Presents information from the field of epidemiology in a less technical, more accessible format. Covers major topics in epidemiology, from risk ratios to case-control studies to mediating and moderating variables, and more. Here is a template for writing a null-hypothesis for a Pearson Correlation: There is no statistically significant relationship between the [insert variable] and [insert variable]. John is an investor. The Pearson correlation has two assumptions: To calculate Pearson correlation, we can use the cor() function. It is independent of the unit of measurement of the variables. Pearson Correlations – Quick Introduction By Ruben Geert van den Berg under Correlation, Statistics A-Z & Basics. Introduction. The most commonly used type of correlation is Pearson correlation, named after Karl Pearson, introduced this statistic around the turn of the 20th century. This book has been developed with this readership in mind. This accessible text eschews long and off-putting statistical formulae in favour of non-daunting practical and SPSS-based examples. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute. Wikipedia Definition: In statistics, the Pearson correlation coefficient also referred to as Pearson’s r or the bivariate correlation is a statistic that measures the linear correlation between two variables X and Y.It has a value between +1 and −1. If not, how do I program the test myself? This book answers these questions and provides an overview of the most common statistical test problems in a comprehensive way, making it easy to find and perform an appropriate statistical test. It is independent of the unit of measurement of the variables where the values of the correlation coefficient can range from the value +1 to the value -1. Found inside – Page 120For example, the Pearson product moment correlation coefficient allows you to test the null hypothesis that the correlation between two interval- or ... Spearman correlation: Spearman correlation evaluates the monotonic relationship. Pearson Product Moment How can you tell if there is a correlation? ∑xy = sum of products of the paired stocks, r = (6 * (13937)- (202)(409)) / (√ [6 *7280 -(202), r = (6 * (13937)- (202) * (409))/(√ [6 *7280 -(202), r = (83622- 82618)/(√ [43680 -40804] * [170190- 167281 ), It helps in knowing how strong the relationship between the two variables is. Save my name, email, and website in this browser for the next time I comment. Pearson Correlation, Sig (2-tailed) and; N. Pearson’s correlation value. Correlation ranges from -1 to +1. Assumptions The calculation of Pearson’s correlation coefficient and subsequent significance testing of it requires the following data assumptions to hold: interval or … ��؎
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�X���ߟ��9�aق�X�qc5�eUb�8�e�� �֩F ˖Ĉ �22˚���i,cb$�Xv�Q²1��Y��em�el�4���Ӳ�=-;�$a�� y�XV ���H$N�5�eF"qZƨl�H���j��2�c��T��S�i�SŞ��*���W�\qb�,*`s�Q��X��ظ8�8��.j��b�el�4�U/{k�4�k��,���2cq�)b�8�e#w��#�$�X��ebd����2%C,�6LcY�fc�P0~Zv�9²Q����j Recall that relations in samples do not necessarily depict the Found insideThis is the only text you’ll need for undergraduate courses in statistical analysis, statistical methods, and quantitative geography. Here the relationship between x and y isn't just "correlated," in the colloquial sense, it is totally deterministic! The given statement is FALSE, since the Pearson r is used for approximate correlation in bivariate data analysis. 3. It measures the strength of the relationship between the two continuous variables. Pearson’s product moment correlation coefficient, or Pearson’s r was developed by Karl Pearson (1948) from a related idea introduced by Sir Francis Galton in the late 1800’s. we need to use another correlation test. Found insidePractitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful. Pearson Correlation Coefficient Example: We seek to determine the relationship between the number of months that students attended college and the number of classes they missed. For example: “The hypothesis is that happiness is related, in some fashion, to income.” When we ask SPSS to calculate the correlation coefficient for two variables (like HAPPINESS and INCOME), SPSS gives us an r statistic (e.g., r = +.45), and a p (probability) statistic (e.g., p = .02). #Pearson correlation test with 0.90 confidence level cor.test(x, y, method = "pearson", conf.level = 0.90) alternative – change the alternative hypothesis (default is “two.sided”) “two.sided” – non-zero For a nice synopsis of correlation, see https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php, The most commonly used type of correlation is Pearson correlation, named after Karl Pearson, introduced this statistic around the turn of the 20th century. A