Consider that you have gathered 10 people and you are going to measure their height and weight. The numerical data you have gathered is the quantitative data sets. Now, suppose one person’s weight is 50 kg and another person’s weight is 60 kg. What is the relationship between their weights? For knowing this, the Pearson correlation coefficient test is required. In this blog, we will apply the Pearson correlation coefficient test to evaluate quantitative data sets. But first, let us know a little bit about the Pearson correlation coefficient test.
Defining the Pearson correlation coefficient test
The Pearson coefficient correlation test is a statistical method used to measure the linear association between two continuous variables. The Pearson correlation coefficient, also known as Pearson's r, is a measure of the strength and direction of a linear relationship between two variables. The coefficient can range from -1 to +1, where:
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A coefficient of +1 indicates a perfect positive linear relationship, meaning that as the value of one variable increases, the value of the other variable also increases.
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A coefficient of -1 indicates a perfect negative linear relationship, meaning that as the value of one variable increases, the value of the other variable decreases.
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There is no linear relationship between the two variables, as indicated by a coefficient of 0.
The Pearson coefficient correlation test is based on the assumption that the data is normally distributed and the relationship between the two variables is linear. It is sensitive to outliers, meaning that a single outlier can greatly affect the correlation coefficient.
The test can be used to determine if there is a significant correlation between two variables. The alternative hypothesis holds that there is a correlation between the two variables, contrary to the null hypothesis that there isn't. The test statistic is the Pearson correlation coefficient, which follows a t-distribution. The p-value is used to determine the significance of the correlation. A small p-value (typically less than 0.05) indicates that the correlation is statistically significant and that there is a linear relationship between the two variables.
Figure 1: Pearson coefficient correlation test
Applying the Pearson correlation coefficient test to evaluate quantitative data sets
Figure 2: Pearson correlation coefficient test amongst the two variables
Applying the Pearson correlation coefficient test to evaluate quantitative data sets involves several steps:
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Collecting the data: The data should be collected in a way that ensures that it is accurate, reliable, and relevant to the research question.
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Checking the assumptions: The Pearson correlation coefficient test assumes that the data is normally distributed and that the relationship between the two variables is linear. It is important to check the normality of the data, using techniques such as histograms, Q-Q plots and the Shapiro-Wilk test. If the data is not normal, it might be necessary to use a non-parametric test or to transform the data.
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Calculating the correlation coefficient: The correlation coefficient, Pearson's r, can be calculated using a calculator, spreadsheet software, or statistical software package. The correlation coefficient can range from -1 to +1, where a coefficient of +1 indicates a perfect positive linear relationship, a coefficient of -1 indicates a perfect negative linear relationship, and a coefficient of 0 indicates no linear relationship between the two variables.
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Test the significance of the correlation: The test statistic is the Pearson correlation coefficient, which follows a t-distribution. The p-value is used to determine the significance of the correlation. A small p-value (typically less than 0.05) indicates that the correlation is statistically significant, and that there is a linear relationship between the two variables.
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Interpretation: The results of the test should be interpreted in the context of the research question and the data. The correlation coefficient indicates the strength and direction of the relationship between the two variables, and the p-value indicates whether the correlation is statistically significant. It's important to note that correlation does not imply causation, and it's important to investigate other factors that might be associated with the relationship.
In summary, applying the Pearson correlation coefficient test to evaluate quantitative data sets involves several steps: collecting the data, checking the assumptions, calculating the correlation coefficient, testing the significance of the correlation, and interpreting the results in the context of the research question and the data. It's important to note that correlation does not imply causation, and it's important to investigate other factors that might be associated with the relationship. We, at ELK Statistics, have helped more than 1000+ Ph.D. students to evaluate quantitative datasets using the Pearson correlation coefficient test. Visit our website https://www.elkconsulting.com.my/ to learn more.