Partial correlation

Explaining correlation, assumptions,coefficients of correlation, coefficient of determination, variate, partial correlation, assumption, order and hypothesis of partial correlation with example, checking significance and graphical representation of partial correlation.

1. Name : dwaiti Roy Application no : 8536ae51e72f11e9a93cbd5fd00aa9e7 AFFILIATION : Banaras Hindu University Partial Correlation CC BY-SA-NC

2. ACKNOWLEDGEMENT Course Name : Academic Writing First of all, I would like to thank Dr. Ajay Semalty and the full team of AW to deliver such a rich content regarding academic writing. It helped a lot in making this presentation. Secondly I’m thankful to all my professors who helped me in preparing the presentation. Lastly I am grateful to the books, without which the presentation would have been incomplete. CC BY-SA-NC

3. What Is Correlation Correlation is a descriptive statistics that explores the degree and direction of association between two or more score series or variables. positive no correlation negative correlation correlation CC BY-SA-NC

4. Assumptions Of Correlation It cannot be generalized beyond the sample or population from where the data belongs. It may not indicate any cause and effect relationship between two or more variables. Correlation cannot predict the value from one variable from that of another. The variables involved in the correlation are random variables , and cannot be manipulated by the researcher. CC BY-SA-NC

5. Coefficient Of Correlation The coefficient of correlation is the ratio which expresses the extent to with changes to one variable are accompanied by the changes of another variable. Generally the coefficient of correlation is measured by Pearson Product M oment Correlation, denoted by ‘r’. CC BY-SA-NC

6. Cont. The general formula for computing product-moment correlation is – where, r = product moment coefficient of correlation, N = total no of paired scores, CC BY-SA-NC

7. Cont. X = the first variable, Y = the second variable. Thus when r is said to be +0.07 that implies two thing – the sign implies the direction of relationship, i.e. if variable X increase variable Y will also increases. And the magnitude implies the strength of relationship. CC BY-SA-NC

8. Coefficient Of Determination Coefficient of determination (r 2 ) is the technique of measuring the strength of variable. It measures how much of the variability in one variable is predictable from its relationship with the other variable . For e.g. - a correlation of r = 0.80 would mean that r 2 = 0.64 (or 64%) of the variance in criterion variable can be predicted from relation with the predictor variable. CC BY-SA-NC

9. Concept of Variate Variate is the weighted composite of two or more directly observable variables that are combined linearly. Thus a statistic may contain one variate (known as univariate statistics , e.g. t-test), two variates (known as bivatiate statistics , e.g. p roduct-moment correlation) or more than two variates (known as multivariate statistics , e.g. multiple regression analysis). CC BY-SA-NC

10. Partial Correlation Special form of correlation between two variables. Part of multivariate statistics involving more than two variables in a sample. Aims at eliminating effects of other variable on both the variables in common. It is the part of product moment r between two given variable that is remained after elimination of components of their association , arising from other variables on both of them. CC BY-SA-NC

11. Assumptions Of Partial Correlation All the variables involved are continuous measurement variable . Scores of variables have unimodal or fairly symmetrical distribution without any marked skewness. The paired scores of each pair of variables are independent of all other scores in the sample. There is a linear association between the scores of every pair. CC BY-SA-NC

12. Order Of Partial Correlation There are different orders of partial correlation depending on the number of variables to be eliminated. If there is no elimination of other variables is to be known as zero order r , indicated as r 12 . If there is elimination of one variable from the other variables is to be known as first order partial r , indicated as r 12.3 . If there is four inter connected variables and two are to eliminate from others is to be known as second order partial r , indicated as r 12.34 . CC BY-SA-NC

13. Hypothesis For Partial Correlation Null hypothesis : There is no partial correlation between variables or the partial correlation is zero and partial r resulted only due to chance. Alternate hypothesis : There is partial correlation between variables or the partial correlation is not zero. CC BY-SA-NC

