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CORRELATION AS TOOL IN DETERMINING VALIDITY AND RELIABILITY OF TEST. earning Outcome: All must have computed correlation coefficient of two data sets. Interpreted the result. 2. identified example of negative and positive correlation 3. recognized range for possible correlation. Read and answer activity 1 below. After 1 hour we will check your answer. Definition: Correlation is a statistical measurement of the relationship between two variables. Possible correlations range from +1 to -1. A zero correlation indicates that there is no relationship between the variables. A correlation of -1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down. A correlation of +1 indicates a perfect positive correlation, meaning that both variables move in the same direction together. Purpose The correlation is a way to measure how associated or related two variables are. The researcher looks at things that already exist and determines if and in what way those things are related to each other. The purpose of doing correlations is to allow us to make a prediction about one variable based on what we know about another variable. For example, there is a correlation between income and education. We find that people with higher income have more years of education. (You can also phrase it that people with more years of education have higher income.) When we know there is a correlation between two variables, we can make a prediction. If we know a group's income, we can predict their years of education. Direction There are two types or directions of correlation. In other words, there are two patterns that correlations can follow. These are called positive correlation and negative correlation. Remember that in a correlational study, the researcher is measuring conditions that already exist. She or he is asking questions of a sample of participants, and finding out in what way pairs of variables are related. For example, a researcher could ask about the participants' yearly income and years of education, to see if those two attributes are correlatedPositive correlation In a positive correlation, as the values of one of the variables increase, the values of the second variable also increase. Likewise, as the value of one of the variables decreases, the value of the other variable also decreases. The example above of income and education is a positive correlation. People with higher incomes also tend to have more years of education. People with fewer years of education tend to have lower income. Here are some examples of positive correlations: 1. SAT scores and college achievement-among college students, those with higher SAT scores also have higher grades 2. Happiness and helpfulness-as people's happiness level increases, so does their helpfulness (conversely, as people's happiness level decreases, so does their helpfulness) This table shows some sample data. Each person reported income and years of education. Participant No. Income Years of Education 125,000 19 100,000 20 40,000 16 35,000 16 41,000 18 29,000 12 35,000 14 24,000 12 9 50,000 16 10 60,000 17 In this sample, the correlation is .79.We can make a graph, which is called a scatterplot. On the scatterplot below, each point represents one person's answers to questions about income and education. The line is the best fit to those points. All positive correlations have a scatterplot that looks like this. The line will always go in that direction if the correlation is positive. 22 20 18 14.- Years of education 12 10 20000 BOOOO 100000 1 10000 Income Negative correlation In a negative correlation, as the values of one of the variables increase, the values of the second variable decrease. Likewise, as the value of one of the variables decreases, the value of the other variable increases. This is still a correlation. It is like an "inverse" correlation. The word "negative" is a label that shows the direction of the correlation. There is a negative correlation between TV viewing and class grades-students who spend more time watching TV tend to have lower grades (or phrased as students with higher grades tend to spend less time watching TV). Here are some other examples of negative correlations: 1. Education and years in jail-people who have more years of education tend to have fewer years in jail (or phrased as people with more years in jail tend to have fewer years of education) 2. Crying and being held-among babies, those who are held more tend to cry less (or phrased as babies who are held less tend to cry more)We can also plot the grades and TV viewing data, shown in the table below. The scatterplot below shows the sample data from the table. The line on the scatterplot shows what a negative correlation looks like. Any negative correlation will have a line with that direction. Participant No. GPA TV in hours per week 1 3.1 14 2 2.4 10 3 2.0 20 4 3.8 7 5 2.2 25 3.4 9 2.9 15 8 3.2 13 9 3.7 4 10 3.5 21 In this sample, the correlation is -.63. 