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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Can Pearson correlation be used as a measure of fit?

In the context of multiple linear regression, is it acceptable to use Pearson correlation to discriminate how well a model fits a data set? Let's say that I have some experimental values that come ...
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94 views

Why is the Pearson correlation 1 when only two data values are available?

I am trying to obtain a Pearson correlation between 6 different variables (represented by columns in the matrix below) with two datapoints each (rows). This is the matrix: ...
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14 views

Instability of one-pass algorithm for correlation coefficient

What should I know about the instability of the Pearson product-moment correlation coefficient? When might I experience problems using this calculation? I will quote the following Wikipedia article ...
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33 views

How is this version of the pearson correlation coefficient derived?

After taking my first semester stats class I started getting more and more into statistics. Currently I've come across this version of the Pearson Correlation Coefficient. Comparing this formula to ...
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20 views
+50

Difference between “common index” and “no common index”

I have been looking at the G*Power tool for Statistical Power Analysis but I am confused by the difference between two of the z-test options. ...
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30 views

Correlation of many 1d vectors

Let's say I have many 1 dimensional vectors of the same dimensions which I want to compare to each other. What I'm really looking for is to check whether they are all very similar, or not, and to ...
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7 views

Pearson r with percentages across time

Data sources: CDC National Survey of Family Growth, CDC vital stats. Population: American women aged 15-44 in 1982, 95, 2002, 2006 Sample sizes: several thousand Can I use Pearson r to show linear ...
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9 views

How can I test if a bivariate correlation is significantly different from a partial correlation?

I have three variables (A, T, C) with n= 1083. The Pearson correlations are as below: A*T= .170 (p<.01) A*C= .370 (p<.01) T*C= -.103 (p<.01) Partial correlation between A and T ...
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31 views

Xlstat and Pearson correlation coefficient: how are p-values calculated?

Someone asked me questions about his outcomes from Xlstat. Since I do not know this software at all, here is the question: How are p-values for Pearson correlation coefficients calculated ($H_1: \rho ...
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91 views

Comparing Averages of Pearson Correlation Coefficients for Significance

How can I test if two averages of Pearson's correlation coefficients are significantly different? For instance, I have data pertaining to participants' estimates of certain percentages (e.g. how many ...
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2answers
91 views

Insignificant slope with statistically significant r value

I collected data of 60 countries to identify whether there is a relationship between average income per person and average life expectancy. However, I am having some trouble interpreting my lin-reg ...
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57 views

Low number of replicates DGE analysis

I am using DESeq for DGE analysis. I have STRANDED RNA-Seq data for 4 developmental stages with no replicates. To have a more reliable DGE I should have replicates and so I obtained (from another lab ...
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1answer
43 views

Chi-squared & Pearson correlation coefficient

I have just ended my math's assignment and my chi-squared test approved the null hypothesis that my data are independent; however, pearson's correlation coefficient is -0.23. Can they therefore be ...
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1answer
103 views

How to best analyze this data?

Im trying to figure out a way to analyze this data that I have: This is data that I pulled from various studies, and each study has a different sample size, and each study reported an obliteration ...
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2answers
70 views

Relationships between health conditions - Spearman's correlation?

I am examining the relationships between health issues in pigs. I want to know which conditions tend to co-occur. All animals have at least one condition and 5 at most. I have coded each condition in ...
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0answers
50 views

Mean pairwise Pearson correlation

Consider a set of $M$ multidimensional observations $X=\{x_i\}_{i=1..M}$ for $x_i\in\mathbb{R}^N$, and define $c_{ij}$ to be the Pearson correlation coefficient between $x_i$ and $x_j$. Is there a ...
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1answer
60 views

Expected Counts in Pearson's Goodness of Fit Test

A Common expression for Pearson's goodness of fit test is $\chi^2 = \sum_i \frac{(O_i - E_i)^2}{E_i}$ Where $O_i$ and $E_i$ are the observed and expected frequencies respectively. Now assuming we ...
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1answer
62 views

Measuring intra-observer correlation

We're far from what you'd call expert statisticians, so we'd like to ask some help in an ongoing medical research. We have 60 subjects. A researcher took at least 3 times the measurements of 8 of ...
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59 views

Evaluating correlation: which test to choose

I want to evaluate the correlation between two samples of data (300 samples, 2 parameters). I've done some researches and I reached these conclusions (correct me if I'm wrong): Pearson's correlation ...
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46 views

Pearson's coefficient and p-value. How do I work out proportions from this?

My results of a Pearson's Correlation are shown below: ...
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8 views

Pearson Correlation Question [duplicate]

I am a beginner on calculating correlations and I would like to ask possibly a very simple question. If I have two variables that I want to perform correlation on, and those variable are of unequal ...
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73 views

Should I compute both Pearson's and Spearman's coefficients of correlation?

I have been reading over some statistics notes, and certain things are introduced without motivation (note: I am a mathematician and not a statistician, so my stats knowledge is woefully inadequate, ...
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1answer
201 views

Correlation between two Decks of cards?