correlation of 1 indicates the data points perfectly lie on a line for which Y increases as X increases. For example, Two distinct distributions Similar gradients of regression line. It implies a perfect positive relationship between the variables. a value above 0.5 and close to 1.0. You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Karl Pearson (1857-1936) “Pearson Product-Moment Correlation Coefficient” has been credited with establishing the discipline of mathematical statistics a proponent of eugenics, and a protégé and biographer of Sir Francis Galton. Hypothesis Testing with Pearson r. Okay, what about hypothesis testing? The correlation coefficient can be misleading if the range of the variable is restricted. A 95% confidence interval was computed of [0.410, 0.559]. The correlation coefficient, r, tells us about the strength and direction of the linear relationship between x and y.However, the reliability of the linear model also depends on how many observed data points are in the sample. <>
Using one single value, it describes the "degree of relationship" between two variables. Strictly speaking, Pearson's correlation requires that each dataset be normally distributed. The coefficient of determination, with respect to correlation, is the proportion of the variance that is shared by both variables. Also, you can use either continuous or dichotomous (e.g., 0/1) variables in a Pearson correlation, but you should not use multi-level categorical variables, for example, four categories of type of car. Taller people tend to be heavier. Pearson Correlation 1. With Pearson r the null hypothesis of no relation is tested. There are three options to calculate correlation in R, and we will introduce two of them below. 7. Pearson's correlation coefficient has a value … �b��Q�����ϫ,&Z�u�I� Knowledge flow provides learning book of Business Statistics and Data Processing. This statistics book covers graphical models, sampling, regression analysis and hypothesis. Statistics collecting and analyzing data to organizing data. The Pearson Product Moment Coefficient of Correlation (r) 2. Pearson's correlation supported the research hypothesis that those stores with fewer fish tended to have healthier fish, whereas those stores with more fish would tend to have fish with lower health quality, r(10) = -.86, p < .05. �Y� �w����4E.j��� ��v�3���/���Y�ʞݙ_��}��N�RfE^�*���y�u�W��r��V����f}V����vu�7.��=���>S�����^�n�1��s1RBj������W�6�SU^��&ǹ��Vv8f�+�ꪼ��4�2���v��ܮ��FG�fݮ>f�~Ɵ�qpgk!V��u�z�~=��DDW���pi��ȥ���ڭEa�z���ё���5[���v���V��~|g~���
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iV�\���7�*�O�\����w��:6|�����0zut��M��v��f���j�ȧOP\�� }x��X�ntD0b�T�9զms����cU�a=����L����+萮2p@���J��������T��FC$5�����W�`���u\�`A{����)s\���%��9X�����R�6/�y!�j��Q����!�G���D�����оQ�,�:_o�6���v�W�V��֏�>3S ��/u\L=����5�dB�M��P���ф[/1(�m��\�f�d|@_��^[����fflv�K�Xuy��E��������)YBa��b����i�&V��sf>70#0�c��ʕDT�������/ �Yx7�z��L�j�/�`XD�Q@�5���˫z(��!%���^1����,pt�L�1��ñ No need to memorize this formula! B1 M1 A1 2.5 1.1b 2.2b 6th Carry out a hypothesis test for zero correlation. Using this method, one can ascertain the direction of correlation i.e., whether the correlation between two variables is negative or positive. For example, if a person is trying to know the correlation between the high stress and blood pressure, then one might find the high value of the correlation, which shows that high stress causes the blood pressure. Comparison tests are used to determine differences in the decretive statistics measures observed (mean, median, etc.). If Y tends to decrease as X increases, the Spearman correlation coefficient is negative. Independent variable is an object or a time period or a input value, changes to which are used to assess the impact on an output value (i.e. The null hypothesis (H 0): The correlation between the two variables is zero. There are 2 stocks – A and B. 1 0 obj
The size of the correlation depends on: 1. Login details for this Free course will be emailed to you, Download Pearson Correlation Coefficient Excel Template, You can download this Pearson Correlation Coefficient Excel Template here –. The Pearson correlation for this sample is r = +0.50. For example, when an independent variable increases, the dependent variable decreases, and vice versa.read more as compared to a correlation coefficient of say -0.40. return to top | previous page | next page, Content ©2016. We can test predictions about whether or not there is a relationship and even about what direction the relationship has. (2-tailed) .017 N 10 10 type school type Pearson Correlation .728(*) 1 Sig. Interpreting SPSS Correlation Output Correlations estimate the strength of the linear relationship between two (and only two) variables. Lets say, for