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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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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16 views

Elements of first list in Kendall must be ordered?

Two ways to execute a Kendall tau test (in R): ...
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44 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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18 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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119 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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43 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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30 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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30 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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43 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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17 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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58 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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49 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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13 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 ...
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1answer
12 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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33 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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20 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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33 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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1answer
37 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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45 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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68 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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139 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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106 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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35 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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17 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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43 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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3answers
109 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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45 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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15 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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69 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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17 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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194 views

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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2answers
246 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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34 views

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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20 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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64 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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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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54 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
583 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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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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45 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
237 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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48 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 ...
2
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1answer
297 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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1answer
197 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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41 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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857 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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102 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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83 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 ...