Need help to understand basic probability problem

[ngungo]

This thread is rather a continuation of http://www.talkstats.com/showthread....-of-data/page3

Let consider following 2 sets of experiments's results. The first row can be read as: The set of experiments Exp1 of the same conditions has a successful rate of 87.89 % for only time period 3.86 with a summary of productivity, min:-2.13 1st:0.23 median:0.57 mean:0.71 3rd:1.00 max:12.26.

> result
      success period   Min. 1st Qu. Median Mean 3rd Qu.  Max.
Exp1    87.89   3.86  -2.13    0.23   0.57 0.71    1.00 12.26
Exp12   91.08  18.14  -1.34    0.36   0.71 0.90    1.25  6.89

For the time being just look at 2 variables, success and period.

> result
      success period   
Exp1    87.89   3.86  
Exp12   91.08  18.14

The set Exp1 has a lower successful rate than the second set Exp12. If just making decision based on this single criterion I would pick Exp12 since it has higher rate of success, but this set takes more than 4 times longer to have the result. Other words, it is less efficient. The question is which method has better productivity. How do I determine that?

[ngungo]

Disclaimer: I don't speak probability language.

Let restate the 1st row in term of real units rather than abstract terms. The 1st row says "in a set of experiments of the same conditions Exp1 with 100 batches of raw material it produces 87.89 batches of products in 3.86 hours."

Similarly, the second row says: "in a set of experiments of the same conditions Exp2 with 100 batches of raw material it produces 91.08 batches of products in 18.08 hours."

If we have few hours to do thing, 4 hours for example, we would choose the first method since we don't have time to do the second.

But if let say we have all the time in the universe, and let say we have 100 hours and enough raw material that we can do 100 batches of raw material at a time, which method do we choose?

1. 87.89*(100/3.86) = 2,276.94 batches
or
2. 91.08*(100/18.14) = 502.09 batches

So we would prefer method Exp1. Do I make any sense?

[ngungo]

I am struggle of putting this problem into the context of probability language. Well, I am not sure that my English is understandable either.

[ngungo]

I'd appreciate someone says something. Anything at all. I am wrong. I don't understand, out of touch, or maybe I don't belong here.

[GretaGarbo]

When I saw that there were several replies to ngungos thread I was glad because I thought that ngungo had received several answers. However it turned out that it was just ngungo asking for a reply. I, and maybe others, found it difficult to understand what ngungo really asked for.

“So we would prefer method Exp1. Do I make any sense?”

Yes, of course it makes sense. I agree.

If you in experiment 1 have a success rate of 87.89% in a time period of 3.86 that makes a success rate of 22.76% per 1 time units (i.e. 0.8789/3.86 = 0.2276).

In experiment 2 you have 91.08% success rate on 18.4 time units that makes a success rate of 4.95 % per one time unit (i.e. 0.9108/18.4).

So experiment 1 has a higher success rate per time unit.

(I think this is the same kind of discussion that is going on in this tread by jamesmartinn in regression analysis “Poisson rate regression Offset”.)

“I don't belong here.”

Of course you belong here!

[ngungo]

Hmmm! "Elementary, my dear Watson" said he.

Thanks GretaGarbo!
Can you elaborate further with the full result here:

> result
      success period   Min. 1st Qu. Median Mean 3rd Qu.  Max.
Exp1    87.89   3.86  -2.13    0.23   0.57 0.71    1.00 12.26
Exp12   91.08  18.14  -1.34    0.36   0.71 0.90    1.25  6.89

The first row can be read as: The set of experiments Exp1 of the same conditions has a successful rate of 87.89 % for only time period 3.86 with a summary of productivity, min:-2.13 1st:0.23 median:0.57 mean:0.71 3rd:1.00 max:12.26.

By a casual look I see the productivity of Exp12 is better than Exp1, except for the max. How do I determine which set of experiments better?

If my explanation or questions are hard to understand please ask me to try again.

[Dason]

How do the min, ..., max relate to success or period?

[ngungo]

Each line of the result table represents a series of experiments that carried out with an exactly same set of conditions. Like, say we brew many batches of beer with same recipe, temperature, pressure.

With the recipe Exp1, it takes a period of 3.86 hours to produce beer. When you have beer you sell them, right? 87.89 percents of the times you make money (net profit); other times your loss due to raw material, utilities and labor expense. The summary of all net profits (or losses) is calculated to min, max ...

Ask me more.

[GretaGarbo]

What is confusing with ngungos data is that it seems to be both a dichotomous variable (that is: success/no success or 0/1) and also a variable that seems to take a large number of values – a variable where it seems meaningful to calculate the mean (and also medians, quartiles and so on).

And this is what Dason asked about (if I understand him correctly):

“How do the min, ..., max relate to success or period?”

So it is not really clear what is the most relevant variable to use as a “performance” variable.

If it really is “profit” that ngungo are asking about then maybe ngungo should use that.

If it is time, the time needed to produce correct=”successful” product, then maybe ngungo should use time as the most interesting variable.

But ngungo started this thread as a probability question. Maybe that was a small question in a long series of questions. Has the probability question been answered?

…

Ngungo: Don’t tell us more than you are allowed to. Is this really a designed experiment where they have randomised different “beer batches” (or something) to different experimental conditions? Did they actually randomise?

[ngungo]

1. I went back to my procedure and realized that "success" is a simple percentage of money making batches to all batches. It is simple enough for my simple mind. GretaGarbo, you are right.

2. I then did the summary all accounting figures of all batches.

3. The time period is independent.

4. I don't think I have revealed any confidential info or propriety yet but I have made sure to check with my client and she said it's safe to say that all data come from a real industrial manufacturing. Not randomized experiments.