Pearson's R Lesson 25 PDF

HYPOTHE SIS TESTING WHAT IS HYPOTHESIS? It is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on the particular property of a population.  PARAMETRIC TEST ST OF RELATIONSHIP TEST OF DIFFERENC CO...

HYPOTHE SIS TESTING WHAT IS HYPOTHESIS? It is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on the particular property of a population.  PARAMETRIC TEST ST OF RELATIONSHIP TEST OF DIFFERENC CORRELATION It is a statistical method used to determine whether a linear relationship between variables exists.  Pearson Product-Moment Correlation The Pearson product-moment correlation coefficient (or Pearson correlation coefficient, for short) is a measure of the strength of a linear association between two variables and is denoted by r. Basically, a Pearson product- moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit.  Types of correlation Positive Correlation - exist when high scores in one variable are associated with high scores in the second variable. Negative Correlation - Exists when high scores in one variable are associated with low scores in the second variable and vise versa. Zero correlation ( no correlation ) - Exists when scores in one variable tend to score symmetrically high not symmetrically low in the other variable.  Correlation Coefficient, r Correlation coefficient r – measures the strength and direction of a linear relationship between two quantitative variables, or tells the magnitude or degree of relationship between two variables. If r is +1 there is a perfect positive correlation If r is -1 there is a perfect negative correlation If r = 0, there is no correlation  Correlation Scale: VALUE OF r INTERPRETATION BETWEEN + 0.80 to + 0.99 High correlation BETWEEN + 0.60 to + 0.79 Moderately high correlation BETWEEN + 0.40 to + 0.59 Moderate correlation BETWEEN + 0.20 to + 0.39 Low correlation BETWEEN + 0.01 to + 0.19 Negligible correlation  Sample table for data presentation Variable r-value interpretati on Social media 0.600 Moderately exposure vs related perceived home-based tasks productivity  The most popular and widely used correlation coefficient is the Pearson Product- moment Correlation coefficient or simply Pearson r. Where: r - correlation coefficient n - number of paired observation x and y - variables ∑ - summation  Example: 1 Compute the value of the correlation coefficient for the data obtained in the study of the number of absences and the final grade of the seven students in the statistics class. Number of Final Studen Absence Grade t s (x) (y) x2 36 y2 7569 xy 522 1 6 87 4 9216 192 2 2 96 225 4356 990 3 15 66 81 5476 666 4 9 74 144 4900 840 5 12 70 25 8100 450 6 5 90 64 𝜮x 𝜮y2= 6724 656 𝜮x = 565 𝜮x2= 579 𝜮xy = 4316 7 8= 82 57 46341  n=7 Σxy = 4316 Σx=57 Σy=565 High correlation Σx2 = 579 Σy2 = 46341  Correlation Scale: VALUE OF r INTERPRETATION BETWEEN + 0.80 to + 0.99 High correlation BETWEEN + 0.60 to + 0.79 Moderately high correlation BETWEEN + 0.40 to + 0.59 Moderate correlation BETWEEN + 0.20 to + 0.39 Low correlation BETWEEN + 0.01 to + 0.19 Negligible correlation  n=7 Σxy = 4316 Σx=57 Σy=565 High correlation Σx2 = 579 A strong negative relationship between a Σy2 = student’s final grade and the number of absences 46341 a student has. That is, the more absences a student has, the lower is his or her grade. 1 2 STATISTICALLY SIGNIFICANT RELATIONSHIP Significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to STATISTICALLY SIGNIFICANT RELATIONSHIP H0: There is no significant relationship between the height and the weight of the wrestlers. Sample interpretation: The critical value table for t at 14 degrees of freedom (two-tailed test) was consulted and t = 2.145 was obtained. Since the calculated t = 4.512 > 2.145 critical t at 14 degrees of freedom and one-tailed test (indicating significant relationship), the null hypothesis that “there is no significant relationship between heights and weights of wrestlers” was rejected. In other words, there is a significant positive relationship between heights and weights of wrestlers.  Age Sugar Level 1 45 99 1.Solve for Pearson’s 2 3 90 66 99 79 r 4 62 70 2.Give the 5 6 56 59 85 82 interpretation 7 54 110 3.Write a null 8 65 90 hypothesis 9 32 64 10 77 101 4.Determine the t- value at 0.05 and the t computed. 5.Test the hypothesis.