14. The Formula of Partial Correlation The first order partial correlation is used to define the process. The formula for computing partial correlation is Where, r 12 = correlation coefficient of variable 1 and 2 r 13 = correlation coefficient of variable 1 and 3 r 23 = correlation coefficient of variable 2 and 3 CC BY-SA-NC

15. Example CC BY-SA-NC

16. Cont. The hypothetical scores have been constructed to simulate the church/crime/population situation for a sample of n = 15 cities. The X variable represents the number of churches, Y represents the number of crimes, and Z represents the population for each city. The cities are grouped into three categories based on population (small cities, medium cities, large cities) with n = 5 cities in each group. CC BY-SA-NC

17. Cont. Here it is seen that as the population increases from on city to another, the number of churches and crimes also increase. Here, r XY = .923 r XZ = .961 r YZ = .961 Partial r allows to hold the population constant and see the underlying effect of churches and crimes. CC BY-SA-NC

18. Logical relationship between no of churches and crimes in 3 cities having different population. CC BY-SA-NC

19. Cont. The computed partial r is 0 in the above case. Thus it can be said that when the population difference is eliminated there is no correlation between churches and crime. CC BY-SA-NC

20. Cont. Relation between no. of churches and no. of crimes after population difference is eliminated. CC BY-SA-NC

21. Another Example Researcher wants to compute correlation between anxiety and achievement controlled from intelligence. If anxiety denote ‘X’, achievement denote ‘Y’ and intelligence denote ‘Z’ then correlation coefficient will be r XY.Z . CC BY-SA-NC

22. Cont. CC BY-SA-NC

23. Cont. r XY = -.369 r YZ = -.245 r XZ = .918 And computed r XY.Z = -.375 The partial correlation is negative. Thus in the above example, if the factor intelligence is eliminated then achievement increases with the decrease in anxiety. CC BY-SA-NC

24. Checking Significance To check significance partial r is transformed into t score and compared with critical t scores. Formula for transforming to t score is Where r p = partial r n = sample size v = total number of variable CC BY-SA-NC

25. Cont. Thus for above e.g. t score for partial r is 1.69 which found not to be significant at 0.05 or 0.01 level against df (n-v) = 7. CC BY-SA-NC

26. Graphical Representation CC BY-SA-NC

27. Cont. Here, ‘a’ = variance shared by variable 1 and 2 ‘b’ = variance shared by variable 1 and 3 ‘c’ = variance shared by variable 2 and 3 and ‘d’ = common variance shared by both variable 1,2 and 3. Thus partial r is the variance shared by variable 1 and 2 , that is devoid of any variance explained by variable 3. CC BY-SA-NC

28. References Das, D., & Das, A.(2017). Statistics In Biology And Psychology(6 th ed.). pg. 162-164. Kolkata: Academic Publisher. Gravetter, F.J., Wallnau, L.B.(2015). Statistics For The Behavioural Sciences(10 th ed.). pg. 502-505. Boston: Cengage Learning. CC BY-SA-NC

29. Further Reading Gravetter, F.J., Wallnau, L.B.(2015). Statistics For The Behavioural Sciences(10 th ed.). Heiman, G.W.,(2011). Basic Statistics for the Behavioural Sciences(6 th ed.). Tabachnick, B.G., Fidell, L.S.,(2013). Using Multivariate Statistics(6 th ed.). CC BY-SA-NC

30. Feedback Of The Course Application Number: 8536ae51e72f11e9a93cbd5fd00aa9e7 The expectation from the course academic learning was very high including to learn about various scopes of academic learning. It met the expectation beautifully. I appreciate the time to time lectures and the self assessment quizzes in every week, which resulted in better understanding of the topic. The additional gain from the course was the knowledge about various OERs. I would like to thank Dr. Ajay Semalty as well as the whole team of AW for arranging such a cohesive course in such a comprehensive manner. CC BY-SA-NC

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