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The study material in the form of ppt covers the topic of Co-relation.

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If the line passing through the pair of values of https://testmyspeed.onl/ variables x and y is curvilinear, then such a relationship is called non linear.

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Slide 1 : JSS MAHAVIDYAPEETHA. A DEGREE A HIGHER PURPOSE.

Correlation Analysis : Correlation Analysis By Ms. Shilpa Bahl Assistant Professor JSSATE, Noida

Meaning of Correlation : Meaning of Correlation To analyze the strength of the relationship or co variation between two variables is called correlation. Correlation  is a bivariate analysis that measures the strengths of association between two variables.  In statistics, the value of the correlation coefficient varies between +1 and -1.  When the value of the correlation coefficient lies around ± 1, then it is said to be a perfect degree of association between the two variables.  As the correlation coefficient value goes towards 0, the relationship between the two variables will be weaker.

Definition of Correlation : Definition of Correlation When the relationship is of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing in brief formula is known as correlation. - Croxton and Cowden

Types of correlation : Types of correlation Positive and negative correlation Linear and non- linear correlation Simple, partial and multiple correlation

Positive and negative correlation : Positive and negative correlation Positive correlation Increasing x: 5 8 10 15 17 Decreasing y: 5 8 10 15 17 Negative correlation Increasing x: 5 8 10 15 17 Decreasing y: 20 18 16 12 10

Linear and non- linear correlation : Linear and non- linear correlation Linear correlation x : 10 20 30 40 50 y : 40 60 80 100 120 Non linear correlation x : 8 9 9 10 10 28 29 30 y : 80 130 170 150 230 560 460 600

Simple, partial and multiple correlation : Simple, partial and multiple correlation Simple correlation: only two variables are chosen to study. Partial correlation: two variables with the effect of other influencing variable. Multiple correlation: relationship between more than three variables.

Methods of correlation analysis : Methods of correlation analysis Scatter diagram method Karl pearson’s coefficient of correlation Spearman’s rank correlation method Method of least squares

Scatter diagram method : Scatter diagram method

Karl pearson’s coefficient of correlation : Karl pearson’s coefficient of correlation Actual mean method r = x = X- y = Y –

Direct Method : Direct Method

Example : Example Subject Age (x) Weight level (y) xy X 2 y 2 1 43 99 4257 1849 9801 2 21 65 1365 441 4225 3 25 79 1975 625 6241 4 42 75 3150 1764 5625 5 57 87 4959 3249 7569 6 59 81 4779 3481 6561 ∑ 247 486 20485 11409 40022

Slide 14 : Put the data in the formula Then r = 48.41

Assumptions : Assumptions When both variables x and y are measured on an interval or a ratio scale. Variables x and y are normally distributed and there is a linear relationship between these variables. There should be a cause and effect relationship between two variables.

Advantages and disadvantages : Advantages and disadvantages It always assumes a linear relationship between two variables The value of coefficient is unduly affected by the extreme values of two variables value. It is lengthy process.

Probable error and standard error : Probable error and standard error The probable error (PE) of coefficient of correlation indicates extent to which its value depends on the condition of random sampling. If r < 6PE, r is taken to be insignificant If r > 6PE , r is taken to be significant

Example : Example r = 0.8 and n = 25, then PE, is PE = 0.048 Thus the limits within which population correlation coefficient (p r ) should fall are 0.752 ≤ p r ≤ 0.848

Spearman’s rank correlation : Spearman’s rank correlation This method is applied in a situation in which quantitative measure of certain qualitative factors such as judgment, leadership, color, taste cannot be fixed but individual observation can be arranged in a definite order (also called rank).

Types : Types When ranks are given When ranks are not given When ranks are equal

Advantages and disadvantages : Advantages and disadvantages Advantages Easy to understand Useful when variables are expressed in qualitative terms. Appropriate when both variables are measured on a ratio scale. Disadvantages A large computational time is required Cannot be applied on a bivariate group data of correlation analysis.

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