Author Topic: lets pretend (Read 15799 times)

MikeK · « **Reply #60 on:** March 07, 2010, 05:09:51 PM »

[quote name=\'Matt Ottinger\' post=\'237100\' date=\'Mar 7 2010, 04:56 PM\']"Fail to reject the null hypothesis"? Really?[/quote]
Want me to send you my college stats book, Matt?

I took 58 credit hours of math in college and MY head is spinning.

rjaguar3 · « **Reply #61 on:** March 07, 2010, 05:09:57 PM »

[quote name=\'Matt Ottinger\' post=\'237100\' date=\'Mar 7 2010, 03:56 PM\'][quote name=\'rjaguar3\' post=\'237097\' date=\'Mar 7 2010, 04:35 PM\']We therefore compute a chi-squared value of 0.66 on 6-1=5 degrees of freedom, which is not significant at the 5% level. Therefore, we fail to reject the null hypothesis that the bonus round difficulty is correlated with the prize amount.[/quote]
If that was supposed to be deliberately obtuse for comedic effect, then I apologize for not getting the joke, but frankly, I'm a pretty smart guy, and I have no idea what you're saying.

"Fail to reject the null hypothesis"? Really?
[/quote]

It was not intended for comedic effect. I'm a math major, and I realize that I used statistics jargon, and I apologize. So I'll explain.

We are hypothesis testing:
H0 (null hypothesis): The bonus round conversion rate is not dependent on the value of the puzzle. In other words, # of wins = p * # of attempts for constant p.
H1 (alternate hypothesis): The bonus round conversion rate does depend on the value of the puzzle. That is, Dan is right.

I chose the standard 5% level of significance, which basically means that I am willing to accept rejecting a true null hypothesis 5% of the time. Therefore, we will reject the null hypothesis if and only if there is a less than 5% chance that results as or more extreme than the results we obtained could occur by chance if the null hypothesis is true.

To conduct our hypothesis test, we compute a chi-square statistic based on the data. We then look at the test statistic and determine the probability that we could get results as or more unlikely due to chance. In our case, our statistic theoretically comes from a chi-square distribution with five degrees of freedom. Statistical tables tell us that there is a 5% chance that a random variable sampled from this distribution will be greater than 11.07. Therefore, there is more than 5% chance that a random variable sampled from this distribution will be greater than our test statistic, 0.66. Therefore, it is highly likely that the result is due to chance. We therefore fail to reject the null hypothesis, which is a fancy way of saying we don't have enough evidence to prove that the bonus round conversion rate does depend on the value of the puzzle.

chad1m · « **Reply #62 on:** March 07, 2010, 05:18:47 PM »

Did you ever consider trying out for the position of Countdown model when it was vacant?

/I'm going to assume you know what you're talking about. Never took much of a liking to detailed math.

rjaguar3 · « **Reply #63 on:** March 07, 2010, 05:22:02 PM »

[quote name=\'chad1m\' post=\'237103\' date=\'Mar 7 2010, 04:18 PM\']Did you ever consider trying out for the position of Countdown model when it was vacant?

/I'm going to assume you know what you're talking about. Never took much of a liking to detailed math.[/quote]

No, but I did appear on ESPN's telecasts of the 2003 and 2004 National Mathcounts competition.

http://www.ascehawaii.org/wiliki/wiliki0604.pdf

dale_grass · « **Reply #64 on:** March 07, 2010, 05:24:39 PM »

[quote name=\'chad1m\' post=\'237103\' date=\'Mar 7 2010, 06:18 PM\']/I'm going to assume you know what you're talking about. Never took much of a liking to detailed math.[/quote]
Head down to your nearest Half Price Books and pick up a beginning stats book. Hypothesis testing is about halfway through.

/When I first saw methods of moments, however, I made a Type II error in my pants.

rjaguar3 · « **Reply #65 on:** March 07, 2010, 05:27:10 PM »

[quote name=\'dale_grass\' post=\'237106\' date=\'Mar 7 2010, 04:24 PM\']/When I first saw methods of moments, however, I made a Type II error in my pants.[/quote]

I'm so glad I wasn't drinking anything when I read this. I might have needed to buy a new monitor otherwise.

WarioBarker · « **Reply #66 on:** March 07, 2010, 06:41:11 PM »

Thanks for the correction, guys -- even if I barely understood it myself. In the most basic terms, no the puzzle difficulty does not correspond to the prize value.

Mr. Armadillo · « **Reply #67 on:** March 08, 2010, 09:54:24 AM »

[quote name=\'chad1m\' post=\'237035\' date=\'Mar 6 2010, 09:40 PM\'][quote name=\'Dan88\' post=\'237030\' date=\'Mar 6 2010, 10:11 PM\']puzzles that have an unnecessary "A" in front of them (like A PUZZLE PIECE)[/quote]If it is in a category like "thing", it should be insanely obvious what that "unnecessary" space is going to be.
[/quote]

Believe it or not, he has a point here. While it shouldn't have any bearing on what a contestant chooses, 99% of Wheel contestants are going to see that one-letter word, know it's an 'A', and therefore pick 'A' for their vowel, whereas they might have chosen something else had that one-letter word not planted the 'A' in their brain.

