Re: [R] How to find statistics like that.
Adai, I recently came across the following definition of a statistic which may be relevent to the discussion. John - Berans (2003) provocative definition of statistics as the study of algorithms for data analysis elevates computational considerations to the forefront of the field. It is apparent that the evolutionary success of statistical methods is to a significant degree determined by considerations of computational convenience. As a result,design and dissemination of statistical software has become an integral part of statistical research. from this it follows that a 'Statistic' is A mathematical function or algorithm for data analysis Duncan Murdoch wrote On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Just curious about your usage: why do you say a p-value is not a statistic? Duncan Murdoch Adaikalavan Ramasamy replied - If my usage is wrong please correct me. Thank you. Here are my reason : 1. p-value is a (cumulative) probability and always ranges from 0 to 1. A test statistic depending on its definition can wider range of possible values. 2. A test statistics is one that is calculated from the data without the need of assuming a null distribution. Whereas to calculate p-values, you need to assume a null distribution or estimate it empirically using permutation techniques. 3. The directionality of a test statistics may be ignored. For example a t-statistics of -5 and 5 are equally interesting in a two-sided testing. But the smaller the p-value, more evidence against the null hypothesis. Regards, Adai __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Just curious about your usage: why do you say a p-value is not a statistic? Duncan Murdoch Regards, Adai On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
If my usage is wrong please correct me. Thank you. Here are my reason : 1. p-value is a (cumulative) probability and always ranges from 0 to 1. A test statistic depending on its definition can wider range of possible values. 2. A test statistics is one that is calculated from the data without the need of assuming a null distribution. Whereas to calculate p-values, you need to assume a null distribution or estimate it empirically using permutation techniques. 3. The directionality of a test statistics may be ignored. For example a t-statistics of -5 and 5 are equally interesting in a two-sided testing. But the smaller the p-value, more evidence against the null hypothesis. Regards, Adai On Thu, 2005-11-10 at 06:05 -0500, Duncan Murdoch wrote: On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Just curious about your usage: why do you say a p-value is not a statistic? Duncan Murdoch Regards, Adai On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
The definition of a statistic that I learned in grad school is that it's a function of a random sample from a population. Any p-value would fit that definition. Andy From: Adaikalavan Ramasamy If my usage is wrong please correct me. Thank you. Here are my reason : 1. p-value is a (cumulative) probability and always ranges from 0 to 1. A test statistic depending on its definition can wider range of possible values. 2. A test statistics is one that is calculated from the data without the need of assuming a null distribution. Whereas to calculate p-values, you need to assume a null distribution or estimate it empirically using permutation techniques. 3. The directionality of a test statistics may be ignored. For example a t-statistics of -5 and 5 are equally interesting in a two-sided testing. But the smaller the p-value, more evidence against the null hypothesis. Regards, Adai On Thu, 2005-11-10 at 06:05 -0500, Duncan Murdoch wrote: On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Just curious about your usage: why do you say a p-value is not a statistic? Duncan Murdoch Regards, Adai On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
-Original Message- From: [EMAIL PROTECTED] [SMTP:[EMAIL PROTECTED] On Behalf Of Adaikalavan Ramasamy Sent: Thursday, November 10, 2005 10:31 AM To: Duncan Murdoch Cc: r-help@stat.math.ethz.ch Subject: Re: [R] How to find statistics like that. If my usage is wrong please correct me. Thank you. Here are my reason : 1. p-value is a (cumulative) probability and always ranges from 0 to 1. A test statistic depending on its definition can wider range of possible values. 2. A test statistics is one that is calculated from the data without the need of assuming a null distribution. Whereas to calculate p-values, you need to assume a null distribution or estimate it empirically using permutation techniques. 3. The directionality of a test statistics may be ignored. For example a t-statistics of -5 and 5 are equally interesting in a two-sided testing. But the smaller the p-value, more evidence against the null hypothesis. Regards, Adai Hi: A statistic is any real-valued or vector-valued function whose domain includes the sample space of a random sample. The p-value is a real-valued function and its domain includes the sample space of a random sample. The p-value has a sampling distribution. The code below, found with Google (sampling distribution of the p-value R command) shows the sampling distribution of the p-value for a t-test of a mean when the null hypothesis is true. Ruben n-18 mu-40 pop.var-100 n.draw-200 alpha-0.05 draws-matrix(rnorm(n.draw * n, mu, sqrt(pop.var)), n) get.p.value-function(x) t.test(x, mu = mu)$p.value pvalues-apply(draws, 2, get.p.value) hist(pvalues) sum(pvalues = alpha) [1] 6 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
