...Correlation as a measure of association summary BSHS/435 January 24 2016 Correlation as a measure of association summary Introduction In this essay I will describe correlation is a measure of association as well as describe different methods of establishing a correlation between variables. In this essay I will also explain advantages and disadvantages of each method, were each must be applied, and provide particular circumstances and examples in which a researcher may want to establish correlation Describe correlations as measured of association "A correlation is a statistical to determine the tendency or pattern for two (or more) variables or two sets of data to very consistently" (Creswell, (2012). any relationships between variables can be positive, negative, or curvilinear. “Measures of association describe the nature of relationships between variables, particularly the strength of the relationship or how closely the variables are related. The strongest relationship is a perfect one, and which a given change is one variable is always associated with a particular change and the other bearable. Rarely, however, are perfect relationships found in human service research" (Monette, Sullivan & DeJong, (2011). Describe different methods of establishing correlations between variables. There are different ways of establishing a correlation between variables such as nominal data. "some data are dichotomous in inform- that is, the variables have only two...
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...Correlation as a Measure of Association Christina Johnson BSHS/435 3/18/2015 Dr. Michele Howser Correlation as a Measure of Association When performing academic research, a researcher must determine not only what it is they are studying but how they are going to describe what they are studying. What a person is studying can be defined as a characteristic or any qualities that possess two or more potential values (Leedy & Ormrod, 2010). Variables usually come in two forms, independent and dependent where the former is manipulated by the researcher and the latter is influenced by the first (Leedy & Ormrod, 2010). Using a statistical process, determining if two or more variables are associated to each other defines correlation (Leedy & Ormrod, 2010). Describing the connection between the variables is how association is measured. Knowledge of correlation as a measure of association, the methods used, and its application in research will assist a researcher in understanding when and how to establish correlation. Correlational Research Studies using correlation are done to observe to what degree different types of variances exists with one variable in relation to another variable (Leedy & Ormrod, 2010). Basically, it is to determine if one characteristic affects another. “A correlation exists if, when one variable increases, another variable either increases or decreases in a somewhat predictable fashion” (Leedy & Ormrod, 2010). When data is collected...
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...Chapter 22 Correlation Coefficients 22 Correlation Coefficients The Meaning of Correlation Correlation and Data Types Pearson’s r Spearman rho Other Coefficients of Note Coefficient of Determination r2 The concept of correlation was introduced in Chapters 1 and 5. Our focus since Chapter 16 has been basic statistical procedures that measure differences between groups -- one-sample, two-sample, and k-sample tests. Now we turn our attention to basic statistical procedures that measure the degree of association between variables. Dr. Wesley Black studied the relationship between rankings of selected learning objectives in a youth discipleship taxonomy between full-time church staff youth ministers and seminary students enrolled in youth education courses at Southwestern Seminary.1 Questionnaires were returned by 318 students and 184 youth ministers.2 Ten objectives in each of five categories (Personal Ministry, Christian Theology and Baptist Doctrine, Christian Ethics, Baptist Heritage, and Church Polity and Organization) were ranked by these two groups. The basic question raised by Black in this study was whether students prioritized discipleship training objectives for youth in the same way as full-time ministers in the field. Using the Spearman rho correlation coefficient, Black found the correlations of rankings generated by students and ministers of the ten items for each of five categories were as follows: Personal Ministry, 0.915; Christian Theology...
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...USING EXCEL TO FIND MEASURES OF ASSOCIATION by Edward F. Stafford, Jr., PhD Professor of Management Science, UAH Purpose of Handout The purpose of this handout is to describe how to obtain measures of association between two variables using the Microsoft Excel software. These measures include covariance and correlation. For the most part, each measure may be obtained in two ways: (1) “by hand”; and (2) by Excel’s fX function operator. “By hand” does not mean to actually do the computations by hand; rather, it means to use Excel for statistical computations as though the fX function operator did not exist. Example Problem An example problem is used to demonstrate all of the features described in this handout. The problem is extracted from Case Problem 2, “National Health Care Association,” Chapter 3 of the Anderson, Sweeney, and Williams textbook assigned for this course. In particular, the “University Hospitals” data is used in this handout. The data are scales indicating respondent’s “degree of satisfaction” in their work, their pay, and their opportunities for promotion. Scale values range from 0 to 100. The actual data values used are shown in Figure 1. The user may acquire these data, user-ready, in an Excel file by going to Dr. Stafford’s home page on the web {http://cas.uah.edu/stafford/}, then clicking on the following, in order: (1) MSC 287; (2) scroll down then Special Handouts; (3) Excel Materials including Instructions for Statistical Calculations {click on...
