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from: Kaohsiung
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| 2021-11-28 18:03:45 | onclick： | Correlation analysis and regression analysis |
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There is a phenomenon in real life. After people form a certain concept, it is difficult to change. Even in the face of facts and evidence, they are still unwilling to accept new concepts. More importantly, this phenomenon is also found in scientific research. First express a view: regression analysis and correlation analysis are the same thing. More specifically: in the research, if we do correlation analysis, we don't have to do regression analysis; Or, if the regression analysis is done, the previous correlation analysis does not need to be retained.
Those who have studied statistics can probably remember that the textbook first talks about correlation analysis, and then regression analysis. Therefore, the impression is that correlation analysis and regression analysis are two independent statistical techniques, and correlation analysis is the basis of regression analysis. In this way, people inadvertently despise correlation analysis and attach importance to regression analysis.
Specific to the field of psychology, too many researchers follow the routine: as long as possible, do correlation analysis first, and then regression analysis. Even the reason for this is that correlation analysis can only know whether there is a relationship between two variables, and regression analysis can predict one variable from another.
In the research report, the results of correlation analysis usually only show the correlation coefficient and give the probability range of significance test (for example, P < 0.05); For the results of regression analysis, the significance test results of regression analysis (e.g., F value, probability range), regression coefficient and even regression equation are usually presented. Therefore, people naturally think that regression analysis is more advanced and correlation analysis is too simple.
In fact, correlation analysis and regression analysis are the same thing. The purpose of regression analysis can also be achieved by correlation analysis. This can be clearly seen through examples. We still use the example of the previous blog post to investigate the relationship between IQ and visual memory of subjects in the two groups (spelling difficulty group and control group).
For all subjects in the two groups, correlation analysis showed that there was a significant positive correlation between IQ and visual memory, r =. 454, P =. 044, effect R2 =. 207; Regression analysis showed that IQ could significantly predict visual memory, f (1,18) = 4.686, β= . 454, P =. 044, R2 =. 207. It is not difficult to find that the test results of the two analyses are the same, including P =. 044, effect R2 =. 207, and correlation coefficient = regression coefficient. If you have the knowledge of effect quantity, it is more clear that the important thing in the investigation of the relationship between two variables is not the correlation coefficient or regression coefficient, but the effect quantity. The results of key indicators (effect quantity) reflected by regression analysis and correlation analysis are the same. Therefore, regression analysis and correlation analysis are the same thing.
Then verify the data of the two groups respectively. For the spelling difficulty group, the correlation coefficient between IQ and visual memory was r = -. 329, P =. 353, and the effect quantity R2 =. 108; Regression analysis shows that f (1,8) = 0.973, β= -. 329, P =. 353, effector R2 =. 108. For the control group, the correlation coefficient between IQ and visual memory was r = -. 039, P =. 915, and the effect quantity R2 =. 002; Regression analysis shows that f (1,8) = 0.012, β= -. 039, P =. 915, R2 =. 002. Obviously, the corresponding correlation coefficient, significance level and effect amount are the same.
Thus, regression analysis and correlation analysis are indeed the same thing, at least for bivariate regression analysis and correlation analysis - although regression analysis is more complex and advanced, for example, some statistics are used, especially those expressed in Greek letters.
What's the use of knowing that "regression analysis and correlation analysis are one thing", that is, the two kinds of analysis are equivalent? This concept can respond to a suggestion of the special working group on statistical significance test of the American Psychological Association: do not present the correlation matrix in the result part, because it is reasonable for researchers to be interested in one or two correlation coefficients. However, if researchers are interested in all correlation coefficients in the correlation matrix, then it is necessary to explain why. Generally speaking, researchers are not interested in all the correlation coefficients in the correlation matrix. Otherwise, they do not use contradiction theory to guide their research. Therefore, the corresponding research is the main aspects without main contradiction or / and no contradiction.
Of course, correlation analysis and regression analysis are more suitable for presenting results. For example, in factor analysis, the correlation matrix between factor scores and between factor scores and the total score of the scale is presented, which can easily investigate the factor structure of a specific scale. For other cases, it is often convenient to present the regression coefficient by regression analysis.
At the same time, understanding that "correlation analysis and regression analysis are one thing" also helps to strengthen the professional quality of researchers. For example, we really value the effect quantity rather than the statistical significance test result, that is, P value.
Finally, it must be noted that the view that "regression analysis and correlation analysis are one thing" was not put forward by me, but heard from Mr. Cheng Changlun. When I was a graduate student, Mr. Cheng taught us the course "mathematical model of experimental design". As a member of the thesis defense, Mr. Cheng points out this problem every year, saying that mathematically, regression analysis and correlation analysis are the same thing. However, the students of the next year, even after observing the dissertation defense of the previous year, will still present both the results of correlation analysis and regression analysis in the dissertation. Oh! The difficulty of changing ideas can be seen from this.
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