example, that r … The Pearson coefficient of correlation measures the extent of the linear relationship between two variables x and y. Essentially, Louvain is a two-step algorithm that maximises the modularity metric, in which for a given network, the … Explain concepts of correlation and simple linear regression 2. Correlation is a measure of relationship between two variables. There is evidence (at 5% level) of a correlation between the daily mean temperature and daily mean pressure. A negative correlation is an effective relationship between two variables in which the values of the dependent and independent variables move in opposite directions. When compared with the other methods of the calculation, this method takes much time to arrive at the results. Example: Use the Correlation procedure to calculate r for the two variables HP (horsepower) and WEIGHT in the WINKS "CAR" database. In the hypotheses below, the Greek letter rho represents the true correlation in the population from which our sample is drawn. PASS Sample Size Software NCSS.com Pearson's Correlation Tests 800-7 © NCSS, LLC. To test H 0: ρ = 0 against the alternative H A: ρ ≠ 0, we obtain the following test statistic: t ∗ = r n − 2 1 − r 2 = 0.939 170 − 2 1 − 0.939 2 = 35.39. Correlation is one of the most common statistics. Found insideAfter introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. Null-hypothesis for a Pearson Product Moment Correlation Independence Question. Whenever any statistical test is conducted between the two variables, then it is always a good idea for the person doing analysis to calculate the value of the correlation coefficient for knowing that how strong the relationship between the two variables is. This prediction is typically based on past research, accepted theory, extensive experience, or literature on the topic. In the sample, Pearson's r = 0.487. Highlights: * Assumes no previous training in statistics * Explains when and why modern methods provide more accurate results * Provides simple descriptions of when and why conventional methods can be highly unsatisfactory * Covers the ... Hypothesis Tests with the Pearson Correlation. We test the correlation coefficient to determine whether the linear relationship in the sample data effectively models the relationship in the population. Use a hypothesis test in order to determine the significance of Pearson’s correlation coefficient. Positive values of correlation indicate that as one variable increase the other variable increases as well. Example: Calculating the t-statistic for Hypothesis Testing on Correlation. We denote the correlation coefficient by, r. If the absolute value of r, | r |, is close to 1 then this indicates that there is a strong correlation between two variables and if the absolute value of r, | r |, is close to 0 then this indicates that there is a … There is evidence (at 5% level) of a correlation between the daily mean temperature and daily mean pressure. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
The correlation coefficient between the variables is symmetric, which means that the value of the correlation coefficient between Y and X or X and Y will remain the same. The relationship between the two variables is linear. For example, Two distinct distributions Similar gradients of regression line. Suppose I have performed a Pearson correlation test using my example data. Found insideMaking statistics—and statistical software—accessible and rewarding This book provides readers with step-by-step guidance on running a wide variety of statistical analyses in IBM® SPSS® Statistics, Stata, and other programs. ChaPtER 8 Correlation and Regression—Pearson and Spearman 183 prior example, we would expect to find a strong positive correlation between homework hours and grade (e.g., r= +.80); conversely, we would expect to find a strong negative correlation between alcohol consumption and grade (e.g., r = −.80). endobj
H 1 represents the alternative hypothesis that the actual correlation of the population is ρ 1, which is not equal to ρ 0. A Nonparametric Statistic A Descriptive Statistic An Inferential Statistic A Power Statistic 1 Points QUESTION 48 What Would The Scatter Plot Show For Data That Produce A … In theory, these are easy to distinguish — an action or occurrence can cause another (such as smoking causes lung cancer), or it can correlate with another (such as smoking is correlated with alcoholism). Both Pearson and Spearman are used for measuring the correlation but the difference between them lies in the kind of analysis we want. By using our website, you agree to our use of cookies (, Pearson Correlation Coefficient Excel Template. The more inclined the value of the Pearson correlation coefficient to -1 and 1, the