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...Quantitative Methods II ©2006 Prentice Hall Lecture 12 14-12-2014 Chapter 13 Linear Correlation and Regression ©2006 Prentice Hall Intended Learning Outcomes (ILOs) • By the end of this lecture, the student should be able to: Understand and explain the terms dependent and independent variable Calculate and interpret the correlation coefficient , the coefficient of determination, and the standard error of estimate Calculate the least squares regression line Construct and interpret confidence and prediction intervals for the dependent variable ©2006 Prentice Hall • In this chapter, we will develop numerical measures to express the relationship between two variables. Is the relationship strong or weak, is it direct or inverse? In addition, we will develop an equation to express the relationship between variables. Then, we will estimate one variable on the basis of another. • - Examples: Is there a relationship between the number of hours that student studies for an exam and the score earned? - Is there a relationship between years of employee experience and the quantity of production? - Is there a relationship between the product price and the purchasing amount of that product? - Is there a relationship between the amount of money spend per month on advertising and the monthly sales? - Is there a relationship between age and blood pressure ? Can we estimate, based on the amount of money spent on advertising in January,...
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...Correlation and Regression Correlation is the measure of two variables normally being x and y. X and y are normally variables of a bivariate distribution. Bivariate distribution (2 variables) for each unit observed having 2 separate and distinct measurements. If the value of one variable is related to the value of another, they are said to be correlated. There are five degrees of correlation that we use; 1. Positive – line goes in upwards direction 2. Negative – line goes in downward direction 3. Perfect – all of the pairs of values will lie on a straight line 4. Partial – values form a pattern or a trend on a graph 5. No correlation – no pattern When showing the workings out of correlation this can be done numerically but the most common and simplest way is by scatter graph. It can only work when one variable is dependant upon the other for example salary spends is dependent on hours worked during a week. As these variables change they will change the plots on the graph. The dependant value will be shown on the y axis and the independent value shown on the x axis. Coefficient Correlation The most common method used to measure coefficient of correlation is Pearson’s product moment as it uses quantitative data. When we use Pearson’s method R = correlation coefficient. R must always fall between -1 and +1 as discussed before. Again as discussed before +1 is perfect positive correlation and -1 is perfect negative correlation; an R=0 is no correlation...
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...mine valid association rules, which are identical to the content Professor Chen introduced to you in class. Note that you do not need to pay more attention to the algorithm or codes of this method. Instead, ideas and related examples are more important for you to understand this method and it is enough to help you complete the assignment. Furthermore, to resolve the problem 2.(c) in EXERCISE 3, you need to read section 5.3.1 to know how to do. This part gives you the concept of multi-level association rule or generalized association rule. 基本阅读：英文资料 5.1,5.2.1 和 5.2.2，这部分内容与老师上课所介 绍的内容一致，不必过分专注于其中的算法和代码部分，更重要的是 理解方法意思,过程及其中的相关例子。扩展阅读：为了解决作业问 题 2 中的（c）小问，你还最好阅读 5.3.1 部分。 Mining Frequent Patterns, Associations, and Correlations Frequent patterns are patterns (such as itemsets, subsequences, or substructures) that appear in a data set frequently. For example, a set of items, such as milk and bread, that appear frequently together in a transaction data set is a frequent itemset. A subsequence, such as buying first a PC, then a digital camera, and then a memory card, if it occurs frequently in a shopping history database, is a (frequent) sequential pattern. A substructure can refer to different structural forms, such as subgraphs, subtrees, or sublattices, which may be combined with itemsets or subsequences. If a substructure occurs frequently, it is called a (frequent) structured pattern. Finding such frequent patterns plays an essential role in mining associations, correlations...
