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Premium member Presentation Transcript Correlational Design : Correlational Design SGDP6013 Research Methods in Education Correlational Research Design : Correlational Research Design Weighing One Variable Against Another Chapter 12 Topics to Be Discussed : Topics to Be Discussed Defines Correlational Research When we use Correlational Research Types of Correlational Design The key characteristics of Correlational Design The steps in conducting a Correlational Study How do we evaluate a Correlational Study 4 Correlational Research : Correlational Research A procedure in which subjects’ scores on two variables are simply measured, without manipulation of any variables, to determine whether there is a relationship Correlational research examines the relationship between two or more non manipulated variables. 5 Correlational Research : Correlational Research What is the relationship between: Height and weight? Birth order and years of education? Cigarettes smoked per day and health care costs? How close to the front you sit in a classroom and your grade in a class? 6 What can correlational research tell us? : What can correlational research tell us? Imagine that researchers find an association between sitting in the front of the classroom and receiving good grades You promptly move to the front of the classroom, and expect your grade will improve Don’t bet money on it… 7 Correlation and Causality : Correlation and Causality With correlational research designs, causality cannot be inferred Example: Researchers want to investigate the link between religious affiliation and alcohol consumption* They measure the number of bars and churches in randomly-selected towns # of Bars # of Churches ? * Example by Professor Kristi Lemm of Western Washington University 8 Pitfalls of correlational research designs : Pitfalls of correlational research designs The researchers find that towns with more bars also have more churches Therefore, religious persons tend to drink more, or perhaps alcohol consumption is a reason people attend church …what is wrong with these conclusions? 9 We cannot infer causation! : We cannot infer causation! Larger towns tend to have more bars and more churches. Therefore, a third (and more likely) explanation: Town Population # of Bars # of Churches 10 Correlational Research : Correlational Research Operational Definition: A statistical analysis of covariant data to determine a pre-existing relationship. Researcher makes no attempt to manipulate an independent variable. Purpose: This research technique is used to relate two or more variables and allow predictions of outcomes based on causative relationships between the variables 11 Correlational Research : Correlational Research Historical Perspective: Karl Pearson introduced modern correlation techniques in 1895 at a Royal Society meeting in London where her illustrated his statistical model using Darwin’s evolution and Galton’s heredity. Improvements were slow coming until the arrival of microcomputers when complex regressional analysis of multiple variables was possible 12 Correlational Research : Correlational Research Example Situation: We, as teachers, practice correlation research often in the forms of pre-tests, quizzes, dip-sticking, etc., where we correlate (based on years of experience) the outcome of these assessments with anticipated final test results. We will often modify our teaching in response to the data to modify the outcome. 13 Correlational ResearchDesign Models (Types) : Correlational ResearchDesign Models (Types) Explanatory Design: Research looks for simple associations between variables and investigates the extent to which the variables are related Prediction Design: Research designed to identify variables that will positively predict outcomes 14 Explanatory Design Model : Explanatory Design Model Key Characteristics of ERD Correlation of two or more variables Data collected at one time Single group At least two scores recorded Correlation Statistical Test- Strength and Direction of correlation determined Researcher draws conclusions from statistics alone 15 Prediction Design : Prediction Design Key Characteristics of PRD Author states that prediction capability is the goal of the research Use of predictor variable followed with a criterion variable Author forecasts future performance 16 Key Characteristics of Correlational Design : Key Characteristics of Correlational Design As suggested by the explanatory & prediction design, CR includes specific characteristics: Displays of scores (scatterplots & matrics) Associations between scores (direction, form, & strength) Multiple variable analysis (partial correlation & multiple regression) 17 Primary Tools for Correlation Designs : Primary Tools for Correlation Designs Mathematical Tools Product-Moment correlation coefficient Coefficient of determination Spearman rho Phi-coefficient Point-biserial correlation Regression lines Graphical Tools Scatter plots Correlation matrixes Simple graphical regressions Venn Diagrams 18 Graphical Tools: Scatter Plots : Graphical Tools: Scatter Plots Scatter plots plot two variables against one another to provide a visual picture of the relationship between the variables. (Warning-Connecting dots on a plot suggests control over the IV and defines a particular trend with outlying point being in error) PowerPoint presentation Of Scatter Plots 19 Simple Scatter Plot: Direction of Association : Simple Scatter Plot: Direction of Association 20 Forms of Association : Forms of Association A. Positive Linear (r=+.75) B. Negative Linear (r=-.68) 21 Forms of Association : Forms of Association F. Curvilinear E. Curvilinear 22 Correlation Matrix : Correlation Matrix Correlation matrixes chart the entire variable set against itself and display the coefficients for each permutation of the matrix. In other words the variances themselves for every combination of variables. 