ABSTRACT
Many research studies in different fields involve simultaneous study of two or more variables. The purpose of such studies is to investigate the rela tionships among the variables. In relationship studies, observations are re corded either in pairs, triples, or more as they exist naturally in the environ ment. Although recording observations, no attempt is made either to control or manipulate the variables. The most important factor in correlation stud ies is covariation. Covariation refers to change in one variable accompanied by a corresponding change in another variable, i.e., how the two variables simultaneously covary. When our study involves only two variables, it is called simple correlation or simple linear correlation. If our study relates to more than two variables, it is called a multiple correlation study. In this chapter, we concentrate on the relationship between two variables. In corre lation studies, our interest is on the strength of the relationship between the variables, i.e., how well the variables are correlated. Correlation is therefore a statistical technique that is used to measure and describe the relationship between two variables. It plays an important role in agriculture, medicine, industry, education, biology, social sciences, and many other areas. A few examples will illustrate the importance and usefulness of correlation stud ies in several areas:
1. Air pressure and altitude (A decrease in air pressure occurs as the al titude increases, and they show a negative relationship.)
2. Rainfall and rise of water levels (When rainfall increases, the water level in dams and rivers increases. Increase in one variable [rainfall] is relative to the increase in another variable [water level). These two variables are said to be positively correlated.)
3. Grades and class attendance of the students in a class 4. Time and population 5. Age and blood pressure 6. Ages of husbands and wives 7. Rainfall and agricultural production 8. Age and insurance premium paid
9. Amount of fertilizer used and amount of crop production 10. Tree trunk diameter and height 11. Diet and body weight 12. Temperature and sale of cool drinks 13. Age of car and number of miles driven 14. The number of miles the car is driven and the resale value 15. Sale proceeds and amount spent on advertising 16. Incidence of cancer and smoking habits 17. Smoking and incidence of heart attack 18. Blood pressure and weight loss 19. Age and pulse rate 20. Amount of fluoride concentration in drinking water and prevalence
of tooth decay among children
Some examples where no correlation is found:
1. Number of human births and fertilizer sales 2. Number of books in libraries and car accidents 3. Grade point averages of students and the number of patients in hospi
tals 4. Number of births in India and rainfall in the United States
METHODS OF STUDYING CORRELATION
The most important methods of displaying and studying correlation are described as follows:
1. Scatter diagram 2. Coefficient of correlation 3. Coefficient of rank correlation 4. Regression line 5. Intraclass correlation
Scatter Diagram
In a scatter diagram the data take the form of paired values of two vari ables such as y and x o r ^ and x2, etc. Each pair is represented in a graph by a dot (v, y). Thus the data plotted in the graph give the scatter diagram.
