A Very Interesting 'Wake Up' Call On Statistics

[MBuzzy]

No, it doesn't.

The die does not know how many times it has been rolled. Every time it is rolled, the chances of any given number coming up is exactly the same. The probability never changes.

If I flip a coin, there is a 50% chance it will land 'heads'. If I flip it a hundred times, there is still a 50% chance it will land 'heads'. If it lands heads 99 times in a row, there is still a 50% chance it will land 'heads' on the 100th flip.

That's why people who play the lottery for a long time think they have a 'better chance' of winning. They don't. They have the same chance as someone who just bought his first ticket ever.

You're right, I'm sorry. I was typing too fast and not reading what I wrote! It made sense in my head!

The concept that I was trying to illustrate is that if you roll a die 1 time, you have a 16.6% chance of rolling any particular number. If you roll at die 10 times, with each roll, you have a 16.6% chance of rolling a particular number, but if you count the number of times that a particular number comes up in the 10 roll set, the probability is still 16.6% for each roll, but you did not necessarily roll 2 (or 1.6) of any particular number. If you roll the same die 100 times, you still have that 16.6% chance of rolling a particular number, but with the larger sample size, it is much more likely that you will roll closer to the 16.6 time of a particular number. As your sample size increase, you are more likely to meet the statistics. For example, if you were to roll 100,000 dice or 1 die 100,000 times, you are more likely to have ACTUALLY rolled the 16.6%.

The point that I'm trying to make is the link between probability and reality, based on the sample size. This is why for statistic research, your sample must be at least n=30 to have statistical significance (I'm talking in Academia). The larger the n, the more reliable your study, especially if you can prove a perfect random sample - which is almost impossible. That is where statistics are the most mutable. It is very difficult to get a truly random sample, there will almost always be some degree of sample bias. Even if you create a spreadsheet and use random number generators, etc...you are still employing some type of sample bias based on who or what actually made it into the spreadsheet unless you can use EVERY occurrence of data set, but even then, your data set may be in correct. I'll stop rambling.

Sorry for the mis-type!

 

[Archangel M]

It when people try to quantify human behavior that we run into trouble IMO. Determining the odds of a die landing is VASTLY different then determining HOW or WHY humans do what they do.

 

[Xue Sheng]

Correct. However, what people sometimes fail to grasp is that each lottery drawing is a new game. All odds are reset. A person who plays every lottery for ten years has the exact same chance to win as a person who plays the lottery for the first time ever, presuming that they each buy one ticket. If you want to increase your chances of winning, buy more tickets per game, not over time.

It would again depend on how many people bought tickets but you are correct in saying if someone buys a ticket every week for a year does not mean with each purchase they have any better chance than they did before but you might be able to show with a statistical probabiklity that that the likelyhood gets better with each purchase. But statistics was a long time ago for me and I am not going to get into it to deeply.

If anyone else wants to here are some Statistical Formulas

Frequently used formulas, Probability formulas, Binomial distribution formulas, Confidence intervals, Sample size, Regression and correlation

Have fun this stuff drove me nuts for 3 semesters waaaaay back in my college days and I am not going back to it.

 

[Gordon Nore]

I came across this on the BBC website and found it very interesting indeed. The number of times that scary sounding statistics are bandied about without context is growing all the time. This is an excellent example of why we should be very careful about what we take on face value.

http://news.bbc.co.uk/1/hi/magazine/7937382.stm

Excellent find, Suke! I shall share this with my teaching colleagues. Perfect lesson on probabilities.

G

 

[Gordon Nore]

Suke,

You'll love this example. In the eighties I was tending bar when the Upper Canada Brewing Company (an upstart brewer at the time) introduced Upper Canada Rebellion, a potent lager at 6% alcohol, rather than the usual five percent. One patron remarked, "I can't understand why I'm getting so drunk on this stuff. It's only one percent stronger than what I usually drink."

"No," I said, "It's twenty percent stronger than what you usually drink."

 

[crushing]

Suke,

You'll love this example. In the eighties I was tending bar when the Upper Canada Brewing Company (an upstart brewer at the time) introduced Upper Canada Rebellion, a potent lager at 6% alcohol, rather than the usual five percent. One patron remarked, "I can't understand why I'm getting so drunk on this stuff. It's only one percent stronger than what I usually drink."

"No," I said, "It's twenty percent stronger than what you usually drink."

How about raising the *standard* tip rate from 15% to 20% because the cost of living has gone up? I think people have gone to 20% because it makes for easier math. ;-)