Hello, everyone, I want to know, how to interpret the results of correlation coefficients. I have noted its explanation from the links
(i) (https://www.andrews.edu/~calkins/math/edrm611/edrm05.htm)
(ii) (http://www.dummies.com/education/math/statistics/how-to-interpret-a-correlation-coefficient-r/) as:
Correlation coefficients whose magnitude are between 0.9 and 1.0 indicate variables which can be considered very highly correlated. Correlation coefficients whose magnitude are between 0.7 and 0.9 indicate variables which can be considered highly correlated. Correlation coefficients whose magnitude are between 0.5 and 0.7 indicate variables which can be considered moderately correlated. Correlation coefficients whose magnitude are between 0.3 and 0.5 indicate variables which have a low correlation. Correlation coefficients whose magnitude are less than 0.3 have little if any (linear) correlation.
But I don't know whether I can use this in Plasma physics statistical study or not?
any help will be appreciated. thanks
Dear Abdur,
You would probably expect higher correlations from your context. The interpretations you have given are actually higher than the well known ones given by Cohen.
Thanks to all for such a good information, but in the journal articles, I didn't find the answer to my question. Also in the article, i didn't see that which range of Pearson correlation coefficient values is classified as very strong, strong, moderate and, weak correlation like the classification of correlation coefficients shown in the link I have provided.
Dear Abdur
Please, read the classification in the following link:
http://purpledreams.com/~mike/math_studies_11/statistics_08.pdf
Good Luck
Dear Abdur, Please note that the value of the correlation coefficient is very much function of the sample size. A value of 0.63 may be just sufficient to be significant for the sample size of 10 or 0.7 value of r will be significant if n=8. In view of this to attach importance without considering the pairs of data involved is meaningless. As far as I understand as a statistician is that significant r means there is a linear relationship between the two variables x and y considered. Second, if you are interested in any predicting model that is interested in predicting y given x then r should be significant first and then should be as high as 0.8. R^2 is always used for interpreting the results like 0.3 significant r means only 9% of the variation in y is due to x and 91% variations is coming due to many other variables. So please indicate why you want to study the correlations, only to know the relationship between various variables considered or you want to proceed further from there? I feel getting significant r is one thing and then to go for prediction is second thing. A high significant r (more than 0.8) will enable you to predict y given x with a meaning attached to it is that it can only explain about 64% or more variation in y given x.
Your question is very general cannot be answered well unless you provide more data like X (Indenpendent variable), Y( dependent variable), n, r and its significance. You may be aware that there also exist spurious correlations like increase in sales of news paper and increase in crime rate of a given area. So, before you calculate r there should be some scientific basis or reason to believe that X and y are correlated.
@Ramnath Takiar, Thank your sir for your time.
Now i understand how to test the significance of correlation and also how to calculate the coefficient of determination r^2 which you have mentioned in your answer.
Hi
1. This assumptions of the sample size, both variables should be normally distributed (normally distributed variables have a bell-shaped curve). Other assumptions include linearity and homoscedasticity. Linearity assumes a straight line relationship between each of the two variables and homoscedasticity assumes that data is equally distributed about the regression line have to be satisfied for all measures of correlation coefficients and hypotheses testing.
2. The Correlation is used to test relationships between quantitative variables or categorical variables. In other words, it’s a measure of how things are related. The study of how variables are correlated is called correlation analysis.
3. A correlation coefficient gives a numerical summary of the degree of association between two variables .
4. Types:
Pearson r correlation: Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. For example, in the stock market, if we want to measure how two stocks are related to each other, Pearson r correlation is used to measure the degree of relationship between the two. The point-biserial correlation is conducted with the Pearson correlation formula except that one of the variables is dichotomous.
Kendall rank correlation: Kendall rank correlation is a non-parametric test that measures the strength of dependence between two variables. If we consider two samples, a and b, where each sample size is n, we know that the total number of pairings with a b is n(n-1)/2.
Spearman rank correlation: Spearman rank correlation is a non-parametric test that is used to measure the degree of association between two variables. The Spearman rank correlation test does not carry any assumptions about the distribution of the data and is the appropriate correlation analysis when the variables are measured on a scale that is at least ordinal.
5. If the assumptions of normality is not assured, or the sample size is not satisfied Kendall rank correlation or Spearman rank correlation could be developed.
6. For testing the significance between different samples non-parametric tests could be developed. If you have two groups you can develop Wilcoxon test for related samples, and Mann-Whitney for unrelated samples.
7. For three samples, Friedman test for related samples, and Kruskal-Wallis for unrelated samples.
Regards,
Zuhair
Please refer to:
1.Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.
2.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.
Regards,
Zuhair
Dear Abdur Rauf
Attached are few documents it may help you.
Regards,
Zuhair
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