If anyone is scrolling by here and wants to attempt to explain hypothesis testing (traditional & P-value method) to an idiot, I'd sure appreciate it. Cuz, I'm feelin' real stupid over here & have a test in just over 24 hrs.
Is there something specific you want to ask? I took statistics and might be able to help you.
Quoting from Wikipedia: "...statistical tests are used to determine how likely it is that the overall effect would be observed if no real relation as hypothesized exists."
If on a call toss, you call heads and the coin turns up heads, you would know that it was chance. A moron might think the fact that he called it caused it to turn up heads.
His hypothesis is that his words caused the coin to come up heads -- that those two things are related.
We test this hypothesis to see if it is likely that they are related or not.
"If that likelihood is sufficiently small (e.g., less than 1%), the existence of a relation may be assumed. Otherwise, any observed effect may as well be due to pure chance."
Wikipedia says one example of sufficiently small is less than 1%. That can be true for scientific phenomenon, and for social science, the percentage is often less than 5%. The percentage level you're aiming to be below is the P-value.
Going back to the moron and the coin, this is a social science experiment so we'll agree to set the P-value at 0.05. 0.05 = 5%, which means if there's more than a 5% chance that the things are unrelated, we'll agree they are unrelated.
*Below* the P-value! Well, that right there is more than I've got from the class. Thank you!
Here's a specific question: If a problem is something like: A sample of 47 jelly beans yield a mean weight of .45 grams, with a standard deviation of 1.23 using a significance level of .01 to determine if the mean is equal to .47. (I just made this up, I suspect it makes no sense)
Where does the significance level come in? I know that I'd want to do a t-test looking for the mean, and I now see what the P-value involves, but why do I need a significance level? The teacher never seemed to explain that. Not that he explained anything.
The significance level is where our agreed upon point of the P-value is. I said that a tiny bit incorrectly before. The P-value you get from your experiment can be either above or below the significance level. If it's below the signficance level, then the experiment was a success.
Say your factory makes jelly beans. (Yum.) You sell those jelly beans in packages of 100 grams each. The beans are not always perfectly the same size, so you can't guarantee that every package is EXACTLY 100 grams. The government says, "Hey, if packages are less than 100 grams, you are exploiting the customer and you'll be fined."
You don't have the money to weigh every single package, so what do you do? You say to the government, "Hey, if I weigh one out of every 1000 packages, every single day, and 99% of the samples I weigh are 100 grams or higher, will that allow me to label my packages as being 100 grams each?"
The government will say yes. (Because it's not interested in weighing all your damn jellybean packages either.)
The null hypothesis is that the mean is NOT equal to or greater than 100 grams. The alternative hypothesis is that the mean is equal to or greater than 100 grams. (That's what you want to try to show. The way to show it is to show with a certain confidence that the opposite (the null hypothesis) is false. The significance level is 0.01. (Which is 1 minus 99%)
You run your samples, and come up with a mean weight of 101 grams, with a p-level of 0.0085. The mean is above what you want, and the p-level is below your significance level. SUCCESS!
Edited because zeroes are important.
From Wikipedia:
"For example, an experiment is performed to determine whether a coin flip is fair (50% chance of landing heads or tails) or unfairly biased, either toward heads (> 50% chance of landing heads) or toward tails (< 50% chance of landing heads). (A bent coin produces biased results.)
Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips. The p-value of this result would be the chance of a fair coin landing on heads at least 14 times out of 20 flips. The probability that 20 flips of a fair coin would result in 14 or more heads is 0.058. Thus, the (upper tailed) p-value for the coin turning up heads at least 14 times out of 20 total flips is 0.058.
Because there is no way to know what percentage of coins in the world are unfair, the p-value does not give the chance that the coin is unfair. It measures the chance that a fair coin would give the same result, which is an independent value."
DEE!!!! YOU ARE A GODDESS! I got a 77 on my stats test! I'd been getting 30-40% on my quizzes, but I got a 77 on the test! And I think you helped me a LOT! THANK YOU!!!
Quoting from Wikipedia: "...statistical tests are used to determine how likely it is that the overall effect would be observed if no real relation as hypothesized exists."
If on a call toss, you call heads and the coin turns up heads, you would know that it was chance. A moron might think the fact that he called it caused it to turn up heads.
His hypothesis is that his words caused the coin to come up heads -- that those two things are related.
We test this hypothesis to see if it is likely that they are related or not.
"If that likelihood is sufficiently small (e.g., less than 1%), the existence of a relation may be assumed. Otherwise, any observed effect may as well be due to pure chance."
Wikipedia says one example of sufficiently small is less than 1%. That can be true for scientific phenomenon, and for social science, the percentage is often less than 5%. The percentage level you're aiming to be below is the P-value.
Going back to the moron and the coin, this is a social science experiment so we'll agree to set the P-value at 0.05. 0.05 = 5%, which means if there's more than a 5% chance that the things are unrelated, we'll agree they are unrelated.
Part Two in a minute!
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Here's a specific question: If a problem is something like: A sample of 47 jelly beans yield a mean weight of .45 grams, with a standard deviation of 1.23 using a significance level of .01 to determine if the mean is equal to .47. (I just made this up, I suspect it makes no sense)
Where does the significance level come in? I know that I'd want to do a t-test looking for the mean, and I now see what the P-value involves, but why do I need a significance level? The teacher never seemed to explain that. Not that he explained anything.
Reply
Say your factory makes jelly beans. (Yum.) You sell those jelly beans in packages of 100 grams each. The beans are not always perfectly the same size, so you can't guarantee that every package is EXACTLY 100 grams. The government says, "Hey, if packages are less than 100 grams, you are exploiting the customer and you'll be fined."
You don't have the money to weigh every single package, so what do you do? You say to the government, "Hey, if I weigh one out of every 1000 packages, every single day, and 99% of the samples I weigh are 100 grams or higher, will that allow me to label my packages as being 100 grams each?"
The government will say yes. (Because it's not interested in weighing all your damn jellybean packages either.)
The null hypothesis is that the mean is NOT equal to or greater than 100 grams.
The alternative hypothesis is that the mean is equal to or greater than 100 grams. (That's what you want to try to show. The way to show it is to show with a certain confidence that the opposite (the null hypothesis) is false.
The significance level is 0.01. (Which is 1 minus 99%)
You run your samples, and come up with a mean weight of 101 grams, with a p-level of 0.0085. The mean is above what you want, and the p-level is below your significance level. SUCCESS!
Edited because zeroes are important.
From Wikipedia:
"For example, an experiment is performed to determine whether a coin flip is fair (50% chance of landing heads or tails) or unfairly biased, either toward heads (> 50% chance of landing heads) or toward tails (< 50% chance of landing heads). (A bent coin produces biased results.)
Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips. The p-value of this result would be the chance of a fair coin landing on heads at least 14 times out of 20 flips. The probability that 20 flips of a fair coin would result in 14 or more heads is 0.058. Thus, the (upper tailed) p-value for the coin turning up heads at least 14 times out of 20 total flips is 0.058.
Because there is no way to know what percentage of coins in the world are unfair, the p-value does not give the chance that the coin is unfair. It measures the chance that a fair coin would give the same result, which is an independent value."
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Thank you again! I'm going to try to apply this to some problems before the test tomorrow! You rock so much!
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