I've written a program to simulate an overhand card shuffle. Each card is numbered, with suit going from CLUBS, DIAMONDS, HEARTS, SPADES and the rank from Two ...
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1answer
175 views

Deviance vs Pearson goodness-of-fit

I am trying to come up with a model by using negative binomial regression (negative binomial GLM). I have a relatively small sample size (greater than 300), and the data are not scaled. I noticed that ...
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75 views

Pearson's chi-square goodness of fit test

I am trying to perform a Pearson's chi-square goodness of fit test on my Generalized Linear Model to measure how well the model fits my data. Below is my code: ...
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88 views

Help interpreting Pearson's R p-values

I am trying to understand what these results mean for my analysis. The p-value seems extremely high, although the actual correlations do seem to reflect my data. ...
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36 views

How to calculate the first principal component from multi-data sets (using WGCNA)

I have a bunch of datasets (gene expression profiles). From the datasets, I am gonna analyze co-expression profiles using WGCNA ...
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1answer
131 views

Pearson correlation between discrete variable that's mostly 0 and a standard normal variable

Suppose I want to estimate the correlation between $X\sim N(0,1)$ and $Y$, where $Y \in \{-1,0,1\}$ and is equal to zero for 99 per cent of the sample. Sample size is 10 million. What are the ...
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1answer
103 views

Pearson's correlation for time series requires normally distributed data?

In order to use Pearson's correlation to measure the similarity of two time series, is normal distribution of both time series a necessary condition?
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92 views

Why is Pearson's correlation coefficient defined the way it is?

$$ r = \frac{{\rm Cov}(X,Y)}{ \sigma_{X} \sigma_{Y}} $$ I do not understand this equation at all. Where does it come from? From my personal understanding ${\rm Cov}(X,Y)$ comes from that fact that ...
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47 views

Should I use Pearson Correlation or Linear Regression to show the linearity of two sets of numbers?

I have two sets of acceleration data in terms of time. In one set the acceleration increases more linearily than another set. How can I show the linearity difference of the two set of data best? ...
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169 views

How to understand the correlation coefficient formula?

Can anyone help me understand the Pearson correlation formula? the sample $r$ = the mean of the products of the standard scores of variables $X$ and $Y$. I kind of understand why they need to ...
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45 views

Asymptotic distribution of Pearson Chi Square?

Suppose under $H_1$, $X_i$'s are independent random variables with $\mathrm{Poisson}(\theta_i)$. Under the null hypothesis, $X_i$'s are IID from $\mathrm{Poisson}(\theta)$. Define pearson chi square ...
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145 views

How outliers can effect the correlation results (Spearman and Pearson)?

How outliers can effect the correlation results (Spearman and Pearson)? I have two series of data. The source of the data are different but both are temperature that are measured by different ...
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82 views

Goodness of fit using frequency tables with low counts

I have two frequency tables, one representing observed data and one representing modeled data. I am looking for a Goodness of Fit measure, checking whether the model data fits the observed data. ...
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137 views

A question from a test in statistics?

I got the following question in my finals, but the teacher claims I didn't answer this right, I chose a. as the right answer, what is the right answer and why? ...
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127 views

Pearson correlation of 3 variables

I am interested in whether or not a "correlation" of three variables is something, and if what, what would this be? Pearson product moment correlation coefficient ...
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1answer
65 views

Suitable analysis for my data…?

everyone, I'm new at the statistical analysis so I need some help from more experienced people. I'm working with biological data from gene expression analysis. I have 5 treatments (1 parental toxin; 3 ...
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1answer
115 views

Comparing four correlation coefficients

I have four sets of data grouped by stages (Stage 1-4) with each having their own correlation coefficient. The 4 sets of data has the same dependent and independent variables with 1st n=106, 2nd n=23, ...
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31 views

Are 7-point Likert items always ordinal? [duplicate]

I'm doing a study that (among other things) examines the relationship between the quantity of comments students receive in online discussion forums and the following motivational factors: sense of ...
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1answer
88 views

Computing a circular-linear partial correlation

The CircStats toolbox for MATLAB (http://bit.ly/18C1SCF) implements a procedure to compute a correlation between a linear and a circular variable. Specifically, the ...
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31 views

Rescaling columns of bootstrapped matrix when using matrix multiplication to compute correlation coefficients

If I have $n$ samples and want to compute the pairwise correlation coefficients between $l$ and $m$ variables, I can construct the matrices $A_{l,n}$ and $B_{n,m}$. If I then subtract the mean and ...
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229 views

If linear regression is related to Pearson's correlation, are there any regression techniques related to Kendall's and Spearman's correlations?

Maybe this question is naive, but: If linear regression is closely related to Pearson's correlation coefficient, are there any regression techniques closely related to Kendall's and Spearman's ...
2
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1answer
434 views

Statistical meaning of pearsonr() output in Python

I have calculated the Pearson correlation by using pearsonr(var1, var2) I understand that the first number is the Pearson correlation and the second number is ...
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1answer
511 views

Are two Pearson correlation coefficients different?

I am aware of this question here, which mine was listed as a duplicate of, but it does not fully answer my question. It did however help me progress a little further so thanks, I couldn't find it ...
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119 views

Within-subject correlation before deciding on correlation structure in GEE

I want to have a look at the correlation coefficient for repeated measures in $x$ number of individuals. This will help me chose which correlation structure will best fit in GEE (Generalized ...
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1answer
315 views

Analysis of compounds using PCA - selecting the right PCA “type” for the data…?

I'm completing scientific analysis of chemical compounds in consumer products. As a non-statistician, I would really appreciate any thoughts from the experts here. My data is non-normal so I've used ...
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114 views

Test of Difference between 2 Sets of Pearson Correlations

Suppose I have two sets of Pearson correlation coefficients -- call them set A & set B, and they are of the same size. How do I systematically compare the correlations in A against B? E.g., I want ...
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28 views

Is the square of coefficient of variation an ascending function of exponent c? [duplicate]

Suppose that $x$ is a random variable with any distribution that takes only positive values. If $z=x+1$, can the following inequality hold for constants $c_2>c_1>0$? ...
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1answer
51 views

Pearson's r over time

I have a Pearson's r for the same variables for 4 different periods of time. (4 different years). How can I find the Pearson's r for all of them put together? Here are the years and the related ...