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...course, otherwise referred to as the level of significance. Analysis of covariance (ANCOVA): A variant of the analysis of variance (ANOVA) in which scores on the dependent variable are adjusted to take into account (control) a covariate(s). For example, differences between conditions of an experiment at pre-test can be controlled for. Analysis of variance (ANOVA): An extensive group of tests of significance which compare means on a dependent variable. There may be one or more independent (grouping) variables or factors. ANOVA is essential in the analysis of most laboratory experiments. Association: A relationship between two variables. Bar chart: A picture in which frequencies are represented by the height of a set of bars. It should be the areas of a set of bars, but SPSS Statistics ignores this and settles for height. Bartlett’s test of sphericity: A test used in MANOVA of whether the correlations between the variables differ...
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...The Effects of Socialization on Attitudes Regarding Homosexuality in Relation to the Implicit Associations Test Elaina Lucido Department of Psychological and Brain Sciences Indiana University Bloomington Abstract In this study, I investigated whether explicit measures of personal attitudes regarding homosexuality are correlated with implicit measures of personal preference between heterosexuality and homosexuality. Participants were first given a self-report survey in order to gauge their explicit attitudes or prejudices in regards to homosexuals in society. Then, a Sexuality IAT was administered in order to test for a suggested implicit preference for Straight over Gay or vice versa. Overall average scores on the Sexuality IAT revealed implicit preferences for heterosexuality over homosexuality. When the explicit and implicit measures were paired together, correlation analysis revealed that there was no statistically significant correlation between the two. The Effects of Socialization on Attitudes Regarding Homosexuality in Relation to the Implicit Associations Test Attitudes and behaviors towards homosexuality are usually attributed to the moral standings, values, upbringing, and personal experiences of an individual. Opinions regarding the acceptance of homosexuality in America have changed drastically within the past decade partly due to an increased population of younger generations and open homosexuals within the United States. Dimock, et al...
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...university of phoenix | Correlation Paper | | | Amber Kluever | 2/29/2016 | | Correlation is a measure of association that tests whether a relationship exists between two variables. It indicates both the strength of the association and its direction, direct or inverse. I am trying to find out if there is a relationship between A. PTSD and B. AODA, whether there is a relationship between the two depends on the strengths between them. Each method views variables not in isolation, but instead as systematically and meaningfully associated with, or related to, other variables. For example, using correlation coefficient which indicate the strength of association between two variables the (X,Y) it also describes correlation that reflects mutual relations of r of 1.0 (positive or negative) indicates an perfect linear relation, while 0 indicates that neither X or Y can be predicted by a linear equation. In these types of cases when the r is positive then there is an increase in both X and Y. Now if the r is negative it’s an increase in just the X and a decrease in the Y. Another method that is commonly used is the dichotomous variable also knows as the discrete variable which has two separate parts. An example of this would be measuring sound waves but having to measure in two different parts one high and the other low. The advantages of correlation are that it is used for research to be carried out, either by using experiments or taking surveys. The major advantage...
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...A Correlation Analysis of English Language Proficiency and Performance in Content-Area Cognitive Skills Kate O’Neill - Zayed University Peter M. Theuri – Northern Kentucky University Abstract: Literature is replete with studies indicating the need to develop students’ language skills. Little research has emphasized the importance of language proficiency in enhancing learning or performance in specific content-area courses. This study investigates whether a student’s English language proficiency can be associated with her performance in specific cognitive skills (knowledge, comprehension, application, and analysis) in an introductory accounting course. While the results show no association between TOEFL and performance, the mean of the English composition courses do show a significant association with knowledge and comprehension cognitive skills scores on the first financial accounting course. No associations were attached to the application and analysis cognitive skills. The results are meaningful to faculty in balancing language proficiency with quality instruction in content-area courses. Introduction and Reference Context: English as a language of instruction has quickly taken precedence in most of the universities and colleges around the world. What has also become commonplace is the interchange of students from country to country. The term “international students” has traditionally been attributed to students who matriculate in colleges...
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...of the dive duration (DD) to a depth D = 180 is given by the regression equation DD = 2.69 + 0.0138D = 2.69 + 0.0138 × 180 = 5.174 | Points Earned: | 1/1 | Correct Answer: | 5.174 | Your Response: | 5.174 | 4. | The dives varied from 40 meters to 300 meters in depth. Plot the regression line from x = 40 to x = 300. Which of the lines in the figure below is the correct regression line? | | A. | Blue | B. | Yellow | C. | Red | | To plot the line, compute DD = 3.242 minutes when D = 40 meters, and DD = 6.83 minutes when D = 300 meters. | Points Earned: | 0/1 | Correct Answer: | A | Your Response: | C | | Biochemical oxygen demand (BOD) measures organic pollutants in water by measuring the amount of oxygen consumed by microorganisms that break down these compounds. BOD is hard to measure...
