Interpreting Correlation Coefficient

You are interested in knowing whether wealthier people are happier. You collected data
from fifty people about their incomes and their overall happiness levels on a scale of 1 to
10. Upon analyzing the results, you find that the correlation coefficient has a value of?0.25.
On the basis of this data, respond to the following:
• How would you interpret the correlation coefficient in terms of strength and direction?
Correlation coefficient is a statistical analysis that is used in indicating the association between
dependent variable and independent variable. Therefore, the correlation of +0.2 indicates weak
correlation between peoples income independent variable and happiness level dependent level
(Adler and Parmryd, 2010).
According to this information, there would be a low association between one’s income
increasing and there increase in happiness. Therefore only 20% portion of happiness would be
covered incase one’s income is increased.
• How would the results be affected if you increased the number of subjects in the study to
one thousand?
Increasing the number of subject samples would increase the density of the scatter point on a
scatter diagram, it would also increase the mean of the observations determined. Increasing the
subject samples size, the confident interval would be high while the correlation would move
close to zero.
As the subject sample goes up, the coefficient of correlation would fluctuate at less strength
towards the true value for the population.
Why might that affect the overall correlation?
There would be a further weak linear relationship between income independent variable and
happiness dependent variable when the number of subject would be increased fifty people to one
thousand people. The correlation coefficient would tend to move close to zero. Correlations that
are obtained on small subject samples would produce realistic large correlation coefficient as
compared to large subject samples.
• How important is it to randomly select subjects? Explain in detail using an example of a
sample that might not be truly representative of the population.
Random samplings are important concepts in the jurisdiction of research statistical methods.
Random sampling would therefore mean a method that would be used to select an individual
from a population to be involved in study research. Therefore, this would mean that samples