The Pearson product-moment correlation coefficient is a measure of the linear relationship between two variables $X$ and $Y$, giving a value between +1 and −1.

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Why is Pearson's ρ only an exhaustive measure of association if the joint distribution is multivariate normal?

This assertion was raised in the top response to this question. I think the 'why' question is sufficiently different that it warrants a new thread. Googling "exhaustive measure of association" did not ...
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14 views

Comparing dependent pearson's r coefficients - second level

I would like to test whether activation in condition A is more similar to activation in condition B or C. Activation is measured by sampling every two seconds throughout the experiment, and all three ...
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1answer
22 views

Advice on correlation

Dear Cross validated community, I need some guidance with statistics on my sample set. I collected plants at 7 sites following an environmental gradient. Data consists of • 7 sites along spatial ...
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12 views

Pearson's or Spearman's? Ordinal data transformed into continuous

I've got a cohort who took a survey with questions answered on a scale of 0-5. A standard scoring system turns the results of the survey into five "scores" measuring different things, each from 0-100. ...
3
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1answer
50 views

What is Pearson's r association strength?

I am trying to grasp the concept of magnitude-of-effect estimations, as opposed to standard null hypothesis testing procedures. According to a paper by (Snyder & Lawson, 1993) the ...
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0answers
68 views

What statistical test should I use if the relationship between two variables is neither linear nor monotonic?

I am confused. My scatterplot says that the relationship between the two variables is not linear, so I can't use Pearson's correlation and neither is it monotonic, so I can't use Spearman's ...
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14 views

Where can I find a derivation of the Spearman's rho sampling equation? [duplicate]

Can anyone give me a derivation of the Spearman's rho sampling equation: $r_s = 1 - {\sum^N_{i=1} d_i^2 \over n(n^2-1)}\\ \: \:\: = { \sum^N_{i=1} R(x_i) R(y_i) -n \left({n+1\over 2}\right)^2 ...
2
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3answers
85 views

finding p-value in pearson correlation in R

Is it possible to find the p-value in pearson correlation in R? To find the pearson correlation, I usually do this ...
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2answers
134 views

Independent and Dependent variables use different scales

How to deal with questionnaire, where 40 questions that represent 8 independent constructs use 5-point Likert's scales and another 5 questions that represent dependent variable use 6-points Likert's ...
0
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0answers
22 views

When is it necessary to convert confidence intervals as per this link?

I have this link http://onlinestatbook.com/2/estimation/correlation_ci.html Where they mention taking Pearson's $r$ and using the Fisher transformation and standard error to convert confidence ...
-1
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1answer
62 views

Cutoff values for Pearson and Spearman r

I did not get many responses over how to compute $p$ values given Spearman $\rho$ and Pearson $r$ so I will try something else: I see that when you are using the Spearman $\rho$ value, you can use ...
4
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1answer
32 views

Differences in correlation for individual and aggregated data

I have a sample of 1 million articles form the web with various features. I'm in the progress of selecting features to use in a metric/predictor for article quality. To get some insight into the data ...
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3answers
73 views

What kind of statistical test is appropriate for this?

Variable X designates a group label (group 1, group 2, etc). Each group represents an amount of time spent watching TV. For example group 1 might watch TV less than an hour a week, group 2 watches 1-2 ...
2
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1answer
98 views

Intuitive explanation for when Pearson correlation coefficient equals 1

Whenever I teach a complicated formula, I always demonstrate to the class that it works intuitively in extreme cases. For example, when all the data values are equal, the standard deviation is 0. Not ...
19
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1answer
256 views

Shrunken $r$ vs unbiased $r$: estimators of $\rho$

There has been some confusion in my head about two types of estimators of the population value of Pearson correlation coefficient. A. Fisher (1915) showed that for bivariate normal population ...
3
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1answer
106 views

How to interpret the residual colors on a mosaic plot?

