Pearson Correlation Test and Hypothesis Testing: A Statistics View

This statistics assignment provides a detailed explanation of the Pearson linear correlation test, outlining its purpose in determining the significance of the correlation between variables. It discusses the underlying assumptions, including the linear relationship of the population, absence of outliers, independence of residual errors, and consistent spread of y-value distributions. The assignment defines key statistical concepts such as the T statistic, degrees of freedom, P-value, alternative hypothesis, 95% confidence interval, and sample estimate. Furthermore, it explains two methods—the P-value approach and the confidence interval approach—to determine whether to reject the null hypothesis, concluding that in the given scenario, the null hypothesis cannot be rejected based on the provided P-value and confidence interval.

STATISTICS
STUDENT ID:
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The purpose of the Pearson linear correlation test is to ascertain if the underlying correlation
between the variables of interest is significant or not. The various assumptions in this regards
are stated below (Hillier, 2016).
 The underlying population has a linear relationship and the average y value is
modelled with corresponding average x value.
 The outliers are not present which implies that for any x value, there is normal
distribution of y values about the line.
 There is no pattern for the residual errors highlighting that they are independent.
 The different y value distributions tend to assume same spread and shape about the
line.
1) T statistic – It is widely used in hypothesis testing especially when the underlying
distribution is student t. It refers to the ratio of the amount by which there is departure of
parameter’s estimated value from the value hypothesised and the standard error (Eriksson &
Kovalainen, 2015).
2) Degree of Freedom – It captures the number of independent quantities which may be
assigned to a given statistical distribution (Flick, 2015).
3) P value – Under the scenario where there is a true null hypothesis, the p value captures the
probability of getting the observed results (Hair, Wolfinbarger, Money, Samouel & Page,
2015).
4) Alternative Hypothesis – The statement which highlights the presence of the real effect
related results being present. It is the contrary of null hypothesis which essentially represents
the situation when the real effect is not significant (Flick, 2015).
5) 95% confidence interval – It refers to the interval where it can be estimated with 95%
probability that the population parameter would lie (Eriksson & Kovalainen, 2015).
6) Sample Estimate – This indicates the point estimate which represents the sample
characteristics. An example in this regards is the sample mean estimate which is taken as the
mean of the underlying population assuming a representative sample (Hair, Wolfinbarger,
Money, Samouel & Page, 2015).

PART 2
To determine if the null hypothesis would be rejected or not, consideration needs to be given
to the following two methods or approaches.
P value approach
In the given result of the hypothesis test, the p value is indicated as 0.65 while the
corresponding significance level is taken as 0.05. Since p value >α, hence the available
evidence does not suffice to warrant null hypothesis rejection. This implies non-acceptance of
alternative hypothesis (Flick, 2015).
Confidence Interval Approach
In the given result of the hypothesis test, the 95% confidence interval does contain the value
of 0 which indicates that zero can be the possible value of the correlation coefficient. As a
result, it cannot be concluded that the correlation coefficient differs significantly from zero
Thus, the rejection of null hypothesis is not permissible which implies non-acceptance of
alternative hypothesis (Hillier, 2016).

References
Eriksson, P. & Kovalainen, A. (2015) Quantitative methods in business research 3rd ed.
London: Sage Publications.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015) Essentials of
business research methods. 2nd ed. New York: Routledge.
Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill
Publications.