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BPCC 104- Block-3 - This is about Psychology or Tarot and it's notes as per the subject code and
B A Honours Psychology (BAPCH1)
Indira Gandhi National Open University
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PsychologyPreview text
Computation of Measures of Variability
BLOCK 3
CORRELATION
Measures of Central Tendency and Variability
BLOCK INTRODUCTION
Block 3 of this course mainly focuses on the topic correlation. The block has been divided in to two units unit 6 and unit 7. Unit six focuses on the theoretical information about correlation, including the concept, direction and magnitude of correlation. Properties, uses and limitations of correlation will also be covered. Unit seven , on the other hand, deals with the computation of correlation where you will learn to compute correlation with the help of Pearsonís product moment correlation and Spearmanís rank order correlation.
Correlation adolescents. Or a researcher may be interested in finding out if there exists any relationship between psychological wellbeing and job satisfaction of employees in an organisation. In such cases, correlation will help the researcher study the relationship and also understand its direction and magnitude.
In research studying relationship between two or more variables could be an important objective and this can be studied with the help of correlation.
In the present unit, we will focus on the concept of correlation, its direction and magnitude. The properties, uses and limitations of correlation will also be covered besides other methods of correlation.
6 CONCEPT OF CORRELATION, DIRECTION
AND MAGNITUDE OF CORRELATION
Let us take another example, to understand the concept of correlation.
A research was carried out by a researcher on relationship between years of experience and monthly income earned by junior managers in an organisation (hypothetical data). The data given is as follows:
Table 6: Years of experience and monthly income of junior managers Junior Managers Years of Experience Monthly income John 1 25, 000 Ravi 2 30, 000 Maria 3 35, 000 Kuldeep 4 40, 000 Salma 5 45, 000
Looking at this data, what do you understand? You may notice that as the years of experience is increasing, the monthly income earned by the junior managers is also increasing. Thus, it can be inferred that in case of these junior managers, there is a positive relationship between the years of experience and the monthly income.
Let us take another example,
An experimenter was carrying out a study on relationship between hours of practice in a certain task and number of errors committed by the participants. The data obtained from the same is given as follows:
Table 6: Hours of practice in certain task and number of errors Participants Hours of Practice Number of errors Rehman 4 20 Sophia 5 12 Navjyot 7 8 Anjali 1 30 Rahul 2 24
Correlation : An Introduction
As we look at this data, it can be seen that as the hours of practice is increasing, the number of errors committed by the participants is decreasing. Thus, it can be said that there is a negative relationship between hours of practice and number of errors committed.
With the above examples, you must have developed some idea about what is correlation. Let us now look at the concept of correlation and also focus on its direction and magnitude.
Correlations can be used to study relationship between two or more variables. It is a measure of association between two or more variables and this relationship is determined not only in terms of direction, whether negative or positive but also in terms of its magnitude, whether high or low. However, it will not provide information about any causal relationship between the variables.
Sir Francis Galtonís contribution to development of correlation is noteworthy. He carried out studies on individual differences and also studies on the influence of heredity. He studied the association between the height of parents and that of their children with the help of bivariate distribution (that studies relationship between two variables) and found that the parents who are tall have children who are also tall (Veeraraghavan and Shetgovekar, 2016). Further, in 1986, Karl Pearson put forth mathematical procedure for correlation.
Correlation can be categorised in to linear and nonlinear correlation. These are discussed as follows:
Linear Correlation: Linear correlation is denoted by a single straight line in a graph that denotes linear relationship between given two variables. Such a graph indicates whether increase in one variable leads to increase in another variable and vice versa, or decrease in one variable leads to increase in another variable and vice versa. For example, if the scores on emotional intelligence increase or decrease, the scores on self esteem also increase or decrease. Linear relationship is graphically represented in figure 6.
Nonlinear correlation: As opposed to linear relationship, in nonlinear relationship. The relationship between two given variables is not denoted by a straight line. Thus, the relationship is curvilinear as denoted in figure 6.
Fig. 6: Linear Correlation
Variable A
Variable B
Correlation : An Introduction
Fig. 6: Negative Correlation
No Correlation or Zero Correlation: It may so happen that there is no relationship between the two variables. In such a case the correlation will be zero (this will be further clear as we discuss the magnitude of correlation). Thus, in this case the relationship is neither positive or negative. There are such variables where there might be no relationship, for example, there may be no correlationship between height of persons and years of their work experience or there may exist no relationship between weight of persons and attitude towards environment. No correlation is represented in form of scatter diagram in figure 6.