This is a mosaic plot of contingency table dataset HairEyeColor described here. How do I interpret the colors representing residuals? What is the difference ...
4
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2answers
45 views

Compute a Pvalue from the averaged Pearson and Spearman rho

On the one hand, Pearson correlation is sensitive to outliers, while Spearman is not. On the other hand, if you have quantitative data, Spearman will treat it like ordinal data. How about averaging ...
0
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2answers
61 views

Correlation Coefficient for lag $k$ in Time Series Data

Formula of Pearson Correlation Coefficient is : $$r_{xy}=\frac{\sum_{i=1}^{n}(x_i-\bar x)(y_i-\bar y)}{\sqrt{\sum_{i=1}^{n}(x_i-\bar x)^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar y)^2}}$$ In Time series ...
0
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2answers
125 views

Coefficient for a zero lag cross-correlation different from Pearson correlation r

Reading around I understood that using a cross correlation with lag zero should give the same results of a normal pearson correlation. It happens that this is not the case for me. What could be the ...
0
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0answers
22 views

How to compare Pearson correlation coefficients from spatial data [duplicate]

Dear "Cross Validated" community, First I want to introduce my data to you, so that you can get a clear overview regarding the problem I´m confronted with. For some urban studies I´ve got a spatial ...
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2answers
117 views

How to compare two Pearson correlation coefficients

Since a few days I do not get ahead when trying to compare two Pearson correlation coefficients. Imagine that I've got two datasets where on each I do a correlation between Land Surface Temperature ...
0
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52 views

Remove column which has weak correlation between other

I have data set which contains 12 feature columns. The last one has Pearson correlations between 0.001 and 0.09. For Spearman and Kendall correlations are worth. Can improve the performance of ...
10
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2answers
195 views

Why is Pearson parametric and Spearman non-parametric

Apparently Pearson's correlation coefficient is parametric and Spearman's rho is non-parametric. I'm having trouble understanding this. As I understand it Pearson is computed as $$ r_{xy} = ...
3
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1answer
56 views

Making two vectors uncorrelated in terms of Kendall Tau correlation

Assume that we have two normalized $n\times 1$ vectors $\bf x$ and $\bf y$. In terms of Pearson correlation, these two signals are uncorrelated if ${\bf x}^T {\bf y} = 0$. Now, assume that ${\bf x}^T ...
0
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0answers
23 views

Does Pearson correlation need mutual rated items in collaborative filtering?

I am working on collaborative recommender system and for computing user x user similarity I use Pearson correlation coefficient. My recommender system works with movie ratings. I need to make sure I ...
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2answers
81 views

The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
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23 views

How to find anti-correlated subsequences in correlated time series?

Say I have two time series $X_t$ and $Y_t$ (with $ 1 \leq t \leq N$), which have a high positive Pearson correlation. Say I also have reason to believe there are subsequences $X_{tj}, Y_{tj}$ (where, ...
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1answer
61 views

Relation between $R^2$ and the covariate correlation matrix

I'm quite new to Statistics and I'm facing a problem. Is there any relation between $R^2$ and the correlation matrix of the covariates? A short example is (case with 2 covariates) : A7 ~ A1 + A2 ...
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89 views

Can we combine two groups to enhance power for analysis if there are no group differences on the variables?

I am reading a peer-reviewed paper on psychology and found the author use pearson r on sex (nominal variable): The correlation table And then the authors conclude no gender difference on all ...
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26 views

To obtain Pearson type III parameters and shift value

How to obtain Pearson type III parameters and shift value? I am using R and if you can give me an instruction, it would be helpful. I have used pearsonFitML function from PearsonDS package, but I can ...
0
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1answer
38 views

Is this the right way of finding the Pearson coefficient?