30 20 20 Hours per week of Ty 10 20 2.5 3.0 3.5 4.0 SPAStrength Correlations, whether positive or negative, range in their strength from weak to strong. Positive correlations will be reported as a number between 0 and 1. A score of 0 means that there is no correlation (the weakest measure). A score of 1 is a perfect positive correlation, which does not really happen in the "real world." As the correlation score gets closer to 1, it is getting stronger. So, a correlation of .8 is stronger than .6; but .6 is stronger than .3. The correlation of the sample data above (income and years of education) is .79. Negative correlations will be reported as a number between 0 and -1. Again, a 0 means no correlation at all. A score of -1 is a perfect negative correlation, which does not really happen. As the correlation score gets close to -1, it is getting stronger. So, a correlation of -.7 is stronger than -.5; but -.5 is stronger than -.2. Remember that the negative sign does not indicate anything about strength. It is a symbol to tell you that the correlation is negative in direction. When judging the strength of a correlation, just look at the number and ignore the sign. The correlation of the sample data above (TV viewing and GPA) is -.63. Imagine reading four correlational studies with the following scores. You want to decide which study had the strongest results: -.3 -.8 4 .7 In this example, -,8 is the strongest correlation. The negative sign means that its direction is negative. Advantage 1. An advantage of the correlation method is that we can make predictions about things when we know about correlations. If two variables are correlated, we can predict one based on the other. For example, we know that SAT scores and college achievement are positively correlated. So when college admission officials want to predict who is likely to succeed at their schools, they will choose students with high SAT scores. We know that years of education and years of jail time are negatively correlated. Prison officials can predict that people who have spent more years in jail will need remedial education, not college classes. Disadvantage 1. The problem that most students have with the correlation method is remembering that correlation does not measure cause. Take a minute and chant to yourself: Correlation is not Causation! Correlation is not Causation! I always have my in-class students chant this, yet some still forget this very crucial principle. We know that education and income are positively correlated. We do not know if one caused the other. It might be that having more education causes a person to earn a higher income. It might be that having a higher income allows a person to go to school more. It might also be some third variable. A correlation tells us that the two variables are related, but we cannot say anything about whether one caused the other. This method does not allow us to come to any conclusions about cause and effect.Interpretation of Coefficient of Correlation R Descriptive level 1,0 Perfect Correlation Between 0.75 to 0.99 High Correlation Between 0.51 to 0.74 Moderately high Correlation Between 0.31 to 0.50 Moderately low Correlation Between 0.01 to 0.30 Low Correlation 0.00 No correlation 1. Pearson Product- Moment Coefficient of Correlation The most commonly used measure of correlation is the Pearson Product- Moment coefficient of correlation, It is denoted by a small letter r. The formula is as follows: , r = coefficient of correlation , x= the first set of test scores Y= the second set of test scores , n= total number of pairs of scores Example 1. Calculate the coefficient of correlation using Pearson Product- Moment of the two sets of test scores in Algebra and Geometry of ten ( 10) students. Subject Scores Algebra 18 15 13 16 13 10 13 15 10 14 Geometry 19 17 14 15 14 11 12 14 13 17Solutions: Algebra (x) Geometry (y) 18 19 342 324 361 15 17 255 225 289 13 14 182 169 196 16 15 240 256 225 13 14 182 169 196 10 11 110 100 121 13 12 156 169 144 15 14 210 225 196 10 13 130 100 169 14 17 238 196 289 =137 146 2045 1933 2186 The value of the Pearson Product- Moment Coefficient of Correlation is positive ( 0.81) , which implies that there is a high correlation between algebra and Geometry scores. This means that when the scores in algebra are increased ( or decreased) then the scores in GeometryThe value of the Pearson Product- Moment Coefficient of Correlation is positive ( 0.81) , which implies that there is a high correlation between algebra and Geometry scores. This means that when the scores in algebra are increased ( or decreased) then the scores in Geometry are also increased( or decreased). 2. Spearman Rank Difference Coefficient of Correlation The spearman's rank- difference coefficient of correlation is applicable when the set of scores is in terms of rank- order rather than in terms of a continuous interval scale, and when the set of scores is small. This technique may also be applied even if numerical values in form of scores are available; ranks may be preferred as they are found to be necessary under certain conditions. In actual studies, when pairs of test scores are less than 25 , it is often advisable to ranks these scores and to compute the strength of their relationship by using spearman Rank- Difference method instead of computing the Pearson Product -Moment Coefficient of Correlation. The rank- difference coefficient of correlation is called rho, which is written as in symbol. The formula is given below. , D is the difference between ratings of first and second score , n is total number of pairs. Example 2. Is there any degree of correlation in the ranks of the contestants given or assigned by two members of the board of judges in a duet contest? Contestan First Second Judge judge wUN DO On W H 4IGTM CO O W H Solution: Contestan First Second D Judge judge Innmono Total The value of the Spearmen Ran- Difference Coefficient of Correlation is 0.90, which indicates a high positive correlation between two sets of ranks given by two judges