stronger the association between the two variables. These authors have found, however, that a more precise estimate of the standard deviation of the Z values obtained from ranks is 1.060/( 3) A directional hypothesis is a prediction made by a researcher regarding a positive or negative change, relationship, or difference between two variables of a population. A small p-value is an indication that the null hypothesis is false. Correlation is transitive for a limited range of correlation pairs. statisticslectures.com - where you can find free lectures, videos, and exercises, as well as get your questions answered on our forums! Found inside – Page 13Conduct a hypothesis test evaluating the signicance of a correlation. The Pearson correlation is generally computed for sample data. As with most sample ... CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. Pearson Correlation. In these results, the Pearson correlation between porosity and hydrogen is about 0.624783, which indicates that there is a moderate positive relationship between the variables. Output: Pearson's product-moment correlation data: x and y t = 1.4186, df = 5, p-value = 0.2152 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.3643187 0.9183058 sample estimates: cor 0.5357143 Cookies help us provide, protect and improve our products and services. You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Pearson Correlation Coefficient (wallstreetmojo.com). We can use the correlation coefficient to test whether there is a linear relationship between the variables in the population as a whole. 4. The third step is to compute the sample value of Pearson's correlation (click here for the formula). Performing a hypothesis test will help us decide whether the correlation of .23 is due to random Null Hypothesis. p-values for the two tests are identical. Hypothesis Test of : Pearson Correlation Pearson's r measures the linear relationship between two variables, say X and Y. Pearson Correlation Coefficient. One of the most common errors found in the media is the confusion between correlation and causation in scientific and health-related studies. Pearson's r measures the linear relationship between two variables, say X and Y. Note: The most commonly used method is the Parametric correlation method. A correlation of 1 indicates the data points perfectly lie on a line for which Y a. the sample correlation is zero b. the population correlation is zero c. there is a non-zero correlation for the general population d. there is a non-zero correlation for the sample A typical threshold for rejection of the null hypothesis is a p-value of 0.05. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. ��Jz�T���.�b�CɌ������;+�����+,a8���P��a�B�;���Ak�#@��;q�I67T ���[�� !U?C=z��U3;nv�u���������Va��~Z��w�#������Vk�槪[ܑ�l��Tk�ly*�~�T��������i�E��hf��C���,�6�g"���c�ڸ��g_�����$
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�ؙ"s��Μ���V�~��q�S|*��S�����e��.~�"4��S�7�SssVBsWn�*����۬�qOKl'�.̧Z0��e��T� remember the null hypothesis, and to differentiate it from the null for Pearson's correlation. Alternative hypothesis Pearson, Kendall, Spearman), but the most commonly used is the Pearson’s correlation coefficient. By the end of this session students will be able to: 1. There are several types of correlation coefficients (e.g. Example 3 – Validation using Zar Zar (1984) page 312 presents an example in which the power of a correlation coefficient is calculated. Correlation coefficients range from -1.0 (a perfect negative correlation) to positive 1.0 (a perfect positive correlation). An example of negative correlation would be the amount spent on gas and daily temperature, where the value of one variable increases as the other decreases. Negative values of correlation indicate that as one variable increases the other variable decreases. Hypothesis Testing with Pearson's r (Jump to: Lecture | Video) Just like with other tests such as the z-test or ANOVA, we can conduct hypothesis testing using Pearson’s r. To test if age and income are related, researchers collected the ages and … Enter a value that specifies the alternative hypothesis value of the correlation parameter in the Pearson correlation parameter field. > cor(fat$age,fat$pctfat.brozek, method="spearman"), > cor.test(fat$age,fat$pctfat.brozek, method="spearman"), alternative hypothesis: true rho is not equal to 0. The closer correlation coefficients get to -1.0 or 1.0, the stronger the correlation. Assumptions (3) 4c Two sensible interpretations or observations. However, we would Correlation analysis example You check whether the data meet all of the assumptions for the Pearson’s r correlation test. Let’s first assess whether there is evidence of a significant Pearson correlation between the hardness of the concrete and the amount of cement used to make it. For example, if we increase the age there will be an increase in the income. For example, you might want to find out whether basketball performance is correlated to a person's height. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. When two sets of numbers move in the same direction at the same time, they are said to have a positive correlation. Pearson’s correlation coefficient is represented by the Greek letter rho ( ρ) for the population parameter and r for a sample statistic. For example a correlation value of would be a “moderate positive correlation”. We test the correlation coefficient to determine whether the linear relationship in the sample data effectively models the relationship in the population. It is calculated as (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2. Date last modified: January 6, 2016. For example, if the unit of measurement of one variable is in years while the unit of measurement of the second variable is in kilograms, even then, the value of this coefficient does not change. Proponent 3. The … x���_s�6���]�����l�($�'�Sʖ�Mn+�^[[y��a,���Ȓ�'�o�@$�A�$��ݍn��8�?{�7ߜ? If the correlation coefficient is 0, it indicates no relationship. Positive correlations imply that as x increases, so does y. Let’s check if there is any association between the two variables ( normal and hyperventilating breathing) for a minimum of 4 students. Spearman’s correlation in statistics is a nonparametric alternative to Pearson’s correlation. Positive Correlation occurs when two variables display mirror movements, fluctuating in the same direction, and are positively related. Here is a template for writing a null-hypothesis for a Pearson Correlation: 8. Praise for the Second Edition "This book should be an essential part of the personal library of every practicing statistician." —Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes ... Thus we reject the null hypothesis that there is no (Spearman) correlation between age and Brozek percent fat (r = 0.27, p-value = 1.07e-05). This coefficient is calculated as a number between -1 and 1 with 1 being the strongest possible positive correlation and -1 being the strongest possible negative correlation. Definition: The correlation coefficient, also commonly known as Pearson correlation, is a statistical measure of the dependence or association of two numbers. As a financial analyst, the CORREL function is very useful when we want to find the correlation between two variables, e.g., the correlation between a in Excel is one of the easiest ways to quickly calculate the correlation between two variables for a large data set. Now, if the variable is switched around, then the result, in that case, will also be the same, which shows that stress is caused by the blood pressure, which makes no sense. The Index, Reader’s Guide themes, and Cross-References combine to provide robust search-and-browse in the e-version. The results from WINKS (in part) are: Variables used : HP and WEIGHT Number of cases used: 38 Pearson's r (Correlations Coefficient) = 0.9172 R-Square = 0.8413 Test of hypothesis to determine significance of relationship: Your email address will not be published. Correlation is a statistical technique that shows how strongly two variables are related to each other or the degree of association between the two. Not only the presence or the absence of the. <>>>
Some people have argued that T is in some ways superior to the other two methods, but the fact remains, everyone still uses either Pearson or Spearman. The naming of the coefficient is thus an example of Stigler's Law.. Definition. A hypothesis test for correlation will start with a null hypothesis of "zero correlation." Now in bivariate data analysis the plot is either oval or circle but Pearson r is a measure of above which gives an approximate result assuming that the distribution is … To test H 0: ρ = 0 against the alternative H A: ρ ≠ 0, we obtain the following test statistic: The Pearson correlation is a measure for the strength and direction of the linear relationship between two variables of at least interval measurement level. Getting a correlation is generally only half the story, and you may want to know if the relationship is statistically significantly different from 0. That is, if Y tends to increase as X increases, the Spearman correlation coefficient is positive. Found insideWith jargon-free language and clear processing instructions, this text covers the most common statistical functions–from basic to more advanced. Unless we reject the null hypothesis, we won’t reject the null hypothesis. Therefore the Pearson correlation coefficient between the two stocks is -0.9088. Found insideThis unique approach—presented in language accessible to both students new to research as well as current practitioners—guides the reader in fully understanding the research options detailed throughout the text. Found insideResearch Methods for the Biosciences is the perfect resource for students wishing to develop the crucial skills needed for designing, carrying out, and reporting research, with examples throughout the text drawn from real undergraduate ... The calculation of the Pearson coefficient is as follows. The second step is to choose a significance level. 