I want to see the effect of discounts on sales. The discount is always 100 off and occurs in select months. I want to see what effect the 100 discount has on sales. I found the Pearson coefficient to ...
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15 views

Standard deviation of squared sample correlation coefficient

Suppose I have two vectors of samples from Bernoulli random variables and I would like to compute (at least approximately) the standard deviation of the estimated Squared Pearson correlation ...
0
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1answer
184 views
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21 views

Assesing the probability of error of an estimate given the Pearson correlation coefficient

Let $X$ and $Y$ be two random variables with a Pearson correlation coefficient of $R>0$. Let $\{(x_i,y_i)\}_{i=1}^N$ be $N$ pair realizations of both random variables. Given $E>0$, what's the ...
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75 views

non normal data - bootstrap pearson r or kendall tau?

This may be a follow up on these questions: Pearson's or Spearman's correlation with non-normal data How robust is Pearson's correlation coefficient to violations of normality? ...
3
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1answer
88 views

Testing correlation and the t-statistic used in Simple Linear Regression

Given $H_0$ : $\rho=0$ and $H_A$ : $\rho\neq0$, we use the test statistic $t_{n-2}$ , which is $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$. I have to show that $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ equals ...
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1answer
27 views

Elements of first list in Kendall must be ordered?

Two ways to execute a Kendall tau test (in R): ...
5
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2answers
225 views

How to get p-values or confidence intervals for pearson correlation coefficient when the sample is small and potentially non-Gaussian?

The p-values provided by the built-in Matlab and Pylab Pearson correlation functions are stated to be inaccurate for small sample sizes, or when the samples are not normally distributed. The python ...
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29 views

Correlation of two means, with known variance

I would like to estimate the correlation of two variables, A and B. For the first variable I have made three independent ...
5
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3answers
733 views

How to use Pearson correlation correctly with time series

I have 2 time-series (both smooth) that I would like to cross-correlate to see how correlated they are. I intend to use the Pearson correlation coefficient. Is this appropriate? My second question ...
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2answers
135 views

Correlation choice when attribute values are given in intervals

I am trying to find the correlation between two continuous variables but the values of one of them are originally given in intervals ([1-5] ,[6-9],...). What is the best approach to deal with this? ...
4
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1answer
47 views

Problem with Application of Pearson's Chi-Squared test

I'm using Pearson's chi-squared test to to compare the knowledge of two independent groups on knowledge about contact lens. But the number of respondents in group A is n = 200 and the number of ...
0
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94 views

Fisher exact test (9x2) vs pearson chi-square (SPSS)

I am doing one analysis where I have 9 different conditions and only two options as outcome. I have done a pearson chi-square test, and in some of the cases I violated the assumption that expected ...
2
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2answers
190 views

Cross validation with Pearson correlation coefficient - is testing one tailed enough?

My method of cross validation is to first split my sample into two sub-samples, with 80% respectively 20% of the observations, and then to correlate the predicted values of my model (created with the ...
0
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26 views

Correlation parameter with small nonlinear sample like hour / day of week?

I have a dataset of magnitudes Y which gives the scale / magnitude of some event. Each event is also timestamped: Y = [(time1,mag1), (time2,mag2),...] I want to ...
3
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1answer
119 views

Generate random correlated categorical variables

Lets say I want to generate 100 observations of 2 likert scaled, normally? distributed variables with 10 categories (1-10) and a pearson correlation of f.e. ~0.8. I am aware that using pearson ...
0
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1answer
68 views

Pearson Correlation has quizzy results

I investigated experiments with SPSS and following values were out. I have a question that in which case is possible to get Feature 1 in Group A+B as significant p<.05 while either Group A and B ...
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16 views

Should I use pearson correlation or MI test?

I'm relatively new to statistics hence my confusion. I am trying to measure the relationship between SMEs who do business in two markets and the level of tax compliance costs they face. The premise is ...
0
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1answer
15 views

Pearson Correlation of Device Values

I have a device which obtains velocity based values over a period of 1 minute (average). I also have another device with which I am comparing that device. Now the velocity values can be quite random, ...
0
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2answers
46 views

Student's test for correlation coef

In one of the articles I found such a statement: The significance of the correlation coefficient was then verified using Student's t test for independent variables Is this incorrect or did I ...