DESCRIBING RELATIONSHIP

Correlation – another statistical method used in analyzing test results.  This is the tool that we are going to utilize if we want to determine the relationship or the association between scores of students in two different subjects. It refers to the extent to which the distribution are linearly related or associated between two variables.

Coefficient Correlation – extent of correlation is indicated numerically. The Coefficient Correlation (r_xy) also known as the Pearson Product Moment Correlation Coefficient in honor to Karl Pearson who developed the said formula.

          2 ways in identifying correlation between variables:

1.   Using the formula;

2.   Using the scatter point or scattergram.

Kinds of Correlation:

1.   Positive Correlation – high scores in distribution x are associated with high scores in distribution y. This means that as the value of x increases the value of y too increases or as the value of x decreases, the y values will also decrease.

2.   Negative correlation –high cores in distribution x are associated with low scores in distribution y. Low scores in high distribution x are associated with high scores in in distribution y. This means that as the value of x increases, the value of y decrease or when the values of x decrease, the value of y increase.

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3.   Zero Correlation – no association between scores in distribution x and in scores in distribution y. No single can be drawn that best fitted to all points as shown in the scattergram of zero correlation.

Pearson Product Moment Correlation:

R_xy=     (n) (Σxy) –(Σx)(Σy) 

     [(n)( Σx²) - (Σx)²] [(n)(Σy²) – (Σy)²]

Graph:

Scattergram of Correlation

Scattergram of Positive Correlation

 

 Scattergram of Negative Correlation

Scattergram of Zero Correlation

     Computation of Correlation Coeffecient Using Pearson r:

Analysis:

          The value of the correlation coefficient is r_xy = 0.93, which means that there is a very high positive correlation between the scores of 10 students in mathematics and in science. This means that students are good in mathematics are also good in science.

Spearman Rho Coefficient

          Another way of finding the correlation between two variables is the Spearman rho Correlation coefficient and is denoted by a Greek letter rho (ρ). The Spearman rho correlation coefficient (ρ) is a measure of correlation when the given sets of data are expressed in ordinal level of measurement rather than raw scores as in Pearson r.

Formula:

                    

                        ρ =1 -6 ∑D2

                             N(N2-1)

Where:

                   ρ = Spearman rho Correlation Coefficient value

                   D = difference between a pair of ranks

                   N = number of students/cases

Steps in Solving Spearman rho Correlation Coefficient:

   1.   Rank the scores in the distribution if raw scores are given.

   2.   Find the difference between each pair.

   3.   Square the difference.

   4.   Find the summation of the squared difference.

   5.   Solve the value of the Spearman rho Correlation Coefficient using its formula.

          REFLECTION:

                   There are many ways on how can we measure the relationship of different scores, test items and so on.

                  One way to measure the relationship between two variables such as score of students and different subjects is the correlation, Through this technique, teachers are able to recognize what are the possible reason about high performance in a test or low performance in a test. It can also measure the relationship between two groups of score.