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- 2. key concepts: Typesof correlation Methods of studying correlation a) Scatter diagram b) Karl pearson’s coefficient of correlation c) Spearman’s Rank correlation coefficient d) Method of least squares
- 3. Correlation: Thedegree of relationship between the variables under consideration is measure through the correlation analysis. The measure of correlation called the correlation coefficient .
- 4. Correlation isa statistical tool that helps to measure and analyze the degree of relationship between two variables. Correlation analysis deals with the association between two or more variables.
- 5. Positive relationships water consumption and temperature. study time and grades. Negative relationships: alcohol consumption and driving ability. Price & quantity demanded
- 6. Types of Correlation TypeII Correlation Simple Multiple Partial Total
- 7. Simple correlation:Under simple correlation problem there are only two variables are studied. Multiple Correlation: Under Multiple Correlation three or more than three variables are studied. Ex. Qd = f ( P,PC, PS, t, y ) Partial correlation: analysis recognizes more than two variables but considers only two variables keeping the other constant. Total correlation: is based on all the relevant variables, which is normally not feasible.
- 8. Types of Correlation TypeIII Correlation LINEAR NON LINEAR
- 9. Linear correlation:Correlation is said to be linear when the amount of change in one variable tends to bear a constant ratio to the amount of change in the other. The graph of the variables having a linear relationship will form a straight line. Ex X = 1, 2, 3, 4, 5, 6, 7, 8, Y = 5, 7, 9, 11, 13, 15, 17, 19, Y = 3 + 2x Non Linear correlation: The correlation would be non linear if the amount of change in one variable does not bear a constant ratio to the amount of change in the other variable.
- 10. Scatter Diagramis a graph of observed plotted points where each points represents the values of X & Y as a coordinate. It portrays the relationship between these two variables graphically.
- 11. Height Weight Height of A Weight of A Height ofB Weight of B A linear relationship
- 12. Moderate PositiveCorrelation Weight Shoe Size r = + 0.4
- 13. Perfect NegativeCorrelation Exam score TV watching per week r = -1.0
- 14. Moderate NegativeCorrelation Exam score TV watching per week r = -.80
- 15. Weak negativeCorrelation Weight Shoe Size r = - 0.2
- 16. No Correlation(horizontal line) Height IQ r = 0.0
- 17. Simple &Non Mathematical method Not influenced by the size of extreme item First step in investing the relationship between two variables
- 18. Can not adoptthe an exact degree of correlation
- 19. No distinctionbetween explanatory (x) and response (y) variable. The null hypothesis test that r is significantly different from zero (0). Requires both variables to be quantitative or continuous variables Both variables must be normally distributed. If one or both are not, either transform the variables to near normality or use an alternative non- parametric test of Spearman Use Spearman Correlation coefficient when the shape of the distribution is not assumed or variable is distribution-free.
- 20. There islinear relationship between two variables, i.e. when the two variables are plotted on a scatter diagram a straight line will be formed by the points. Cause and effect relation exists between different forces operating on the item of the two variable series.
- 21. Pearson’s ‘r’is the most common correlation coefficient. Karl Pearson’s Coefficient of Correlation denoted by- ‘r’ The coefficient of correlation ‘r’ measure the degree of linear relationship between two variables say x & y.
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- 25. It summarizesin one value, the degree of correlation & direction of correlation also.
- 26. Always assumelinear relationship Interpreting the value of r is difficult. Value of Correlation Coefficient is affected by the extreme values. Time consuming methods
- 27. When statisticalseries in which the variables under study are not capable of quantitative measurement but can be arranged in serial order, in such situation pearson’s correlation coefficient can not be used in such case Spearman Rank correlation can be used. R = 1- (6 ∑D2 ) / N (N2 – 1) R = Rank correlation coefficient D = Difference of rank between paired item in two series. N = Total number of observation.
- 28. a) Problems whereactual rank are given. 1) Calculate the difference ‘D’ of two Ranks i.e. (R1 – R2). 2) Square the difference & calculate the sum of the difference i.e. ∑D2 3) Substitute the values obtained in the formula.
- 29. b) Problems whereRanks are not given :If the ranks are not given, then we need to assign ranks to the data series. The lowest value in the series can be assigned rank 1 or the highest value in the series can be assigned rank 1. We need to follow the same scheme of ranking for the other series. Then calculate the rank correlation coefficient in similar way as we do when the ranks are given.
- 30. This methodis simpler to understand and easier to apply compared to karl pearson’s correlation method. This method is useful where we can give the ranks and not the actual data. (qualitative term) This method is to use where the initial data in the form of ranks.
- 31. Cannot beused for finding out correlation in a grouped frequency distribution. This method should be applied where N exceeds 30.
- 32. UNIT 3 Correlation Problems 1.Scatter Plot 2. Karl Pearson 3. Spearman Rank
- 33. Scatter Plot Manually XY 3 25 4.1 25 5 30 6 29 6.1 42 6.3 46
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- 36. Karl Pearson Coefficient ComputationalFormula Correlation Coefficient
- 41. X Y D=X-Y D 7 6 1 3 10 9 5 4 6 8 8 10 9 7 2 2 3 1 4 5
- 44. A B CD D D D D D 1 2 1 2 4 3 3 1 5 4 5 2 5 3 4