On 11/10/2005 7:31 AM, Adaikalavan Ramasamy wrote: If my usage is wrong please correct me. Thank you. Here are my reason : 1. p-value is a (cumulative) probability and always ranges from 0 to 1. A test statistic depending on its definition can wider range of possible values. 2. A test statistics is one that is calculated from the data without the need of assuming a null distribution. Whereas to calculate p-values, you need to assume a null distribution or estimate it empirically using permutation techniques. 3. The directionality of a test statistics may be ignored. For example a t-statistics of -5 and 5 are equally interesting in a two-sided testing. But the smaller the p-value, more evidence against the null hypothesis. Regards, Adai Thanks for your explanation. I think your interpretation is one that is sometimes taught, but I think it's more useful to think of a p-value as just another statistic, whose null distribution (in the ideal case, but not always in practice) is a uniform distribution on (0,1), and whose distribution when the alternative is true (again, ideally) tends to be more concentrated near 0. This takes a lot of the mysticism out of them. Duncan Murdoch On Thu, 2005-11-10 at 06:05 -0500, Duncan Murdoch wrote: On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Just curious about your usage: why do you say a p-value is not a statistic? Duncan Murdoch Regards, Adai On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
On Thu, 10 Nov 2005, Ruben Roa wrote: A statistic is any real-valued or vector-valued function whose domain includes the sample space of a random sample. The p-value is a real-valued function and its domain includes the sample space of a random sample. The p-value has a sampling distribution. The code below, found with Google (sampling distribution of the p-value R command) shows the sampling distribution of the p-value for a t-test of a mean when the null hypothesis is true. Ruben n-18 mu-40 pop.var-100 n.draw-200 alpha-0.05 draws-matrix(rnorm(n.draw * n, mu, sqrt(pop.var)), n) get.p.value-function(x) t.test(x, mu = mu)$p.value pvalues-apply(draws, 2, get.p.value) hist(pvalues) sum(pvalues = alpha) [1] 6 The sampling distribution of a p-value when the null hypothesis is true can be given more simply by this R code: runif() That holds for any valid test, not just a t test, that produces p-values distributed continuously on [0,1]. Discrete distributions can't quite do that without special tweaking. Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
-Original Message- From: Mike Miller [SMTP:[EMAIL PROTECTED] Sent: Thursday, November 10, 2005 12:32 PM To: Ruben Roa Cc: [EMAIL PROTECTED]; Duncan Murdoch; r-help@stat.math.ethz.ch Subject: Re: [R] How to find statistics like that. On Thu, 10 Nov 2005, Ruben Roa wrote: A statistic is any real-valued or vector-valued function whose domain includes the sample space of a random sample. The p-value is a real-valued function and its domain includes the sample space of a random sample. The p-value has a sampling distribution. The code below, found with Google (sampling distribution of the p-value R command) shows the sampling distribution of the p-value for a t-test of a mean when the null hypothesis is true. Ruben n-18 mu-40 pop.var-100 n.draw-200 alpha-0.05 draws-matrix(rnorm(n.draw * n, mu, sqrt(pop.var)), n) get.p.value-function(x) t.test(x, mu = mu)$p.value pvalues-apply(draws, 2, get.p.value) hist(pvalues) sum(pvalues = alpha) [1] 6 The sampling distribution of a p-value when the null hypothesis is true can be given more simply by this R code: runif() That holds for any valid test, not just a t test, that produces p-values distributed continuously on [0,1]. Discrete distributions can't quite do that without special tweaking. Mike Theorem 2.1.4 in Casella and Berger (1990, p. 52). Ruben __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
On 11/10/2005 9:32 AM, Mike Miller wrote: On Thu, 10 Nov 2005, Ruben Roa wrote: A statistic is any real-valued or vector-valued function whose domain includes the sample space of a random sample. The p-value is a real-valued function and its domain includes the sample space of a random sample. The p-value has a sampling distribution. The code below, found with Google (sampling distribution of the p-value R command) shows the sampling distribution of the p-value for a t-test of a mean when the null hypothesis is true. Ruben n-18 mu-40 pop.var-100 n.draw-200 alpha-0.05 draws-matrix(rnorm(n.draw * n, mu, sqrt(pop.var)), n) get.p.value-function(x) t.test(x, mu = mu)$p.value pvalues-apply(draws, 2, get.p.value) hist(pvalues) sum(pvalues = alpha) [1] 6 The sampling distribution of a p-value when the null hypothesis is true can be given more simply by this R code: runif() That holds for any valid test, not just a t test, that produces p-values distributed continuously on [0,1]. Discrete distributions can't quite do that without special tweaking. Nor can most composite null hypotheses, e.g. H0: mu = 0 versus H1: mu 0 A t-test may be an appropriate test, but its p-value is not uniformly distributed when mu is -1, even though the null is true. Duncan Murdoch __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] How to find statistics like that.
I think an alternative is to use a p-value from F distribution. Even tough it is not a statistics, it is much easier to explain and popular than 1/F. Better yet to report the confidence intervals. Regards, Adai On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: On Wed, 9 Nov 2005, Gao Fay wrote: Hi there, Suppose mu is constant, and error is normally distributed with mean 0 and fixed variance s. I need to find a statistics that: Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is 1 Y_i is from group A, and 0 if Y_i is from group B. It is large when beta1=beta2=0 It is small when beta1 and/or beta2 is not equal to 0 How can I find it by R? Thank you very much for your time. That's a funny question. Usually we want a statistic that is small when beta1=beta2=0 and large otherwise. Why not compute the usual F statistic for the null beta1=beta2=0 and then use 1/F as your statistic? Mike __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
