Correlation Standard Error
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Autocorrelation Standard Error
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R Squared Standard Error
is a community of 4.7 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up How to compute P-value and standard error from correlation analysis of R's cor() standard deviation standard error up vote 12 down vote favorite 2 I have data that contain 54 samples for each condition (x and y). I have computed the correlation the following way: > dat <- read.table("http://dpaste.com/1064360/plain/",header=TRUE) > cor(dat$x,dat$y) [1] 0.2870823 Is there a native way to produce SE of correlation in R's cor() functions above and p-value from T-test? As explained in this web (page 14.6) r correlation share|improve this question asked Apr variance standard error 19 '13 at 4:55 neversaint 10.4k50150248 4 Perhaps you're looking for ?cor.test instead. –A Handcart And Mohair Apr 19 '13 at 4:59 add a comment| 2 Answers 2 active oldest votes up vote 20 down vote accepted I think that what you're looking for is simply the cor.test() function, which will return everything you're looking for except for the standard error of correlation. However, as you can see, the formula for that is very straightforward, and if you use cor.test, you have all the inputs required to calculate it. Using the data from the example (so you can compare it yourself with the results on page 14.6): > cor.test(mydf$X, mydf$Y) Pearson's product-moment correlation data: mydf$X and mydf$Y t = -5.0867, df = 10, p-value = 0.0004731 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.9568189 -0.5371871 sample estimates: cor -0.8492663 If you wanted to, you could also create a function like the following to include the standard error of the correlation coefficient. For convenience, here's the equation: r = the correlation estimate and n - 2 = degrees of freedom, both of which are readily available in the output above. Thus, a simple function could be: cor.test.plus <- function(x) { list(x
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Correlation Confidence Interval
and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the http://stackoverflow.com/questions/16097453/how-to-compute-p-value-and-standard-error-from-correlation-analysis-of-rs-cor top standard error of a correlation coefficient up vote 1 down vote favorite I would like to establish the proof for the standard error of a correlation coefficient. Assume that we have two iid samples $\{X_i\}_{i=1}^N$ and $\{Y_i\}_{i=1}^N$ We know that the sample correlation is given by $$\text{SCor(X,Y)}=\frac{\sum_i (X_i - \bar X ) ( Y_i - \bar Y) }{\sqrt{\sum_i (X_i - \bar X )^2 \times \sum_i (Y_i - \bar Y )^2}} $$ http://math.stackexchange.com/questions/439729/standard-error-of-a-correlation-coefficient I would like to avoid distributional assumptions until they are absolutely required. I am struggling to disentangle the products in the expectation to find the first and second moments of the sample correlation. Ultimately of course I am searching for the square root of the variance of the sample correlation. This post is based on the definition found here and I would like to contribute to that page if possible because this is an issue too rarely addressed. Please excuse me if this is too elementary. statistics share|cite|improve this question edited Jul 9 '13 at 16:35 asked Jul 9 '13 at 14:38 7zf 1575 OP wrote: We know that the sample correlation ... is an unbiased estimator ... of Cor(X,Y) ................... Really? How do 'we' know this??? I know it not. –wolfies Jul 9 '13 at 16:15 thank you for pointing this out, I was under the false impression that it was. I updated the post to reflect this. –7zf Jul 9 '13 at 16:30 So, you have scor = numerator/Sqrt[denominator]. The numerator is a symmetric polynomial in power sums, so we can find the moments of the numerator; the same is true for denominator. However, Sqrt[denominator] is not a symmetric polynomial in power sums, so I don't believe y
proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value. The standard error (SE) is the standard deviation of the sampling distribution https://en.wikipedia.org/wiki/Standard_error of a statistic,[1] most commonly of the mean. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate. For example, the sample mean is the usual estimator of a population mean. However, different samples drawn from that same population would in general have different values of the sample mean, so there standard error is a distribution of sampled means (with its own mean and variance). The standard error of the mean (SEM) (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that correlation standard error standard deviation, computed from the sample of data being analyzed at the time. In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the underlying errors.[2][3] Contents 1 Introduction to the standard error 1.1 Standard error of the mean 1.1.1 Sampling from a distribution with a large standard deviation 1.1.2 Sampling from a distribution with a small standard deviation 1.1.3 Larger sample sizes give smaller standard errors 1.1.4 Using a sample to estimate the standard error 2 Standard error of the mean 3 Student approximation when σ value is unknown 4 Assumptions and usage 4.1 Standard error of mean versus standard deviation 5 Correction for finite population 6 Correction for correlation in the sample 7 Relative standard error 8 See also 9 References Introduction to the standard error[edit] The standard error is a quantitative measure of uncertainty. Consider the following scenarios. Scenario 1. For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. Of the 2000 voters, 1040 (52%) state that they will vote for cand