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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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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24 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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8 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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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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3answers
62 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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14 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 ...
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10 views

Inter-rater reliability

Two raters have scored essays based on five criteria. I would like to calculate inter-rater reliability (IRR). Should I calculate IRR on each criterion or just the total score of five criteria? ...
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62 views

Next steps after obtaining a significant Pearson coefficient

Lets say I have an R value of .5 and therefore an $R^2$ value of .25, and a p value < 0.001. (All through the stock cor.test function in R). Is there a way to isolate those cases/observations ...
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16 views

Comparing two pearson coefficents w/ r^2

I have three variables, x,y, z. My sample n is about 17,000. My pearson coeficients & r^2: for x -> z it is 0.187, 0.034 for y -> z it's 0.311, 0.096 testing for significance, I receive a ...
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SPSS: Pearson's r not significant but confidence intervals do not include 0

I have calculated the value of Pearson's r between two variables in SPSS, two tailed. Sample size is 81. The r value is -.21. The p value is .06. When I compute the 95% confidence intervals using ...
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103 views

Correlation analysis: Spearman's $\rho$ is significant, but Pearson's $r$ is not - with likert scale

I am doing a correlation analysis testing summated likert scales. However, one of the correlation analysis shows an unsignificant pearsons r (p = 0.068), BUT spearman's rho is 0.044. What should I ...
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Can the formula developed by Olkin und Siotani (1964) also be used to compare correlations from Spearman's $\rho$ and Cramér's $V$

The followgin formula is normally used for comparing two Pearsons $r$ correlations: Can this formula also be used to compare correlations from Spearman's $\rho$ and Cramér's $V$?
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How to interpret Pearson's $r$, Spearman's $\rho$, Cramér's $\phi_{c}$ and Cramér's $V$ correctly?

Is it right that both Cramér's $\phi_{c}$ (and consequently Cramér's $V$ as well) are similar to the Pearson correlation coefficient, $r$, (and so, to Spearman's $\rho$) in its interpretation, as it ...
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17 views

Pearson Correlation with symmetric pairs?

I am correlating two features in the leaves of a dendrogram for a given tree distance (2,3,...). When i find the pair "A-B" at distance x I will also have the duplicate "B-A" in the same set for ...
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40 views

Correlation tests – multivariate correlation matrix?

I just got comments from a reviewer to a submitted article and didn't understand what I should do very well. Here are the tests I performed: We first used principal components analysis (PCA) to ...
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1answer
89 views

Proof of Point-Biserial Correlation being a special case of Pearson Correlation

I have been examining the use of the Point Biserial correlation as a statistic to measure the relationship between a dichotomous variable and a continuous one. Wikipedia et. al. seem to concur that ...
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2answers
40 views

What are real strengths of association when using Pearson correlation?

I have located a table that breaks downs Pearson's correlation values into 3 categories. See below: My question is this. One could have a large positive correlation of 1 as well as a perfect ...
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1answer
139 views

Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?

There are two Boolean vectors, which contain 0 and 1 only. If I calculate the Pearson or Spearman correlation, are they meaningful or reasonable?
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37 views

Pearson Correlation significant, multiple linear regression not significant of one IV while the reverse is true for another IV

I am studying the effect of a education classroom experiment. I have pre- and post the intervention data on the feeling of competence, the feeling to have influence on study results, extrinsic and ...
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39 views

Calculate Weights in pearson Correlation

I have user, movie data for recommendation purpose, where some of the users have rated relatively very fewer movies in compare to other users.I learned that while using Pearson Correlation to ...
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1answer
187 views

Autocorrelation of discrete time series

I am currently planning on calculating the autocorrelation for various lags given a time series. However, my elements of the time series are "discrete" and abstract classes; i.e., no integers. For ...
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33 views

Pearson Correlation with multiple observations per each level of independent variable

I am giving different doses of a drug to mice and measuring a quantitative response. I want to determine if there is a linear relationship between the dose of the drug and the response. Pearson ...
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1answer
131 views

How to compare the strength of two Pearson correlations?

I've been asked by a reviewer if the Pearson correlations (r-values) presented in a table can be compared to each other so one can claim that one is "stronger" than another (other than just eyeballing ...
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190 views

Is the correlation coefficient better than we think?

In order to measure precisely the influence of one variable $Y$ over $X$ I wanted to use the mutual information because so far I believed that correlation coefficient (Pearson) was only limited to ...
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33 views

Comparison of point-biserial and linear correlation coefficients

I have a continuous variable X that is associated with a continuous outcome Y and a dichotomous outcome Z. If I calculate Pearson's $r$ between X and Y, and the point-biserial coefficient $r_{pb}$ ...
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711 views

How did Karl Pearson come up with the chi-squared statistic?

How did Pearson come up with the following Pearson chi-squared statistics in 1900? $$ K = \sum \frac{(O_{ij} -E_{ij})^2}{E_{ij}} $$ that $$ K \sim \chi^2 $$ Did he have chi-squared in mind and ...
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71 views

Running a Pearson's correlation calculation on binary survey data

I have the following raw survey data output from a survey app: I was asked to run a Pearson's R on the results (1s and 0s). The format that is returned is as follows: I was further ...
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64 views

Formula for computing the Pearson $\chi^2$, comparison with R

I suspect this question is really about basic definition, but I could not find the ressource I need to solve my problem. I want to understand why the pearson $\chi^2$ test statistic, and ...
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1answer
275 views

p-value for weighted Pearson correlation coefficient

I'm computing a weighted correlation coefficient, using the method described here. I'd like to compute a p-value for the resulting r coefficient. How can I do this correctly, given that my r was ...
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1answer
67 views

Correlating two questionnaires with grouped items

I need to correlate employee engagement (gathered data using the 9 item UWES questionnaire) and organizational commitment (gathered data using the 18 item Organizational Commitment Scale). The both ...
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50 views

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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2answers
148 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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1answer
143 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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71 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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61 views

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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1answer
44 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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14 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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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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107 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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149 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
140 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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62 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
73 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
166 views

How to best analyze these data?

I'm trying to figure out a way to analyze these data that I have: These are data that I pulled from various studies, and each study has a different sample size, and each study reported an ...
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88 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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80 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
93 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
119 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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76 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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Pearson's coefficient and p-value. How do I work out proportions from this?

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