Presentation on theme: "Spearman Rho Correlation"— Presentation transcript:
1 Spearman Rho Correlation IntroductionSpearman's rank correlation coefficient or Spearman's rho is named after Charles SpearmanUsed Greek letter ρ (rho) or as rs (non- parametric measure of statistical dependence between two variables)Assesses how well the relationship between two variables can be described using a monotonic functionMonotonic is a function (or monotone function) in mathematic that preserves the given order.If there are no repeated data values, a perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other
2 Spearman Rho Correlation +1-1Perfect PositiveCorrelationNo CorrelationPerfect NegativeA correlation coefficient is a numerical measure or index of the amount of association between two sets of scores. It ranges in size from a maximum of through 0.00 to -1.00The ‘+’ sign indicates a positive correlation (the scores on one variable increase as the scores on the other variable increase)The ‘-’ sign indicates a negative correlation (the scores on one variable increase, the scores on the other variable decrease)2
3 Spearman Rho Correlation CalculationOften thought of as being the Pearson correlation coefficient between the ranked (relationship between two item) variablesThe n raw scores Xi, Yi are converted to ranks xi, yi, and the differences di = xi − yi between the ranks of each observation on the two variables are calculatedIf there are no tied ranks, then ρ is given by this formula:3
4 Spearman Rho Correlation CalculationOften thought of as being the Pearson correlation coefficient between the ranked (relationship between two item) variablesThe n raw scores Xi, Yi are converted to ranks xi, yi, and the differences di = xi − yi between the ranks of each observation on the two variables are calculatedIf there are no tied ranks, then ρ is given by this formula:
5 Spearman Rho Correlation InterpretationThe sign of the Spearman correlation indicates the direction of association between X (the independent variable) and Y (the dependent variable)If Y tends to increase when X increases, the Spearman correlation coefficient is positiveIf Y tends to decrease when X increases, the Spearman correlation coefficient is negativeA Spearman correlation of zero indicates that there is no tendency for Y to either increase or decrease when X increases
6 Spearman Rho Correlation Interpretation cont…/Alternative name for the Spearman rank correlation is the "grade correlation” the "rank" of an observation is replaced by the "grade"When X and Y are perfectly monotonically related, the Spearman correlation coefficient becomes 1A perfect monotone increasing relationship implies that for any two pairs of data values Xi, Yi and Xj, Yj, that Xi − Xj and Yi − Yj always have the same sign
7 Spearman Rho Correlation Example # 1Calculate the correlation between the IQ of a person with the number of hours spent in the class per weekFind the value of the term d²i:1. Sort the data by the first column (Xi). Create a new column xi and assign it the ranked values 1,2,3,...n.2. Sort the data by the second column (Yi). Create a fourth column yi and similarly assign it the ranked values 1,2,3,...n.3. Create a fifth column di to hold the differences between the two rank columns (xi and yi).IQ, XiHours of class per week, Yi1067861002710150992810329972011312112611017
8 Spearman Rho Correlation Example # 1 cont…/4. Create one final column to hold the value of column di squared.IQ(Xi )Hours of class per week(Yi)rank xirank yidid²i861972026-416992838-5251002747-39101505101032910611017112491131236
9 Spearman Rho Correlation Example # 1- ResultWith d²i found, we can add them to find d²i = 194The value of n is 10, so;ρ = x (10² - 1)ρ = −0.18The low value shows that the correlation between IQ and hours spent in the class is very low
10 Spearman Rho Correlation Example # 2:5 college students have the following rankings in Mathematics and Science subject. Is there an association between the rankings in Mathematics and Science subject.StudentAshleyDavidOwenStevenFrankMathematic class rank12345Science class rank
11 Spearman Rho Correlation Example # 2 cont…/Compute Spearman Rhon= number of paired ranksd= difference between the paired ranks(when two or more observations of one variable are the same, ranks are assigned by averaging positions occupied in their rank order)
13 Spearman Rho Correlation Example # 2- ResultResult: ρ = -0.5There is a moderate negative correlation betweenthe Math and Science subject rankings of studentsStudents who rank high as compared to other students in their Math subject generally have lower Science subject ranks and those with low Math rankings have higher Science subject rankings than those with high Math rankings.(The formula for Pearson r and Spearman rho areequivalent when there are no tied)
14 Research Article Title: “Motivation and Attitude in Learning English among UiTM Students in the Northern Region of Malaysia”Purpose:To describe the relationship between the students’ motivation and attitude to their English Language performance
15 Article Cont…/ Method: Used a correlational research design Independent variables:Motivation, attitude, and personal characteristics variables, as measured by a self-report questionnaireDependent variable:English Language performance, measured by the UiTM Preparatory English (BEL100) examination result
16 Article Cont…/ Method: Sampling DesignThe subjects were 139 students from the Perlis Campus, 248 from the Kedah Campus and 233 from the Pulau Pinang Campus.The selection criterion used in attaining the samples was to choose those students who had just received their BEL100 examination result regardless of their status whether as the first timer or repeater for that particular paper.
17 Article Cont…/ Method: Questionnaire Research instrument used was questionnaire that comprised questions on personal characteristics, motivation and attitudes.The instrument was adopted and adapted from Gardner andLambert (1972) so that it is more appropriate, intelligible and meaningful for the sample concerned.The reliability test of the instrument produced a Cronbach Alfa of 0.757, which was satisfactory and acceptable.
18 Article Cont…/ Method: Data AnalysisThe data collected were computed and analyzed using the SPSS 12.Each student’s score on the questionnaire was matched to his or her BEL100 examination grade.The statistical procedures used in this study were the descriptive statistics – mean & standard deviation scores, frequency & percentage, t-test, Spearman Rho Rank-Order Correlation Coefficient & ANOVA.
19 Article Cont…/Result- Correlation between motivation in learning English & English language performanceSpearman Rho rank-order correlation coefficient testVery weak relationship between Intrinsic Motivation & English language performance, which isOne-way ANOVA testIntrinsic Motivation: Critical value of F at alpha = .05 is The obtained F value is 1.63, which is less than the critical value.Extrinsic Motivation: Computed value for the correlation test which is .043 and the obtained value of F for the one-way ANOVA, 2.39.This justifies there is no significant differences between Overall Motivation (Intrinsic Motivation & Extrinsic Motivation) & English language performance.
20 Article Cont…/Result- Attitude in learning English & English language performanceSpearman Rho rank-order correlation coefficient testExists a significant correlation (alpha = .01) between the attitude in learning English & English language performance, which isOne-way ANOVA testF value from the one-way ANOVA test is 6.66, which is greater than the critical value.Mean scoresRespondents received A - M = 3.06, B- M = 2.99, C - M = 2.93, D - M = 2.80), it can be concluded that the respondents who obtained an A (high achievers) have better attitude in learning English compared to the low achievers.This justifies that there is a significant difference between the attitude in learning English & English language performance.