Karl pearson's coefficient of correlation (1)

KARL PEARSON'S COEFFICIENT OF CORRELATION

1. CORRELATION – KARL PEARSON’S COEFFICIENT OF CORRELATION - INTERPRETATION OF CORRELATION COEFFICIENT

2. MEANING OF CORRELATION The method of correlation is developed by Francis Galton in 1885. It is the relationship between two sets of scores or variables.

3. DEFINITION OF CORRELATION Whenever two variables of the same group are so related that the increase or decrease are correspond to the increase or decrease to another or conversely , increase or decrease corresponds to the decrease or increase to another ,they are said to be correlated.

4. TYPES OF CORRELATION On the basis of direction of the relation between variables, there are three types of correlation. That are ,

5. POSITIVE CORRELATION If when the first variable increases or decreases the other also increases or decreases respectively their relationship is said to be Positive correlation , because they move in the same direction. Eg . Intelligence and Achievement

6. NEGATIVE CORRELATION If when the first variable increases or decreases , the other respectively decreases or increases their relationship is said to be Negative correlation , because they move in the opposite direction. Eg . Anxiety and Performance

7. ZERO CORRELATION If there exists no relationship between two sets of measures or variables. Eg . Intelligence and Height.

8. COEFFICIENT OF CORRELATI ON The ratio indicating the degree of relationship between two related variables. For a perfect POSITIVE CORRELATION the coefficient of correlation is +1 . For a perfect NEGATIVE CORRELATION the coefficient of correlation is -1 . Positive coefficient of correlation varies from 0 to +1 . Negative coefficient of correlation varies from 0 to -1 .

9. USES OF CORRELATION It helps to determine the validity of a test. It helps to determine the reliability of a test. It indicates the nature of the relationship between two variables. It helps to ascertain the traits and capacities of pupils.

10. COMPUTATION OF COEFFICIENT OF CORRELATION There are two different methods of computing coefficient of correlation . They are , RANK DIFFERENCE METHOD PRODUCT MOMENT METHOD

11. PRODUCT MOMENT METHOD Most widely used measure of correlation. This method is also known as Pearson’s product moment method in honour of Karl Pearson , who is said to be the inventor of this method. The coefficient of correlation computed by this method is known as the product moment coefficient of correlation or Pearson’s correlation coefficient. It is represented as ‘r’ .

12. The standard formula used in the computation of Pearson’s product moment correlation coefficient is as follows :

13. Where, N - the total no: of scores or cases Ʃ - the summation of the items indicated ƩX - the sum of all X scores ƩX² - each X score should be squared and then those squares summed {the sum of the X squared scores} (ƩX)² - X scores should be summed and the total squared (the squares of the sum of all the X scores)

14. ƩY – the sum of all Y scores ƩY² - each Y score should be squared and then those squares summed (ƩY)² - Y score should be summed and the total squared

15. CALCULATE THE CORRELATION OF THE FOLLOWING DATA SUBJECT SCORES IN TEST 1 SCORES IN TEST 2 A 5 12 B 3 15 C 2 11 D 8 10 E 6 18

16. SUBJECT SCORES IN TEST 1 (X) SCORES IN TEST 2 (Y) XY X² Y² A 5 12 B 3 15 C 2 11 D 8 10 E 6 18 N= ƩX= ƩY= ƩXY= ƩX²= ƩY²=

17. SUBJECT SCORES IN TEST 1 (X) SCORES IN TEST 2 (Y) XY X² Y² A 5 12 60 25 144 B 3 15 45 9 225 C 2 11 22 4 121 D 8 10 80 64 100 E 6 18 108 36 324 N=5 ƩX=24 ƩY=66 ƩXY=315 ƩX²=138 ƩY²=914

18. r = -0.0576 ie , product moment correlation coefficient= -0.0576

19. CALCULATE THE CORRELATION OF THE FOLLOWING DATA INDIVIDUALS SCORE IN TEST X SCORES IN TEST Y A 15 60 B 25 70 C 20 40 D 30 50 E 35 30

20. INDIVIDUAL SCORES IN TEST X SCORES IN TEST Y XY X² Y² A 15 60 B 25 70 C 20 40 D 30 50 E 35 30 N= ƩX= ƩY= ƩXY= ƩX²= ƩY²=

21. INDIVIDUAL SCORES IN TEST X SCORES IN TEST Y XY X² Y² A 15 60 900 225 3600 B 25 70 1750 625 4900 C 20 40 800 400 1600 D 30 50 1500 900 2500 E 35 30 1050 1225 900 N=5 ƩX=125 ƩY=250 ƩXY= 6000 ƩX²= 3375 ƩY²= 13500

22. Product moment correlation coefficient = -0.5

23. INTERPRETATION OF CORRELATION COEFFICIENT The correlation coefficient ‘r’ value was verbally interpreted as per the criteria suggested by Garret (2010). The details were as follows: ‘r’ from 0.00 to ±0.20 denotes negligible correlation . ‘r’ from ±0.20 to ±0.40 denotes low correlation . ‘r’ from ±0.40 to ±0.70 denotes substantial or marked correlation . ‘r’ from ±0.70 to ±1.00 denotes high to very high correlation.

24. ADVANTAGES OF PRODUCT MOMENT CORRELATION It gives a precise and quantitative figure which can be interpreted meaningfully. It helps in establishing the value of the dependent variable from the known value of independent variable.

25. LIMITATIONS OF PRODUCT MOMENT CORRELATION This method assumes that there is a linear relationship between the variables under study regardless of the fact whether it exists or not. Compared to other methods , the computation of correlation coefficient by this method is time consuming. The value of the coefficient is unduly affected by extreme items.

26. ANY DOUBTS?