Since 'A' is obviously an inferior vowel choice to 'I' (or the never-chosen-anyway 'U') in this puzzle, I would argue that A PUZZLE PIECE is harder for the average contestant than PUZZLE PIECE would be, and that the people in charge of writing bonus puzzles know this.

[quote name=\'Matt Ottinger\' post=\'237100\' date=\'Mar 7 2010, 03:56 PM\']"Fail to reject the null hypothesis"? Really?[/quote]

Yep, it's basic statistics. You take a hypothesis, and then you run the numbers to see whether the hypothesis holds. However, you cannot accept/reject the hypothesis, since it's impossible to know whether your data is just the one fluke set in a million that randomly matches the hypothesis, so all you can do is either reject it or fail to reject it.

Honestly, 'null' is the only word in that sentence that is pure mathematical jargon.

Going back to that data set, it brings another question to my mind...just what the hell is the distribution of envelopes on that bonus wheel? Only two 40k, one 45k, and zero 100k/1000k's in 125 spins?

clemon79 · « **Reply #68 on:** March 08, 2010, 11:43:13 AM »

[quote name=\'Mr. Armadillo\' post=\'237144\' date=\'Mar 8 2010, 06:54 AM\']99% of Wheel contestants are going to see that one-letter word, know it's an 'A', and therefore pick 'A' for their vowel, whereas they might have chosen something else had that one-letter word not planted the 'A' in their brain.[/quote]
Then this proves nothing more than the fact that 99% of Wheel contestants are idiots.

wheelloon · « **Reply #69 on:** March 08, 2010, 12:33:00 PM »

[quote name=\'Matt Ottinger\' post=\'237100\' date=\'Mar 7 2010, 04:56 PM\'][quote name=\'rjaguar3\' post=\'237097\' date=\'Mar 7 2010, 04:35 PM\']We therefore compute a chi-squared value of 0.66 on 6-1=5 degrees of freedom, which is not significant at the 5% level. Therefore, we fail to reject the null hypothesis that the bonus round difficulty is correlated with the prize amount.[/quote]
If that was supposed to be deliberately obtuse for comedic effect, then I apologize for not getting the joke, but frankly, I'm a pretty smart guy, and I have no idea what you're saying.

"Fail to reject the null hypothesis"? Really?
[/quote]

Well, if it makes you feel any better jaguar, I understood it lol. Then again, I'm a Physics guy... so I guess I'm no better off null set for null set...

[quote name=\'Mr. Armadillo\' post=\'237144\' date=\'Mar 8 2010, 09:54 AM\']Going back to that data set, it brings another question to my mind...just what the hell is the distribution of envelopes on that bonus wheel? Only two 40k, one 45k, and zero 100k/1000k's in 125 spins?[/quote]

It's never been publicly released, just that it has 24 ole' wedges and there's only one $100k/1kk each time.

/I'm not even touching the rest of the conversation...

MSTieScott · « **Reply #70 on:** March 08, 2010, 10:30:43 PM »

[quote name=\'wheelloon\' post=\'237152\' date=\'Mar 8 2010, 12:33 PM\']It's never been publicly released, just that it has 24 ole' wedges and there's only one $100k/1kk each time.[/quote]
Back in the a.t.g-s days, I seem to recall somebody getting a copy of the rules when the bonus wheel was first introduced and posting the distribution. I was running a 'Net Wheel of Fortune back then and I know I didn't just make up the distribution I used. Hmm -- let me see if I can find any old e-mails...

There we go. As far as I'm aware, when the bonus wheel was first introduced, the distribution was:

(3) Car #1
(3) Car #2 (possibly just six car envelopes total -- I don't remember if it was broken down)
(12) $25,000
(1) $30,000
(1) $35,000
(1) $40,000
(1) $45,000
(1) $50,000
(1) $100,000

And of the few episodes I've seen this season, I've noticed something, and I'm glad to see the numbers back up my observation...

[quote name=\'rjaguar3\' post=\'237097\' date=\'Mar 7 2010, 04:35 PM\']From 9/14/09 to 3/5/10, the bonus round has been played 125 times and won 52 times. The distribution is as follows:
$25,000: 15 solves/39 attempts
$30,000: 19/46
$35,000: 10/23
$40,000: 1/2
$45,000: 0/1
$50,000: 2/6
Cars: 5/8[/quote]
I thought it looked like $30,000 and $35,000 were showing up more frequently this year. Which makes sense from a production viewpoint -- since $25,000 is the lowest amount on the bonus wheel, it almost feel disappointing when a contestant wins "only" that much. But if they get $30,000 or $35,000 -- hey, they did better than the minimum!