How many records (at least) should I have for my correlation (pearson/canonical) to be significant.
123684
I am running Pearson's correlation on an overall sample of 400 respondents.   When I isolate male and female responses, my sample becomes 220 male responses and 180 female responses.   If I further isolate male and female responses by (say) age groups, some sample sizes become as low as 35 responses (for example, for females over the age of 65).  My question: How good are these sample sizes for correlation analysis? (I am looking at the relationship between income levels and overseas travel.)   (I think this has something to do with margin of error but how does this apply to inferential analysis which is based on probability. I can understand its role in descriptive statistics such as results of a political poll).
18045
Let's say I test how variable Y depends on variable X under different experimental conditions and obtain the following graph:    The dash lines in the graph above represent linear regression for each data series (experimental setup) and the numbers in the legend denote the Pearson correlation of each data series.  I would like to calculate the "average correlation" (or "mean correlation") between X and Y. May I simply average the r values? What about the "average determination criterion", $R^2$? Should I calculate the average r and than take the square of that value or should I compute the average of individual $R^2$'s?
24294
I've already read all the pages in this site trying to find the answer to my problem but no one seems to be the right one form me...  First I explain you the kind of data I'm working with...  Let's say that I have an array vector with several names of city, one for each of 300 users. I also have another array vector with scores response to a survey of each user or a continuous value for each user.  I would like to know if exist a correlation coefficient that compute the correlation between these two variables so, between a nominal and a numeric/continuous or ordinal variables.  I've searched on the Internet and in some pages they suggest to use the contingency coefficient or Cramer's V or Lambda coefficient or Eta . For each of this measure the just say that they could be applied for such data in which we have a nominal variable and interval or numerical variable. The thing is that searching and searching, trying to understand every one of them, sometime is written or watching the examples that they are reasonable to use them if you have dichotomous nominal variable, except for Cramer's V, other time is not written any requirement for the type of data. A lot of other pages say that is right to apply regression instead, that is right, but I would just simply like to know if there is a coefficient like pearson/spearman for this kind of data.  I also think that is no so properly to use Spearman Correlation coeff since the cities are not sortable.  I have also built the function of Cramer'sV and Eta by myself (I'm working with Matlab) but for Eta they don't talk about any p-value to see if the coefficient is statistically significant...  In the matlabWorks site there is also a nice toolbox that says to compute eta^2 but the kind of input it needs is not understandable.  Is here someone that have done a test like mine? If you need more detail to understand the kind of data I'm using just ask me and I'll try to explain you better.
19575
X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant predictors of Y. Note that the two other (A, B) variables are significantly correlated with Y outside of the regression.   How should I interpret these findings? X predicts unique variance in Y, but since these are not correlated (Pearson), it is somehow difficult to interpret.  I know of opposite cases (i.e., two variables are correlated but regression is not significant) and those are relatively simpler to understand from a theoretical and statistical perspective. Note that some of the predictors are quite correlated (e.g., .70) but not to the extent that I would expect substantial multicollinearity. Maybe I am mistaken, though.    NOTE: I asked this question previously and it was closed. The rational was that this question is redundant with the question "". Perhaps I do not understand the other question, but I believe these are entirely separate questions, both mathematically and theoretically. My question is entirely independent from if "a regression is significant". Furthermore, several predictors are significant, while the other question entails variables not being significant, so I don't see the overlap. If these questions are redundant for reasons I do not understand, please insert a comment prior to closing this question. Also, I was hoping to message the moderator who closed the other question to avoid identical questions, but I couldn't find an option to do so.
88521
I am doing some calculations on different matrices (mainly in logistic regression) and I commonly get the error "Matrix is singular", where I have to go back and remove the correlated variables. My question here is what would you consider a "highly" correlated matrix? Is there a threshold value of correlation to represent this word? Like if a variable was 0.97 correlated to another one, is this a "high" enough to make a matrix singular?  Apologies if the question is very basic, I wasn't able to find any references talking about this issue (a hint towards any reference would be a big plus!).
1227
Can anyone recommend some books that are considered to be standard references for classical (frequentist) statistics? IE, fairly comprehensive, and also, been around for a while so that typos and mistakes in formulas had a chance to be checked and corrected
35769
I have some pairs of datasets (n=200 or thereabouts), of samples which are non-negative and not normally distributed. I think these pairs of variables are related, probably linearly.   Calculating Spearman's rank correlation on these datasets gives some strange results. The correlation coefficients show that the pairs of variables are weakly, positively correlated (e.g. rho of around 0.4), but the p-values are very low (e.g. 4.1e-10).  My vague understanding of this is that the variables are weakly, positively correlated but the probability of unrelated variables producing the same correlation is very low. Does this mean we can be reasonably certain that a positive correlation exists or have I misunderstood?