Fig. 6: No or Zero Correlation
Besides the direction of the correlation, it is also significant to understand the magnitude or strength of the correlation. Magnitude is denoted by the degree of linearity of the correlationship. Correlationship between any two variables is Coefficient of Correlation that is quantitatively represented. And the range for a coefficient of correlation is between -1 to +1. Thus, coefficient of correlation can be obtained as 0 or -0 or 0 and so on. The number will lie between -1 to +1 and the + and - signs denote the direction of correlation, whether it is positive or negative. The obtained coefficient of correlation can be interpreted with the help of the table 6 given as follows (Mangal, 2002, page 105):
Variable A
Variable B
Variable A
Variable B
Correlation Table 6: Interpretation of Coefficient of Correlation Coefficient of Correlation Range
Interpretation
+ 1 or - 1 This can be interpreted as a correlation that is perfect, though the direction could be positive or negative. + 0 to 0 Correlation is very high + 0 to 0 Correlation is high + 0 to 0 Correlation is moderate + 0 to 0 Correlation is low 0 to + 0 Correlation is negligible 0 No correlation
While interpreting coefficient of correlation it is important to keep in mind the direction based on the positive and negative signs.
6.2 Scatter Diagram
One way in which relationship between two variables can be denoted is by using scatter diagram. Scatter diagram is also called as scatter plot or scatter gram. It is drawn by plotting the two variables in same graph, that is variable A on y axis and variable B on x axis (as shown in figures 6, 6 and 6).
Table 6: Marks obtained by students in Psychology and Sociology class test Students Marks in Psychology Marks in Sociology Peter 25 26 Sarika 45 42 Kamaldeep 78 73 Salman 5 4 Arvind 89 84
For example, we want to study the relationship between marks obtained by five students in Psychology and in Sociology in class test. The data is given in table 6.
Fig. 6: Scatter diagram based on table 6.
0
23
45
68
90
() 22 45. 67 90. 112.
Marks in Psychology
Marks in Sociology
Correlation reliability of a psychological test. Validity is whether a test is measuring what it is supposed to measure and reliability provides information about consistency of a test.
Verification of theory: Correlation can also be used to verify or test certain theories by denoting whether relationship exists between the variables. For example, if a theory states that there is a relationship between parenting style and resilience, the same can be tested by computing correlation for the two variables.
Putting variables in groups: Variables that show positive correlation with each other can be grouped together and variables that show negative correlation can be grouped separately based on the coefficient of correlation obtained.
Computation of further statistical analysis: Based on the results obtained after computing correlation, various statistical techniques can be used like regression. Further, correlation is also used for multivariate statistical analysis, especially for techniques like Multivariate Analysis of Variance (MANOVA), Multivariate Analysis of Covariance (MANCOVA), Discriminant Analysis, Factor analysis and so on (Mohanty and Misra, 2016).
Based on correlation, one can decide whether or not to determine prediction: By computing correlation, it is not possible to predict one variable based on another variable, but based on the information that two or more variables are significantly related to each other, further statistical techniques can be used to make predictions. For example, if we obtain a positive correlation between family environment and adjustment of children, then further statistical techniques can be employed to find if adjustment of children can be predicted based on family environment.
6.3 Limitations of Correlation
Some of the limitations of correlation have been discussed as follows:
As was stated earlier, correlation will not provide any information about cause and effect relationship or causation.
The coefficient of correlation, mainly, Pearsonís product moment correlation and Spearmanís rank order correlation are suitable, when there is a linear relationship between the variables.
With regard to distributions that are discontinuous, the coefficient of correlation obtained may be overestimated or higher.
Sample variations can have an effect on correlation (as is also true with other statistical techniques).
In case of pooled sample, the correlation will be determined by relative position of the scores in X and Y dimensions or variables.
Correlation : An Introduction
Check Your Progress II
- List the uses of Correlation.
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6 OTHER METHODS OF CORRELATION
There are various other methods of correlation as well, that will be discussed in the present section of this unit.