7.4.1.2 - Video Example: Correlation Between Printer Price and PPM 7.4.1.3 - Example: Proportion NFL Coin Toss Wins 7.4.1.4 - Example: Proportion of Women Students Here we discuss how to calculate the Pearson Correlation Coefficient R using its formula and example. 1 st Element is Pearson Correlation values. Naming and history. The larger the sample size and the more extreme the correlation (closer to -1 or 1), the more likely the null hypothesis of no correlation will be rejected. To obtain the P -value, we need to compare the test statistic to a t -distribution with 168 degrees of freedom (since 170 - 2 = 168). Found inside – Page 161Table 15.7 Hypothesis testing using Student's one-sample t Step Bulb life ... of 2000 hours This section looks again at Pearson's correlation coefficient, ... Pearson Correlation Coefficient: Pearson Correlation. Positive Correlation – There exists a positive correlation between two variables when they are said to move in the same direction. The bivariate Pearson Correlation produces a sample correlation coefficient, r, which measures the strength and direction of linear relationships between pairs of continuous variables.By extension, the Pearson Correlation evaluates whether there is statistical evidence for a linear relationship among the same pairs of variables in the population, represented by a … Hypothesis test of correlation. First, we will calculate the following values. Also, variables can have differing quantities of correlation to each other. Example 1 10. For example, a correlation of r = .23 may be observed between test grades and hours studied in a sample of 5th grade students. To assess statistical significance, you can use cor.test() function. This suggests a high level of correlation, e.g. The formula for r is, (in the same way that we distinguish between Ȳ and µ, similarly we distinguish r from ρ). In this You might, therefore, plot a graph of performance against height and calculate the Pearson correlation coefficient. Found inside... the analysis of variance, r for Pearson's correlation coefficient, etc. ... the following statements: Example 1: testing a hypothesis about the means of ... ChiSquareTest; Summarizer; Correlation. 0.2891735. It not only states the presence or the absence of the correlation between the two variables, but it also determines the exact extent to which those variables are correlated. Copyright © 2021 Copyright © 2021. When testing the null hypothesis that there is no correlation between age and Brozek percent body fat, we reject the null hypothesis (r = 0.289, t = 4.77, with 250 degrees of freedom, and a p-value = 3.045e-06). Found insideThe book assists those tasked with constructing qualitative models (based on executive judgment, Delphi, scenario writing, survey methods) or quantitative ones (based on statistical, time series, econometric, gravity, artificial neural ... Correlation coefficients are used to measure how strong a relationship is between two variables.There are several types of correlation coefficient, but the most popular is Pearson’s. The Spearman’s Rank Correlation for this data is 0.9 and as mentioned above if the ⍴ value is nearing +1 then they have a perfect association of rank.. Examples of correlation tests are the Pearson’s r test, Spearman’s r test, and the Chi-square test of independence. <>
The correct calculated value of the test statistic for a null of zero correlation is asked Aug 17, 2019 in Business by Pikachu An accessible introduction to statistics written specifically for education students in the changing educational landscape. Pearson’s Correlation Coefficient To calculate a correlation coefficient, you normally need three different sums of squares (SS). Pearson’s r ranges from -1 to +1. r = 3*352-24*42/√(3*200-242)*(3*644-422)= 0.7559, In this example with the help of the following details in the table of the 6 people having a different age and different weights given below for the calculation of the value of the Pearson R. For the Calculation of the Pearson Correlation Coefficient, we will first calculate the following values, Here the total number of people is 6 so, n=6.
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