23 Correlation Matrix : Correlation Matrix Degree of Association: Determined as a -1.0 to 0 to 1.0 value where as the value 0 shows that there exists no correlation and a value of -1.0 or 1.0 shows a 100% correlation 24 Typical Correlation Matrix : Typical Correlation Matrix 1.School satisfaction 2. Extra-curricular activities 3. Friendship 4. Self-esteem 5. Pride in school 6. Self-awareness 1 2 3 4 5 6 - - - - - - -.33** .24 -.03 -.15 .65** .24* -.09 -.02 .49** .16 .29** -.02 .39** .03 .22 25 Simple Graphical Regression : Simple Graphical Regression Regression lines can be determined both mathematically or graphically and are and indication of the rate of change between two variables. This rate indicates the magnitude of effect one variable has upon another. 26 Simple Graphical Regression : Simple Graphical Regression Slope Depression Scores Regression Line Hours of Internet Use Per Week 14 15 20 10 5 50 41 40 30 20 10 Intercept 27 Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance : Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance Sometimes it is difficult to see all the relationships in a system by just staring at raw data. Plotting a Venn Diagram allows one to graphically represent the intersection of and thus the variance between multiple variables. 28 Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance : Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance Independent Variable Dependent Variable Time on Task Achievement r=.50 Time-on-Task Achievement r squared=(.50)2 Shared variance Bivariate Correlation: 29 Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance : Venn Diagrams and Multi-Variant SystemsCommon Variance vs. Partial Variance Independent Variable Dependent Variable Time on Task Achievement r=.50 r squared=(.50)2 Partial Correlations: use to determine extent to which a mediating variable influences both independent and dependent variable Motivation Time-on-Task Achievement Motivation r squared = (.35)2 30 Flow chart of a Correlational study : Flow chart of a Correlational study Determine if a correlational study best address the research problem Identify the individual study Identify two or more measure for each individual in this study Collect data and monitor potential threats Analyze the data and represent the results Interpret the results 31 Determine if a correlational study best address the research problem : Determine if a correlational study best address the research problem A study related to requiring the identification of the direction and degree of association between two sets of scores It is useful for identifying the types of association Need to explain in complex relationships of multiple factors When researchers use research questions 32 Identify the individual study : Identify the individual study Randomly select the individual/participants to generalize the result The group needs to be of adequate size for use of correlational statistics, such as N=30 33 Identify two or more measure for each individual in this study : Identify two or more measure for each individual in this study Identify two or more characteristics which will be compared of a group, measures of variables in the research questions need to be identified Instrument that measure the variables need to be obtained Instruments should have proven validity and reliability 34 Collect data and monitor potential threats : Collect data and monitor potential threats To administer the instruments and collect at least two sets of data from each individuals Researchers will be overly assured about threats of collecting data sets 35 Analyze the data and represent the results : Analyze the data and represent the results For data analyzing: Pearson’s correlation coefficient Partial correlation coefficient Multiple regression coefficient To represent result: correlational matrix of all variables as well as statistical table (for a regression study) reporting the R and R2 values and the beta weights for each variable 36 Interpret the results : Interpret the results In this step the results of this study are discussing the magnitude and the direction of correlation coefficient Interpretation will includes the impact of intervening variables in a correlational study Regression weight of variables in a regression analysis and developing a predictive equation for use in a predictive study 37 How do we evaluate a correlational Study : How do we evaluate a correlational Study To evaluate correlational study we might follow the criteria given below: Adequacy of sampling for hypothesis testing Display the results in matrices and graphs Assessment of the magnitude of the relationship based on the coefficent of determination, P values, effect size 38 How do we evaluate a correlational Study : How do we evaluate a correlational Study Form of relationships and appropriate statistics Identify predictor and criterion variables Predicted the direction of relationship among variables based on observed data Statistical procedures 39 Slide 40: 40 You do not have the permission to view this presentation. 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