Lesson 1: Pearson Product - Moment Correlation

• Bivariate data


  These are data that involve two variables that are taken from a sample or population.
• Univariate data


  These are data that involve only a single variable.
• Correlation Analysis


  It is a statistical method used to determine whether a relationship between two variables exists.
• Scatterplot


  It shows how the points of bivariate data are scattered.
• The arrangement of the points of bivariate data in a scatterplot is important in making analysis.
• The line that is closed to the points is called the trend line.
• Trend line


  It indicates the direction, either the variables have positive or negative as denoted by the slope of the line.
• In a positive correlation, high values in one variable correspond to high values in the other variable.
• In a negative correlation, high values in one variable correspond to low values in the other variable.
• Direction and Strength of the correlation or relationship


  What are the two elements that should be considered in the analysis of a scatterplot.
• The closeness of the points to the trend line determines the strength of the association.
• The closer the points are to the trend line, the stronger is the correlation.
• Perfect correlation 


  This type of correlation exists when all the points fall in the trend line.
• Perfect correlation


  This correlation maybe positive or negative.
• Perfect correlation 


  This happens only when other variables that may affect the relationship between the two variables are controlled.
• The strength of correlation between two variables can be perfect, strong, moderate, or no correlation.
• The most common coefficient of correlation is known as the Pearson product-moment correlation coefficient.
• It is a measure of the linear correlation (dependence) between two variables X and Y, giving a value between +1 and −1. 

  Pearson's r
• It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s.

  Pearson's r
• If the coefficient value is in the negative range, then that means the relationship between the variables is negatively correlated, or as one value increases, the other decreases.
• If the value is in the positive range, then that means the relationship between the variables is positively correlated, or both values increase or decrease together.
• Correlation coefficient


  Measure of the strength and direction of the linear relationship between two variables
• Perfect positive correlation


  • Trend line contains all the points in the scatterplot and the line points to the right
  • Computed r is 1
• Perfect negative correlation


  • All the points fall on the trend line that points to the left
  • Computed value of r is -1
• No correlation


  • Trend line does not exist
  • Computed value of r is 0
• Absolute value of r


  Indicates the strength of correlation between the two variables
• Sign (positive or negative) of r


  Indicates the direction of correlation
• The formula for computing r.

  A) number of paired values

  B) sum of x values

  C) sum of y values

  D) sum of the products of paired values x and y

  E) sum of x squared values

  F) sum of squared y values

  
• The following table for interpretation of r can be used in interpreting the degree

  A) perfect positive

  B) strong positive

  C) moderately positive

  D) weak positive

  E) negligible positive

  F) no correlation