Pearson Linear Correlation Test: Assumptions and Key Concepts
Verified
Added on 2023/06/05
|4
|664
|141
AI Summary
This article explains the assumptions and key concepts of Pearson linear correlation test, including the T statistic, degree of freedom, p value, alternative hypothesis, 95% confidence interval, and sample estimate. It also discusses the rejection of null hypothesis through the p value and confidence interval approach.
Contribute Materials
Your contribution can guide someone’s learning journey. Share your
documents today.
STATISTICS STUDENT ID: [Pick the date]
Secure Best Marks with AI Grader
Need help grading? Try our AI Grader for instant feedback on your assignments.
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) SampleEstimate–Thisindicatesthepointestimatewhichrepresentsthesample 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 research3rd 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 Research6th ed.New York: McGraw Hill Publications.