In this paper, we will describe and discuss the application of correlation analysis to a real world problem. Our goal is to choose four quantitative variables from the book data set and run a correlation analysis in MYSTAT. To do this, we go to Analyze -> Correlations -> Simple, enter the chosen variables in the selected box and select the uncorrected probability option in the Options tab.
As we know, correlation is a measure of the degree and direction of connection between the values of two variables. This is a statistical measure of the probability of the link between two variables measured on a quantitative scale. Correlation is used in correlation analysis. Correlation analysis is a hypothesis test for the relationships between variables using correlation coefficients.
The direction of the relationship is determined by direct or inverse association of the values of two variables: if the increase in the values of one variable corresponds to the increase in the values of the other variable, the relationship is direct (positive); : if the increase in the values of one variable corresponds to the decrease in the values of the other variable, the relationship is inverse (negative). An indicator of the direction of communication is a sign of the correlation coefficient.
The correlation coefficient is a quantitative measure of the strength and direction of the probabilistic relationship of two variables. It takes values in the range from -1 to +1. It is a measure of direct or inverse proportionality between two variables.
In this assignment, we will calculate Pearson’s correlation coefficient (Statistics How To, 2013).
There are four following variables participate in this assignment:
Energy level
Reaction to pressure
Characterization of life as a whole
Daily activities
The output from MYSTAT is given in the table below:
Matrix of Probabilities:
The probabilities are all reported as 0.000. This means that the probability of type 1 error is less, than 0.001, and we can consider all the coefficients of correlation to be significant even at the 1% level of significance.
The interpretation of correlation coefficients is given below:
The coefficient of correlation between Energy level and Reaction to pressure is 0.336, indicating a moderate positive linear association between the variables. The coefficient of correlation between Energy level and Characterization of life as a whole is 0.536, indicating a strong positive linear association between the variables. The coefficient of correlation between Energy level and Daily activities is 0.468, indicating a moderate positive linear association between the variables.
The coefficient of correlation between Reaction to pressure and Characterization of life as a whole is 0.315, indicating a moderate positive linear association between the variables. The coefficient of correlation between Reaction to pressure and Daily activities is 0.244, indicating a weak positive linear association between the variables. The coefficient of correlation between Characterization of life as a whole and Daily activities is 0.564, indicating a strong positive linear association between the variables.
References
Statistics How To,. (2013). Pearson Correlation: Definition and Easy Steps for Use. Retrieved 3 March 2016, from http://www.statisticshowto.com/what-is-the-pearson-correlation-coefficient/
