Maths Problem

[Lul Thyme]

Originally posted by SpencerH
Some interesting conundrums and proof positive that statisticians dont live in the real world (as I've known for some time). The odds for the monty hall problem and for the birth are 50/50. Those who answered otherwise didnt check their result experimentally and are likely to focus their studies on string theory or voodoo (whichever seems more plausible to their belief systems).

Its funny that you post this in a thread where a poster (gen ludd) didnt really belive us string theorist until he went out and tested it experimentally.

Hows your numerology coming along btw?

[SpencerH]

Originally posted by Lul Thyme

Its funny that you post this in a thread where a poster (gen ludd) didnt really belive us string theorist until he went out and tested it experimentally.

Hows your numerology coming along btw?

I'll get back to this later nonsense later but since I have an appropriate audience I thought I'd ask this question.

I'm reviewing a paper for a journal (not 'Nature' but next tier down) and I've run across a use of statistics that I think is faulty.

The comparison is of three groups using a t-test for samples of unequal sizes. The problem (as I see it) is that the group sizes are 4, 7, and 12. The comparison between the groups with 7 and 12 kids results in a significant difference p=.02.

I've always been skeptical of t-tests performed with low numbers and so have always used non-parametrics for my own studies. The last statistician I worked with reinforced my previous bias but I'm wondering if I'm wrong about this. Does anyone, or everyone, have an opinion?

[SpencerH]

Originally posted by Lul Thyme


Its funny that you post this in a thread where a poster (gen ludd) didnt really belive us string theorist until he went out and tested it experimentally.

Hows your numerology coming along btw?

Wrong.

Gen Ludd realized that its a word game having nothing to do with the actual chances of choosing the prize. Shawnmmmmc was going to test it experimentally.

EDIT: some numerology

Instead of three cups we choose 1,000,000

You pick one then we knock over 999,998 empty cups. By the previous 'logic' you should switch to the non-picked cup since its odds of winning are now only slightly less than 100%.

[Lul Thyme]

Originally posted by SpencerH


Wrong.

Gen Ludd realized that its a word game having nothing to do with the actual chances of choosing the prize. Shawnmmmmc was going to test it experimentally.

EDIT: some numerology

Instead of three cups we choose 1,000,000

You pick one then we knock over 999,998 empty cups. By the previous 'logic' you should switch to the non-picked cup since its odds of winning are now only slightly less than 100%.

OK let me rephrase your problem so were VERY clear.
There are 1000000 cups, only one with something under.
I point to one of 1,000,000.
You remove 999,998 other empty cups.
I can either keep my first cup, or choose the only one left over.
We repeat this many times.

In the long run, I will win WAY more often if I switch, then if I stay.

Do we both agree on this?
If not you are wrong.


By the way t-tests are far away for me, and I cant help you at all with that problem.

I would seem to think if you add the incertitude just to be safe, there is no problem...

[SpencerH]

Originally posted by Lul Thyme


In the long run, I will win WAY more often if I switch, then if I stay.

Do we both agree on this?
If not you are wrong.

You (and the others) are wrong. The odds of picking the correct cup out of 1 million are in no way linked to picking the correct cup out of two choices. They are independent events.

[Kuciwalker]

It's pretty easy to write a computer program to test this, Spencer, or to do it yourself.

[Deity Dude]

Suppose there are 7 cups.
You get to pick 3
Of the 4 remaining I uncover 3 without the prize.
Should u keep your original 3 or switch to the one remaining.






The answer is to trade your 3 cups for the one remaining.

[Snowflake]

Seems to me that you should switch.

[civman2000]

To convert the remaining heathen(s):

Here are a bunch of trials using a random number generator to choose which cup you guess and where the prize is, with 100 cups. In all but one of 50 trials, you win if you switch. Thus this experiment confirms that the odds should be close to 100%.

Guess:  Prize:  Should you switch?
35	33        Yes         
76	24        Yes 
17	59        Yes 
88	83        Yes 
49	33        Yes 
4	36        Yes 
86	46        Yes 
24	37        Yes 
28	99        Yes 
39	86        Yes 
6	27        Yes 
69	94        Yes 
44	5        Yes 
81	10        Yes 
3	46        Yes 
78	96        Yes 
43	53        Yes 
43	8         Yes 
20	90        Yes 
84	98        Yes 
85	55        Yes 
81	41        Yes 
69	97        Yes 
94	77        Yes 
88	71        Yes 
68	80        Yes 
51	25        Yes 
59	59        [b]No[/b]
45	55        Yes 
68	45        Yes 
8	11        Yes 
16	8          Yes 
14	50        Yes 
84	64        Yes 
31	65        Yes 
45	27        Yes 
17	37        Yes 
40	60        Yes 
53	62        Yes 
3	34        Yes 
22	32        Yes 
85	33        Yes 
56	99        Yes 
99	49        Yes 
46	97        Yes 
25	37        Yes 
2	47        Yes 
6	36        Yes 
71	81        Yes 
7	54        Yes

(the first column is the number of the cup you guess first, and the second column is where the prize is)

[Lul Thyme]

Does that convince you?
Why dont you try it with say 7 cups 10 times.
That shouldnt be too long, and should be VERY convincing.

Then you can explain to us what you didnt understand.

Or you can keep saying that we live in fantasy land, while not even daring to actually try it.

[KrazyHorse]

Originally posted by SpencerH
Some interesting conundrums and proof positive that statisticians dont live in the real world (as I've known for some time). The odds for the monty hall problem and for the birth are 50/50. Those who answered otherwise didnt check their result experimentally and are likely to focus their studies on string theory or voodoo (whichever seems more plausible to their belief systems).

Too bad you don't know what the hell you're talking about.

[SpencerH]

Originally posted by KrazyHorse

Too bad you don't know what the hell you're talking about.

Au contraire, I know lots about voodoo.

OK, I realized my error with the cup choice question (knowingly eliminating the empty cups positively selects for the prize) and I misread the birth question (in my defense I was reading it while also reading some sequence data).

No-one has a comment about the t-test and low n then?

[KrazyHorse]

I have no idea what the hell a t-test is. I'm not a statistician. I'm a pseudo-mathematician and statistical physicist.

[Snowflake]

I would also like to hear it if anybody has a concete answer to that question. I myself have been quite suspicious about statistical inferences based on low numbers. However we use it a lot at work here.

[Lul Thyme]

Im glad you figured out the cup and birth questions...

Well I know what a t-test is, but have not close to enough knowledge to be confident about an answer to your question.

BTW its not just with t-tests you have to be quite suspicious statistical inferences based on low numbers...

Being suspicious is always a good start.

Try computing what the confidence intervals are on your tests or something to give you and idea if it seems justifiable.