Zeeshan Asghar : Zeeshan Asghar 08021220-025 Correlation : Correlation Correlation can be easily understood as co relation. To define. correlation is the average relationship between two or more variables. When the change in one variable makes or causes a change in other variable then there is a correlation between these two variables.These correlated variables can move in the same direction or they can move in opposite direction. Not always there is a cause and effect relationship between the variables when there is a change; that might be due to uncertain change.Simple Correlation is a correlation between two variables only; meaning the relationship between two variables. Event correlation and simple event correlation are the types of correlations mainly used in the industry point of view. CorrelationCont.. : CorrelationCont.. Formula Correlation Example : Correlation Example Let's assume that we want to look at the relationship between two variables, height (in inches) and self esteem. Perhaps we have a hypothesis that how tall you are effects your self esteem (incidentally, I don't think we have to worry about the direction of causality here -- it's not likely that self esteem causes your height!). Let's say we collect some information on twenty individuals (all male -- we know that the average height differs for males and females so, to keep this example simple we'll just use males). Height is measured in inches. Self esteem is measured based on the average of 10 1-to-5 rating items (where higher scores mean higher self esteem). Here's the data for the 20 cases (don't take this too seriously -- I made this data up to illustrate what a correlation is): Correlation ExampleCONT.. : Correlation ExampleCONT.. Histogram for each variable : Histogram for each variable CONT.. : CONT.. Calculating the Correlation : Calculating the Correlation CONT.. : CONT.. CONT.. : CONT.. The first three columns are the same as in the table above. The next three columns are simple computations based on the height and self esteem data. The bottom row consists of the sum of each column. This is all the information we need to compute the correlation. Here are the values from the bottom row of the table (where N is 20 people) as they are related to the symbols in the formula Cont.. : Cont.. Now, when we plug these values into the formula given above, we get the following (I show it here tediously, one step at a time) Types of Correlation : Types of Correlation In Research Methodology of the Management, Correlation is broadly classified into six types as follows :(1) Positive Correlation(2) Negative Correlation(3) Perfectly Positive Correlation(4) Perfectly Negative Correlation(5) Zero Correlation(6) Linear Correlation Sufyan Ahmed : Sufyan Ahmed 08021220-040 Positive Correlation : Positive Correlation When two variables move in the same direction then the correlation between these two variables is said to be Positive Correlation.When the value of one variable increases, the value of other value also increases at the same rate.For example the training and performance of employees in a company. Positive Corelation : Positive Corelation Negative Correlation : Negative Correlation In this type of correlation, the two variables move in the opposite direction. When the value of a variable increases, the value of the other variable decreases.For example, the relationship between price and demand. Negative Correlation : Negative Correlation Perfect Positive Correlation : Perfect Positive Correlation When there is a change in one variable, and if there is equal proportion of change in the other variable say Y in the same direction, then these two variables are said to have a Perfect Positive Correlation. Perfect Positive Correlation : Perfect Positive Correlation Perfectly Negative Correlation : Perfectly Negative Correlation Between two variables X and Y, if the change in X causes the same amount of change in Y in equal proportion but in opposite direction, then this correlation is called as Perfectly Negative Correlation. Perfectly Negative Correlation : Perfectly Negative Correlation Zero Correlation : Zero Correlation When the two variables are independent and the change in one variable has no effect in other variable,then the correlation between these two variable is known as Zero Correlation. Zero Correlation : Zero Correlation Linear Correlation : Linear Correlation If the quantum of change in one variable has a ratio of change in the quantum of change in the other variable then it is known as Linear correlation. Linear Correlation : Linear Correlation Syed Ali Raza : Syed Ali Raza 08021220-026 It is designed to range in value between 0.0 and 1.0 : It is designed to range in value between 0.0 and 1.0 Degrees : Degrees Methods Of Determining Correlation : Methods Of Determining Correlation We shall consider the following most commonly used methods.
(1) Scatter Plot
(2) Kar Pearson’s coefficient of correlation
(3) Spearman’s Rank-correlation coefficient. M.owais : M.owais 08021220-023 Scatter Plot ( Scatter diagram or dot diagram ): : Scatter Plot ( Scatter diagram or dot diagram ): In this method the values of the two variables are plotted on a graph paper. One is taken along the horizontal ( (x-axis) and the other along the vertical (y-axis). By plotting the data, we get points (dots) on the graph which are generally scattered and hence the name ‘Scatter Plot’. Scatter Plot cont.. : Scatter Plot cont.. i) If all points lie on a rising straight line the correlation is perfectly positive and r = +1 (see fig.1 )
ii) If all points lie on a falling straight line the correlation is perfectly negative and r = -1 (see fig.2)
iii) If the points lie in narrow strip, rising upwards, the correlation is high degree of positive (see fig.3)
iv) If the points lie in a narrow strip, falling downwards, the correlation is high degree of negative (see fig.4)
v) If the points are spread widely over a broad strip, rising upwards, the correlation is low degree positive (see fig.5)
vi) If the points are spread widely over a broad strip, falling downward, the correlation is low degree negative (see fig.6)
vii) If the points are spread (scattered) without any specific pattern, the correlation is absent. i.e. r = 0. (see fig.7) Waqas Qamar : Waqas Qamar 08021220-008 Karl Pearson’s : Karl Pearson’s 2) Karl Pearson’s coefficient of correlation: It gives the numerical expression for the measure of correlation. it is noted by ‘ r ’. The value of ‘ r ’ gives the magnitude of correlation and sign denotes its direction. It is defined as
r = Spearman’s Rank Correlation Coefficient : Spearman’s Rank Correlation Coefficient This method is based on the ranks of the items rather than on their actual values. The advantage of this method over the others in that it can be used even when the actual values of items are unknown. For example if you want to know the correlation between honesty and wisdom of the boys of your class, you can use this method by giving ranks to the boys. It can also be used to find the degree of agreements between the judgements of two examiners or two judges. Spearman’s Rank Correlation Coefficientcont.. : Spearman’s Rank Correlation Coefficientcont.. The formula is :
where R = Rank correlation coefficient
D = Difference between the ranks of two items
N = The number of observations.