Pearson Correlation in Quantitative Reasoning

Pearson Correlation
Quantitative Reasoning Assignment
Student’s Name
Institution Affiliation

Pearson Correlation
Pearson linear correlation is statistics that measures the level of linear relationship between to
variables, say X andY (Hassett & Stewart 2006). It computed as Pearson’s correlation coefficient.
The possible values of correlation coefficient are between -1 and +1. Values close to ± , indicate
high perfect relationships between the associate variables. A negative value indicates a negative
correlation between two variables; whereas the positive values suggest a positive relationship
(Jackson, 2015). According to Sharma (2005), Pearson’s correlation is centered on the following
assumptions:
I. The two variables are affected by an enormous number of independent forces such
that they result in a normal distribution.
II. There exists a linear association between the two variables. The two variables
produce a straight line on the scatter diagram’s plots.
III. There is a cause and effect association between the forces affecting the distribution of
items in the two series.
Meaning of output items
I. Statistic, t:
Is a standard value computed from the sample data, during a hypothetical test
especially t-distribution, when parameters like standard deviation, of a population are
unknown(Richardson, 2011). It’s used in a hypothesis test for instance to compare
the mean of two variables. To make a decision in the hypothesis test, t-statistic is
compared with its critical value, determined at set significance level and degree of
freedom. When t-statistic is greater than the critical value, there’s a significance
difference between the variables(Montgomery & Runger, 2010).

Pearson Correlation
II. Degree of freedom
This is the number of observations provided by the sample data that is used to
determine the unknown parameters of the population(Richardson, 2011). It’s used
together with the significance level, to determine the critical value of the statistical
tests from respective tables such as t , F∧Chi square for t , F and Chi- square test
respectively.
III. p-value: this is the probability of finding the values equal to or great than the
observed results (Brunson, 1987). Higher values indicate, there is statistical
significance, while lower indicates there’s no statistical significance. Thus, large p-
values indicates that data is in line with the null hypothesis (Ruppert, 2014). To
determine the statistical significance especially in hypothesis test, p- value,
α =0.05=5 % is used as the cut-off point. When p- value, is less than0.05 the
observed results is rejected (Null hypothesis), and when p- value is greater than 0.05,
null hypothesis is accepted. In this case, alternative hypothesis is rejected, suggesting
that there’s no statistical significance between variables.
IV. Alternative hypothesis: This is a hypothetical statement that is opposite to null
hypothesis. It’s a hypothesis that requires supporting evidence (Crossley, 2000).