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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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 ...
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45 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 ...
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36 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 ...
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8 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 ...
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45 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 ...
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39 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 ...
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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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72 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 ...
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44 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 ...
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141 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} = ...
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42 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 ...
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18 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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60 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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17 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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48 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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69 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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19 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 ...
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28 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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12 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 ...
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131 views
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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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51 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? ...
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73 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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23 views

Elements of first list in Kendall must be ordered?

Two ways to execute a Kendall tau test (in R): ...
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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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24 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 ...
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216 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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112 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? ...
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40 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 ...
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73 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 ...
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124 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 ...
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21 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 ...
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84 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 ...
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59 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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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 ...
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14 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, ...
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40 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 ...
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37 views

Comparing two different questionnaires but both on a 5-point likert scale

I have three self-reporting questionnaires, all on a 5-point likert scale. Is it possible for me to use a Pearson moment correlation to compare the summation of measures between two questionnaires? If ...
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42 views

Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum?

Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum? Is there an easy mathematical explanation to this as $r^2$ is squared and don't add ...
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65 views

What is the relation between multiple-regression and pearson's r?

What is the relation between these two, not $r^2$, but Pearson's $r$ and multiple $r$?
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57 views

Cross-correlation vs. Pearson Correlation

In general terms, what is the difference(s) between cross-correlation with lag = 0 and Pearson correlation?
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114 views

Testing uniformity of data

I need to test if a vector of observed values are uniform distribution. Lets assume: This values are not a sample, but my entire universe. I have a dataset of 12000 observations, where most of the ...
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689 views

How to interpret Matthews correlation coefficient (MCC)?

The answer for the question Relation between the phi, Matthews and Pearson correlation coefficients? shows that the three coefficient methods are all equivalents. I'm not from statistics, so it ...
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241 views

How to determine the correlation between data sets with the same period but different sample rates?

I am trying to determine the correlation between two sets of data points which span the same time period (20 minutes) but have different resolutions. The first set was recorded at 1-minute intervals, ...
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33 views

Is the following statistical analysis valid/correct? And if so, what is it called?

I've used a method of statistical analysis based on my own insight to determine if age correlates with a variable X over time. Each participant has a different number of records for X with different ...
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52 views

Does the ratio fallacy apply when calculating a Pearson's correlation between one ratio variable and one absolute variable (no common term)?

Am I committing the ratio fallacy when I calculate the Pearson's correlation between a variable x/y and a variable z, with no common terms? I have found a similar question to mine here but the reader ...
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19 views

test multiple samples correlation

I have two samples with multiple variables. I compute pearson correlation coefficients between each variables pairs within each sample. How can I compare efficiently corresponding pearson coefficients ...
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73 views

Significance testing between two sets of Pearson's correlation coefficients

I have been reading through questions here to find an answer to my question but didn't find a satisfactory one. Here is my scenario: I have a system computing an algorithm on each of 100 units (so ...
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255 views

Correlation using Logistic Regression and Pearson

I am so sorry, I am beginner in statistic analysis, I have project using R to analyze the correlation between dependent variables and independents variables. In this case I have two dependent ...
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61 views

Point Biserial correlation coefficient in Java

I've recently installed Apache Commons Math library to help me with some basic statistics in my project. Basically, what I need is to calculate the correlation coefficient for 2 arrays, which I can ...