Partial Correlation: In partial correlation, the relationship between two variables is studied by controlling the influence of a third variable. For example, if we are studying the relationship between emotional intelligence and self concept of adolescents, we may partial out or control the third variable, for instance, family environment.
Part Correlation: This is also called as Semipartial Correlation. This is in a way similar to partial correlation, but here as the correlationship between two variables is studied, the influence of third variable on one of the variables is controlled. Taking the example discussed under partial correlation, the influence of family environment only on emotional intelligence is controlled and not on self concept.
Multiple correlation: In multiple correlation, one variable is correlated with many other variables. For example, self concept will be correlated with various other variables like emotional intelligence, achievement motivation, quality of life and so on.
Biserial Correlation: In biserial correlation, the relationship is measured between a continuous variable and an artificially dichotomous variable. A dichotomous variable is a variable that can be categorised into two. For example, Socio-Economic Status could be high and low. An example of biserial correlation would be relationship between achievement motivation and high and low emotional intelligence. Here, achievement motivation is a continuous variable and emotional intelligence is a variable that is artificially dichotomous.
Point-Biserial Correlation: In point biserial correlation, the relationship is measured between a continuous variable and a naturally dichotomous variable. Examples of naturally dichotomous variables are gender (male and female), religion (Hindu and Muslim) and so on. For example, point biserial correlation can be used when we want to find out relationship between work motivation (continuous variable) and gender (naturally dichotomous variable).
Tetrachoric Correlation: When both the variables are artificially dichotomous, then tetrachoric correlation can be computed to study the relationship between the two variables. For example, tetrachoric
Correlation : An Introduction Biserial Correlation
Point-Biserial
Tetrachoric Correlation
Phi Coefficient
Correlation
6 LET US SUM UP
In the present unit, we mainly discussed about the concept of correlation. Correlation can be used to study relationship between two or more variables. It is a measure of association between two or more variables and this relationship is determined not only in terms of direction, whether negative or positive, but also in terms of its magnitude, whether high or low. Correlation can be categorised in to linear and nonlinear correlation and these were discussed in the present unit with the help of figures. The concept of scatter diagram was also briefly discussed in this unit. Scatter diagram is also called as scatter plot or scatter gram and is drawn by plotting the two variables in same graph, that is, variable A on y axis and variable B on x axis. Further in the unit, we also discussed about the properties, uses and limitations of correlation that are relevant, so as to know when exactly to use correlation. In the last section of this unit, we focused on the other methods of correlation including partial correlation, part correlation, multiple correlation, biserial correlation, point biserial correlation, tetrachoric correlation and phi- coefficient. In the next unit, we will learn how to compute coefficient of correlation with the help of Pearsonís product moment correlation and Spearmanís rank order correlation.
6 KEY WORDS
Biserial Correlation: In biserial correlation, the relationship is measured between a continuous variable and an artificially dichotomous variable.
Correlation: It is a measure of association between two or more variables and this relationship is determined not only in terms of direction, whether negative or positive.
Linear Correlation: Linear correlation is denoted by a single straight line in a graph that denotes linear relationship between given two variables.
Multiple correlation: In multiple correlation, one variable is correlated with many other variables.
Nonlinear correlation: Here the relationship is not denoted by a straight line but it is curvilinear.
Negative Correlation: The negative correlation denotes that increase in one variable leads to decrease in another variable or decrease in one variable leads to increase in another variable.
No Correlation or Zero Correlation: When there is no relationship between the two variables, the correlation will be zero. Thus in this case the relationship is neither positive or negative.
Part Correlation: This is also called as Semipartial Correlation. Here as the relationship between two variables is studied, the influence of third variable on one of the variables is controlled.
Partial Correlation: In partial correlation, the relationship between two variables is studied by controlling the influence of a third variable.
Point-Biserial Correlation: In point biserial correlation, the relationship is measured between a continuous variable and naturally dichotomous variable.
Correlation Check Your Progress III
Give a brief description and nature of variables 1 and 2 for other methods of correlation
Method of Correlation
Description Variable 1 Variable 2
Partial Correlation
The correlationship between two variables is studied by controlling the influence of a third variable.
Variable is continuous in nature
Variable is continuous in nature
Part Correlation The correlationship between two variables is studied, the influence of third variable on one of the variables is controlled
Variable is continuous in nature
Variable is continuous in nature
Multiple Correlation
Variable is continuous in nature
Variable is continuous in nature
Biserial Correlation
The correlationship is measured between a continuous variable and an artificially dichotomous variable.
