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Understanding the P-value
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I'm having difficulty understanding the p-value.
It is said to reject the null hypothesis when the p-value is small. Smaller than the significance level.
So does that mean in a hypothesis test, the p-value represents the area of the null hypothesis? Therefore because the p-value is small, it would imply the probability of the null hypothesis being unlikely?
statistics hypothesis-testing
asked Dec 18 '16 at 23:31
useruser
298314
$endgroup$
add a comment |
$begingroup$
I'm having difficulty understanding the p-value.
It is said to reject the null hypothesis when the p-value is small. Smaller than the significance level.
So does that mean in a hypothesis test, the p-value represents the area of the null hypothesis? Therefore because the p-value is small, it would imply the probability of the null hypothesis being unlikely?
statistics hypothesis-testing
asked Dec 18 '16 at 23:31
useruser
298314
$endgroup$
add a comment |
$begingroup$
I'm having difficulty understanding the p-value.
It is said to reject the null hypothesis when the p-value is small. Smaller than the significance level.
So does that mean in a hypothesis test, the p-value represents the area of the null hypothesis? Therefore because the p-value is small, it would imply the probability of the null hypothesis being unlikely?
statistics hypothesis-testing
asked Dec 18 '16 at 23:31
useruser
298314
$endgroup$
I'm having difficulty understanding the p-value.
It is said to reject the null hypothesis when the p-value is small. Smaller than the significance level.
So does that mean in a hypothesis test, the p-value represents the area of the null hypothesis? Therefore because the p-value is small, it would imply the probability of the null hypothesis being unlikely?
statistics hypothesis-testing
statistics hypothesis-testing
asked Dec 18 '16 at 23:31
useruser
298314
asked Dec 18 '16 at 23:31
useruser
298314
asked Dec 18 '16 at 23:31
useruser
298314
asked Dec 18 '16 at 23:31
useruser
298314
asked Dec 18 '16 at 23:31
useruser
298314
298314
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.
Less technical, lets say the null hypothesis is actually true. With p-value we calculate the probability that the statistic would be the same as or more extreme than the value we calculate from the sample(e.g. sample mean). So we can interpret p-value as how much our null hypothesis supports our data. If that probability is lower than a pre-determined level, we conclude that it is unlikely that null hypothesis is actualy true.
https://en.wikipedia.org/wiki/P-value
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
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add a comment |
$begingroup$
I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter.
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show.
The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more.
Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%.
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
$endgroup$
add a comment |
$begingroup$
The $p$-value represents the probability that an event as unlikely at the observed one could have happened under the assumption that the null hypothesis is true.
It doesn't really represent the 'area of the null hypothesis', because $p$-values are specific to given observations.
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.
Less technical, lets say the null hypothesis is actually true. With p-value we calculate the probability that the statistic would be the same as or more extreme than the value we calculate from the sample(e.g. sample mean). So we can interpret p-value as how much our null hypothesis supports our data. If that probability is lower than a pre-determined level, we conclude that it is unlikely that null hypothesis is actualy true.
https://en.wikipedia.org/wiki/P-value
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
$endgroup$
add a comment |
$begingroup$
In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.
Less technical, lets say the null hypothesis is actually true. With p-value we calculate the probability that the statistic would be the same as or more extreme than the value we calculate from the sample(e.g. sample mean). So we can interpret p-value as how much our null hypothesis supports our data. If that probability is lower than a pre-determined level, we conclude that it is unlikely that null hypothesis is actualy true.
https://en.wikipedia.org/wiki/P-value
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
$endgroup$
add a comment |
$begingroup$
In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.
Less technical, lets say the null hypothesis is actually true. With p-value we calculate the probability that the statistic would be the same as or more extreme than the value we calculate from the sample(e.g. sample mean). So we can interpret p-value as how much our null hypothesis supports our data. If that probability is lower than a pre-determined level, we conclude that it is unlikely that null hypothesis is actualy true.
https://en.wikipedia.org/wiki/P-value
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
$endgroup$
In statistics, the p-value is the probability that, using a given statistical model, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or more extreme than the actual observed results.
Less technical, lets say the null hypothesis is actually true. With p-value we calculate the probability that the statistic would be the same as or more extreme than the value we calculate from the sample(e.g. sample mean). So we can interpret p-value as how much our null hypothesis supports our data. If that probability is lower than a pre-determined level, we conclude that it is unlikely that null hypothesis is actualy true.
https://en.wikipedia.org/wiki/P-value
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
answered Dec 18 '16 at 23:48
baris_esmerbaris_esmer
919
919
add a comment |
add a comment |
$begingroup$
I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter.
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show.
The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more.
Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%.
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
$endgroup$
add a comment |
$begingroup$
I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter.
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show.
The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more.
Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%.
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
$endgroup$
add a comment |
$begingroup$
I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter.
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show.
The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more.
Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%.
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
$endgroup$
I lightly rewrite this already outstanding /r/eli5 comment, to simplify it further. I changed "New Yorker to "Utahn" as the latter's shorter.
Suppose you want to show that, say, Texans eat more than Utahns do. What you're really trying to prove is that Texans do not eat the same or less amount as Utahns do. This statement ("Texans and Utahns eat the same amount") is something called your "null hypothesis". Hypothesis testing has the goal of disproving the null hypothesis to prove what you're trying to show.
The idea of statistical testing is to say "well, assuming that Texans and Utahns did eat the same amount, how likely would we get the data we did? The chance of getting the data you got if, in fact, they did eat the same amount is called a p-value. For instance, if we say that p = 0.05, we mean that if Texans and Utahns ate the same amount, there'd be a 1/20 chance to observe the kinds of results we did observe. The lower the p-value, the less likely your null hypothesis is true, and the more confidence you have that, in fact, Texans do eat more.
Significance is the lowest p-value you'll accept as "strong enough" evidence. Lower significance thresholds decrease your chances of a false positive (i.e., finding that Texans eat more when in fact they don't), but increase your chances of a false negative (concluding that you don't know that Texans eat more, when in fact they do). Usually 5% is the weakest significance anyone takes seriously, but for situations where there's extreme cost to a false positive, you may choose a much lower number like 0.1%.
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
answered Jan 25 at 5:30
Greek - Area 51 ProposalGreek - Area 51 Proposal
3,196769105
3,196769105
add a comment |
add a comment |
$begingroup$
The $p$-value represents the probability that an event as unlikely at the observed one could have happened under the assumption that the null hypothesis is true.
It doesn't really represent the 'area of the null hypothesis', because $p$-values are specific to given observations.
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
$endgroup$
add a comment |
$begingroup$
The $p$-value represents the probability that an event as unlikely at the observed one could have happened under the assumption that the null hypothesis is true.
It doesn't really represent the 'area of the null hypothesis', because $p$-values are specific to given observations.
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
$endgroup$
add a comment |
$begingroup$
The $p$-value represents the probability that an event as unlikely at the observed one could have happened under the assumption that the null hypothesis is true.
It doesn't really represent the 'area of the null hypothesis', because $p$-values are specific to given observations.
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
$endgroup$
The $p$-value represents the probability that an event as unlikely at the observed one could have happened under the assumption that the null hypothesis is true.
It doesn't really represent the 'area of the null hypothesis', because $p$-values are specific to given observations.
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
answered Dec 18 '16 at 23:42
man_in_green_shirtman_in_green_shirt
8531129
8531129
add a comment |
add a comment |
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