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...MKT 424 EXAM 3 REVIEW GUIDE CHAPTER 18 Characterizing Relationships Between Variables • 1. Presence: whether any systematic relationship exists between two variables of interest • 2. Direction: whether the relationship is positive or negative • 3. Strength of Association: how strong/consistent the relationship is (strong, moderate, weak) o Relationships should be assessed in this order How to Analyze Relationships 1. Choose variables to analyze 2. Determine if the variables are interval/ratio or nominal/ordinal 3. Use the correct relationship analysis a. For two interval/ratio variables – use correlation b. For two nominal/ordinal variables – use cross-tabs 4. Does a relationship exist? 5. If relationship exists, determine the direction a. Monotonic will be increasing/decreasing b. Nonmonotonic will be looking for a pattern 6. Assess the strength of relationship a. With correlation – size of coefficient denotes the strength b. With cross-tabs – the pattern is assessed Cross-Tabulations and Chi Square • Cross-tabulations o Consists of rows and columns defined by the categories classifying each variable. Used for nonmonotonic relationships o Sometimes referred to as an “r x c” table (rows x columns) ▪ Crosstabulation cell – intersection of a row and a column o Interested in inner cells to determine relationship before statistically...
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...Positive Semi-definiteness of Some Non-Pearsonian Correlation Matrices SK Mishra Department of Economics North-Eastern Hill University Shillong, Meghalaya (India) mishrasknehu@yahoo.com I. Introduction: A correlation matrix, ℜ , is a real and symmetric m × m matrix such that − 1 ≤ rij ∈ ℜ ≤ 1; i, j = 1,2, ... , m. Moreover, rii = 1. The Pearsonian (or the product moment) correlation coefficient, e.g. r12 (between two variates, say x1 and x 2 , each in n observations), is given by the formula: r ( x1 , x2 ) = cov(x1 , x2 ) / var(x1 ) ⋅ var(x2 ) … (1) 1 n 1 n 2 where, x a = ∑k =1 x ka ; cov( x1 , x 2 ) = ∑k =1 x k 1 x k 2 − x12 x 2 and var( xa ) = cov( xa , xa ); a = 1, 2. n n A little of algebra also gives us the identity: r ( x1 , x2 ) = (1 / 4) [var(x1 + x2 ) − var(x1 − x2 )] var(x1 ) ⋅ var(x 2 ) … (2). The Pearsonian correlation matrix is necessarily a positive semi-definite matrix (meaning that all its eigenvalues are non-negative) since it is the quadratic form of a real matrix, X ( n, m ). It also implies that if ℜ is not a positive semi-definite matrix, then X ( n, m) is not a real matrix. II. Robust Measures of Correlation: The Pearsonian coefficient of correlation as a measure of association between two variates is highly prone to the deleterious effects of outlier observations (data). Statisticians have proposed a number of formulas, other than the one that obtains Pearson’s coefficient of correlation, that are considered to be less affected by...
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...data. Descriptive statistics tell us information about the distribution of our data, how varied the data are, and the shape of the data. Now we are also interested in information related to our data parameters. In other words, we want to know if we have relationships, associations, or differences within our data and whether statistical significance exists. Inferential statistics help us make these determinations and allow us to generalize the results to a larger population. We provide background about parametric and nonparametric statistics and then show basic inferential statistics that examine associations among variables and tests of differences between groups. Parametric and Nonparametric Statistics In the world of statistics, distinctions are made in the types of analyses that can be used by the evaluator based on distribution assumptions and the levels of measurement data. For example, parametric statistics are based on the assumption of normal distribution and randomized sampling that results in interval or ratio data. The statistical tests usually determine significance of difference or relationships. These parametric statistical tests commonly include t-tests, Pearson product-moment correlations, and analyses of variance. Nonparametric statistics are known as distribution-free tests because they are not based on the assumptions of the normal probability curve. Nonparametric statistics do not specify conditions about parameters of the population but assume...
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