Variable is continuous in nature
Variable is artificially dichotomous
Point-Biserial The correlationship is measured between a continuous variable and naturally dichotomous variable
Variable is continuous in nature
Variable is naturally dichotomous
Tetrachoric Correlation
It is used when both the variables are artificially dichotomous
Variable is artificially dichotomous
Variable is artificially dichotomous
Phi Coefficient It is used when both the variables are naturally dichotomous
Variable is naturally dichotomous
Variable is naturally dichotomous
One variable is correlated with many other variables (continuous).
Correlation : An Introduction
6 UNIT END QUESTIONS
Explain the concept of correlation with a focus on its direction and magnitude.
Discuss linear and nonlinear correlation with the help of diagrams.
Describe the properties of correlation.
Explain the uses and limitations of correlation.
Describe other methods of correlation.
Computation of Coefficient of Correlation
Table 7: Difference between Parametric and Nonparametric statistics Parametric Non-parametric The assumed distribution is normal.
The assumed distribution may not be normal. It can be any distribution. The variance is homogeneous.
The variance could be heterogeneous or no assumption is made with regard to the variance. The scales of measurement used are interval or ratio.
The scales of measurement used are nominal or ordinal. The relationship between the data needs to be independent.
There is no assumption with regard to the independence of relationship between the data. Mean is the measure of central tendency that is used here.
Median is the measure of central tendency that is used here.
It is more complex to compute when compared to the non parametric techniques.
It is simple to calculate.
Can get affected by outliers. Is comparatively less affected by outliers.
In the next section, we will learn how to compute Pearsonís product moment correlation.
7 PEARSONíS PRODUCT MOMENT
CORRELATION
Pearsonís product moment correlation is one of the methods to compute coefficient of correlation. This is mainly used when the assumptions of parametric statistics are met. This method is named after Karl Pearson, who invented this method. It is denoted by ërí.
7.2 Assumptions of Pearsonís Product Moment Correlation
The assumptions of Pearsonís product moment correlation are as follows:
The variables used to compute ërí are continuous in nature and the scales of measurement are interval and ratio.
The distribution of the variables in this method is unimodal and it is close to symmetrical. The distribution need not be normal.
The pairs of scores involved are independent in nature and are in no way connected with other.
There is a linear relationship between the two variables. A scatter gram thus drawn with the help of scores in the two variables, will denote a straight line.
ërí is mainly used to ascertain the sign and size of the correlation that can be positive, negative or zero correlation and will range between -1 to +1.
Correlation
7.2 Uses of Pearsonís Product Moment Correlation
It helps in determining the relationship between two variables quantitatively. With quantification, it is possible for us to compare.
Based on ërí, regression equation can be computed. Thus, after computing ërí, it is possible to compute regression and determine whether one variable can be predicted based on another variable.
ërí can be used in computation of reliability and validity of psychological tests.
It will also assist in computation of factor analysis.
7.2 Computation of Pearsonís Product Moment Correlation
There are two main methods that we will discuss for computing Pearsonís product moment correlation. They are discussed as follows:
Method 1: The formula for the first method is give below,
rxy = Σxy/ N σxσy
Where,
r = Correlation
x = Deviation of any score of X from the mean of X
y = Deviation of any score of Y from the mean of Y
Σxy = Indicates the sum of all the products of deviation (that is, each x deviation is multiplied by its corresponding y deviation)
σx = Standard deviation of scores in X
σy= Standard deviation of scores in Y
N = Total number of participants (frequencies)
The formula can be simplified as follows
σx = √ Σx 2 / N
σy = √ Σy 2 / N
Thus, by substituting the values for σx and σy, the following is obtained :
r = Σxy/ N √ Σx 2 / N √ Σy 2 / N
= Σxy/ √ Σx 2 Σy 2
Let us understand this method and steps involved in it, with the help of an example,
A researcher wanted to study the relationship between data 1 (X) and data 2 (Y). The data is given below:
BPCC 104- Block-3 - This is about Psychology or Tarot and it's notes as per the subject code and
Course: B A Honours Psychology (BAPCH1)
University: Indira Gandhi National Open University
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