93460
I get this question frequently enough in my statistics consulting work, that I thought I'd post it here. I have an answer, which is posted below, but I was keen to hear what others have to say.  Question: If you have two variables that are not normally distributed, should you use Spearman's rho for the correlation?
87369
It is a general and maybe basic question, but it will help me to avoid a mistake. To test the dependence of continuous variable on nominal with parametric test (t-test, ANOVA), "the data has to be normally distributed" (distribution have to be not much violated from normal).   But I don't clearly understand: I have to test the normality of the continuous data together (whole sample) or the normality of data in every single group?   And if my groups have small sizes (n=4-6), and therefore I fail to reject null, does this indicate a permission to use parametric methods?  Can anyone provide me a link to some good examples of statistical (biomedical) hypothesis testing with R (google did not helped)?
69293
How do you tell if the correlations at different lags obtained from the cross-correlation (ccf function) of two time series are significant.
8460
Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
113676
Why do statisticians discourage us from referring to results as "highly significant" when the $p$-value is well below the conventional $\alpha$-level of $0.05$?  Is it really wrong to trust a result that has 99.9% chance of not being a Type I error ($p=0.001$) more than a result that only gives you that chance at 99% ($p=0.01$)?
56880
I remember that Pearson correlation works for continuous variables and also if one is continuous and the other a dummy. For the latter, it does not provide a correlation but provides a portion. What is the best approach, when we have 2 dummy variables. Would you suggest to calculate correlation for them or what is a good way to look at the relationship between 2 dichotomous variables. Ex: gender and religious status.
70908
I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple question.  Suppose I have three random variables $A$, $B$, $C$. Is it possible to have these three relationships satisfied? $$ \mathrm{corr}[A,B] = 0.9 $$ $$ \mathrm{corr}[B,C] = 0.8 $$ $$ \mathrm{corr}[A,C] = 0.1 $$ My intuition is that it is not possible, although I can't see right now how I can prove this conclusively.
53181
I am trying to analyze data based on a sample size of around 50 and would appreciate advice on which statistical test would be most appropriate. Participants, on a single questionnaire, were asked to complete two different sections. Variable 1: rating Likert items on a scale from 1-5 (strongly agree to disagree). Variable 2: rating Likert items of a validated tool on a scale of 1-9, which is averaged to obtain a single number.  My research question is: Do those who 'agree' with the statement in the first section significantly differ in terms of their scores on the variable 2, compared to those who 'disagree'? (ex. Do participants tend to 'agree' with "I like to read books for pleasure." have higher IQs (variable 2) than those who 'disagree'?)  I was advised by a colleague to run a one-way ANOVA with variable 1 (categorical) as IV and variable 2 (continuous) as DV.   Question 1: My independent variable is the three groups: 'agree', 'neutral', and 'disagree.' (I combined strongly agree with agree because of low frequencies and likewise for strongly disagree and disagree.) However, there are many more participants in the 'agree' category than in the 'disagree' category. The distribution is, on average, around 44 agrees, 3 neutrals, and 3 disagrees. Do the (very) unequal sample sizes prevent me from performing ANOVA, or any other tests? Which test would be most appropriate for this analysis?  Question 2: I would like to run analyses on all of the Likert items, which is more than 10 statements. (ex. Seeing how IQs correlate with agreement to many statements including “I like to read books for pleasure,” “I watch a lot of TV,” “I exercise more than 30 minutes each week,” etc.) I was planning to do a Bonferroni correction to adjust for the multiple tests. Would this be correct, and help make my analyses more robust? Note: The continuous data are not normally distributed (there is negative skewness), but I seem to be able to correct the skewness using logarithmic transformation.  Any advice or suggestions for papers to read would be appreciated. Thank you!
8353
There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is,  $$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$  What is the tightest bound you can give for $\rho$?
86805
I have a population of phone calls - 200,000.  There are different reasons for each call, but lets assume the number of reasons is known. i.e. 7 different call reasons: 1) Check on order 2) Cancel order 3) Billing information 4) Account information etc...  My question is, I want to get a statistically significant sample size so the number of calls I listen to in my sample are representative of the distribution of the reasons in the overall population of 200,000 calls.  What should the sample size be? Which methods to use to calculate the sample size?