 by 0.01. In the normalized system, when a car gets a score of 0, it has a very intuitive and also mathematically sound meaning: that the car is the last (in that category) out of all cars in consideration. When we artificially "fudge" this result to make it 0.01, this meaning is lost. What if there is another car which is second from last and genuinely gets a score of 0.01? How do we differentiate this from our artificial 0.01 correction? Hence, I am not in favor of this. But certainly thanks for the suggestion!

Originally Posted by pnredkar

How about this: We are using '1' the multiplicative identity for the top car. How about using it as the (geometric) mean value. Suppose we decide the penalty factor, say '2' as an example. The best car gets "1 * 2" while the worst car gets "1 / 2" (or 0.5).

Will this satisfy your intuitive constraint

A very interesting suggestion and thanks for it. Yes, it does satisfy the intuitive constraint for the best and the worst case. However, I could see two potential issues:

1. What about the in-between cars? Currently, the formula is simple: normalized score = (x-xmin)/(xmax-xmin); Note that the final difference in normalized scores is linearly proportional to the actual values of "x". In other words, the distribution of normalized scores is the same as of original values. How do you get the geometric series for all in-between values? And also, won't this change the type of distribution? If so, it will introduce errors similar to those of using pure ranking positions as used by Smartcat in the first place. Note that the distribution of ranks (1 through 26) is an uniform distribution whereas the distribution of actual values under any category is not uniform (it could be normal, or something else also).

2. With scale of 0 to 1, the nice property is that multiplication of any numbers (for any number of categories) between 0 to 1 is also a result between 0 to 1. I somehow like this property. This will be lost if some cars are given points such as 2 or 1.5. But this may be a relatively minor point.

By the way, my apologies if I have misunderstood your suggestion and the above points are not true. Please clarify if that is the case. Anyway, thanks a lot for suggestion.

Actually I have thought of a method to take care of this. I will work on this tonight (hopefully will get some time) and will post new results here late tonight. That method has some advantages and some drawbacks, and we will see what happens to the results. May be another revision will be required to take care of the drawbacks

Thanks,
-AD