Pearson Correlation Coefficient

   Classroom teachers are often interested in determining the relationship between two sets of variables or scores. For instance, determining the relationship of vocabulary and comprehension, the teacher wants to know whether the relationship of these learning areas denotes high, low or negligible. The degree that describes the relationship between the two sets of variables is known as correlation(r). Correlation Coefficient is the ratio that expresses the nature of relationship between two corresponding sets of observations, measurements, variables, or scores. The numerical value of the coefficient is an indication or expression of the strenght of relationship (it ranges from 0 to 1) while the symbol (+ or -) that goes with it tells the direction of the relation.

At the end of the lesson, the students should be able to:

1. Define correlation.

2.  Solve for the correlation.

3. Correctly interpret the computed coefficient of correlation.

    The teacher will discuss about Correlation Coefficient and will give an activity.

Pearson’s correlation coefficient is the test statistics that measures the statistical relationship, or association, between two continuous variables.  It is known as the best method of measuring the association between variables of interest because it is based on the method of covariance.  It gives information about the magnitude of the association, or correlation, as well as the direction of the relationship.

Interpretations: 

0 to ± 0.20 = slight correlation/ almost negligible relationship

± 0.21 to ± 0.40 = low correlation/ small negligible relationship

± 0.41 to ± 0.70 = moderate correlation/ substantial negligible relationship

± 0.71 to ± 0.90 = high correlation/ marked negligible relationship

± 0.91 to ± 1 = very high correlation/ very dependable relationship

Example:

From our table:

• Σx = 247
• Σy = 486
• Σxy = 20,485
• Σx2 = 11,409
• Σy2 = 40,022
• n is the sample size, in our case = 6
• 6(20,485) – (247 × 486) / [√[[6(11,409) – (2472)] × [6(40,022) – 4862]]]

                  r= 0.5298

   The range of the correlation coefficient is from -1 to 1. Our result is 0.5298 or 52.98%, which means the variables have a moderate positive correlation.

Activity:

   Solve for the correlation of the ff. data and interpret the computed correlation coefficient.

Data:

X-scores in teacher made test in vocabulary

Y-scores in a standardized vocabulary exercise

   Correlation coefficient are used in statistics to measure how strong a relationship is between two variables.

   If an increase in level of one variable is associated with an increase in the other, the relationship is positive. If an increase in one is associated with a decrease in the other, the relationship is negative (an inverse correlation).

   A correlation coefficient provides a more precise indication of the degree of the relationship between two variables. The value of a correlation coefficient can range from +1 (a perfect positive correlation) to -1 (a perfect negative correlation). The null hypothesis is that there is no predictable relationship between the two variables (correlation coefficient = 0). While a significant correlation between variables allows us to make predictions from one to the other, it does NOT establish a causal relationship.

   For variables that are continuous and normally-distributed, calculate Pearson r.

http://www.statisticshowto.com/probability-and-statistics/correlation-coefficient-formula/

https://www.statisticssolutions.com/pearsons-correlation-coefficient/

http://psc.dss.ucdavis.edu/sommerb/sommerdemo/correlation/summary.htm

Lubrica, M. B. & Sajise, M. T. 2017- 2018. Elementary Statistics. Benguet State University CAS.

Balagtas, M. U., et. al. 2005. Assessment for Learning. Philippine Normal University.