Pearson's correlation coefficient
Download as PPTX, PDF0 likes660 views
The document discusses Pearson's correlation coefficient, a statistical method developed by Francis Galton to assess the relationship between two variables. It covers definitions, types of correlation (positive, negative, and zero), methods of computation, and the significance and limitations of Pearson's method. The document also provides an example calculation and emphasizes the advantages and disadvantages of using Pearson's correlation coefficient.
Pearson's correlation coefficient
- 2. Submitted by: Group B Name Roll Batch Md. Topu Kawser 28 58thB Azizul Haque Bhuiyan 07 58thB Md Maidul Islam Chowdhury 06 58thB Kaptusha akter monisha 26 59thB Ramnunsang bawm 37 58thB Department of Business Administration Dhaka International University.
- 3. 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.
- 4. 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.
- 5. Coefficient Of Correlation • 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.
- 6. Uses Of Correlation • IT HELPS TO DETERMINE THE VALIDITY OF A TEST. • IT HELPS TO DETERMINE THE RELIABILITY OF A TEST. • IT CAN BE USED TO ASCERTAIN THE DEGREE OF THE OBJECTIVITY OF A TEST. • IT CAN ANSWER THE VALIDITY OF ARGUMENTS FOR OR AGAINST A STATEMENT. • IT INDICATES THE NATURE OF THE RELATIONSHIP BETWEEN TWO VARIABLES. • IT PREDICTS THE VALUE OF ONE VARIABLE GIVEN THE VALUE OF ANOTHER RELATED VARIABLE. • IT HELPS TO ASCERTAIN THE TRAITS AND CAPACITIES OF PUPILS.
- 7. Types Of Correlation On the basis of direction of the relation between variables, there are three types of correlation. That are POSITIVE CORRELATION NEGATIVE CORRELATION ZERO CORRELATION
- 8. POSITIVE CORRELATION NEGATIVE 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. Example . Intelligence and Achievement. 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. Example . Anxiety and Performance.
- 9. ZERO CORRELATION If there exists no relationship between two sets of measures or variables. Example . Intelligence and Height.
- 10. Computation Of Coefficient Of Correlation There are two different methods of computing coefficient of correlation . they are , • Rank difference method • PRODUCT MOMENT METHOD or pearson's correlation coefficient .
- 11. 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’ . Pearson's correlation coefficient (r) is a measure of the linear association of two variables. Correlation analysis usually starts with a graphical representation of the relation of data pairs using a scatter diagram. The values of correlation coefficient vary from –1 to +1.
- 12. The standard formula used in the computation of Pearson’s product moment correlation coefficient is as follows :
- 13. Where, • N - the number: of pairs of data • 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) • 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
- 14. Calculate the correlation of the following data INDIVIDUALS SCOREIN TEST X SCORES IN TEST Y A 15 60 B 25 70 C 20 40 D 30 50 E 35 30
- 15. INDIVIDUAL SCORES I N TEST X SCORES I N TEST Y XY X² Y² A 15 60 B 25 70 C 20 40 D 30 50 E 35 30 N= ƩX= ƩY= ƩX Y= ƩX²= ƩY²=
- 16. INDIVIDUAL SCORES INTEST X SCORES INTEST 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
- 19. Pearson's correlation coefficient = -0.5
- 20. How to evaluate a correlation • The values of ‘r’ always fall between -1 and +1 and the value does not change if all values of either variable are converted to a different scale. • For eg. If the weights of the students were given in pounds instead of kilograms , the value of ‘r’ would not change.
- 21. Advantages of pearson's correlation coefficient 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.
- 22. Limitations of pearson's correlation coefficient 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.
- 23. Thank you