Research Methods: Bivariate Correlation - Cengage, PDF

Chapter 12 The Correlational Research Study Bivariate Correlations Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved....

Chapter 12 The Correlational Research Study Bivariate Correlations Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  12.1 An Introduction to Correlational Research Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Review: Goals of the Scientific Approach o Describe behavior What happens? o Predict behavior What varies with what? o Explain behavior What causes what? Enables control of behavior Copyright @ Wan Wang  Types of Research o Describe behavior What happens? Descriptive research (survey, naturalistic observations, case studies) Does not assess relationship o Predict behavior What varies with what? Correlational research o Explain behavior What causes what? Enables control of behavior Experimental research Copyright @ Wan Wang  Introduction What is the goal of the correlational research strategy? – To establish that a relationship exists between variables and to describe the nature of the relationship  Relationships can be described—not explained  There is no attempt to manipulate, control, or interfere with the variables Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  12.3 Applications of the Correlational Strategy Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Prediction A correlational study demonstrating a relationship between two variables – Allows researchers to use knowledge about one variable to help predict or explain the second variable The two variables – Predictor variable: the first variable – Criterion variable: the second variable (being explained or predicted) – Regression: to find the equation that produces the most accurate predictions of Y (the criterion variable) for each value of X (the predictor variable) Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Reliability and Validity and Evaluating Theories Both reliability and validity – Commonly defined by relationships that are established using the correlational research design Correlational research design can be used to address many theoretical questions. – For example, correlational studies of IQs of identical twins Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 12.2 The Data and Statistical Analysis for Correlational Studies Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Calculating a Correlation Coefficient A correlation coefficient measures and describes the relationship between two variables. – It describes three characteristics of a relationship:  Direction  Form  Consistency or strength Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Copyright @ Wan Wang  The Direction of the Relationship Positive relationship: two variables change in the same direction. – As one variable increases ► the other variable increases. Negative relationship: two variables change in opposite directions. – As one variable increases ► the other variable decreases. Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  The Form of the Relationship Linear relationship: the data points in the scatter plot tend to cluster around a straight line. – Positive linear relationship: each time the X variable increases by one point, the Y variable increases in a consistently predictable amount.  A Pearson correlation describes and measures linear relationships when both variables are numerical scores from interval or ratio scales. Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Linear and Monotonic Relationships Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Quantitative vs. Categorical Variables o Quantitative: meaningful numerical value Scores on rating scales (well-being, self-esteem), percentages Lower to higher; less to more Discrete or continuous o Categorical: qualitatively distinct category Numerical value assigned to categories are arbitrary Meeting location of spouses, major, Netflix categories, marital status, etc. Discrete Copyright @ Wan Wang  Column Depiction of Data Copyright @ Wan Wang  Visual Depictions of Data Copyright @ Wan Wang  Describing Associations: When both variables are quantitative. o Correlation Coefficient Pearson’s r Two variables at the ratio or interval level Spearman’s rank-order r Two variables at the ordinal level Point-biserial r One dichotomous (2 categories) variable with one continuous variable Copyright @ Wan Wang  Evaluating Relationships for Non-Numerical Scores from Nominal Scales If both variables are non-numerical – Evaluate by organizing the data in a matrix  Categories of one variable form the rows; categories of the second variable form the columns.  Apply the chi-square test Succeed Fail College Graduate 17 3 No College 12 8 Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  How Accurate were you in your estimate? Remember this? Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Confidence Interval - How precise is the estimate? o r is a point estimate. o 95% CI may include the true population correlation o Precision: narrower CI 95% CI [-.07, -.64] vs. 95% CI [.05,.07] Copyright @ Wan Wang  Sample Size and Precision o Small sample size Unstable estimate of effect size r =.37, 95% CI [-.07, -.64] – wider CI Implication for future studies? -.06,.01, -.47…all possible o Large sample size More stable estimate of effect size r =.06, 95% CI [.05,.07] – narrower CI Implication for future studies? Copyright @ Wan Wang  Statistical Significance (Extremely simplified) o Broadly: The likelihood that the association is not due to chance. o p-value The likelihood that the sample’s association came from a population in which there is no association Significant: p <.05 (5%) Unlikely Non-significant: p =.05 or p >.05 Likely Effect Size & DO NOT only rely on p-values Confidence Interval matter! Copyright @ Wan Wang  CIs and Statistical Significance o When the 95% CI does not include zero E.g., r =.31, 95% CI [.24,.38] The result is statistically significant (p <.05) The correlation found in the sample is unlikely to have come from a population in which the association is zero. o When the 95% CI includes zero E.g., r =.02, 95% CI [-.32,.34] Not statistically significant; non-significant (p >.05) Cannot rule out: true population correlation is zero. Copyright @ Wan Wang  Effect Size - How strong is the relationship? o The magnitude, or strength, of a relationship between two or more variables. o Correlation coefficient r Cohen’s d: difference between two means R-squared (R2): based on proportion of variance shared by two or more variables We are just here to say “hello”. Don’t be scared of us  Copyright @ Wan Wang  Interpreting and Statistically Evaluating a Correlation Interpreting and Statistically Evaluating a Correlation – Coefficient of determination: the squared value of a correlation – Measures the percentage of variability in one variable that is determined, or predicted, by its relationship with the other variable Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Effect Size, Significance, Sample Size o Larger or moderate effect size (i.e., stronger association) More likely to be statistically significant o A very small effect Might be statistically significant for a large sample o Small samples Easily influenced by chance events Copyright @ Wan Wang 12.4 Strengths and Weaknesses of the Correlational Research Strategy Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Strengths Describes relationships between variables Nonintrusive—natural behaviors High external validity Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Weaknesses of the Correlational Research Strategy Weaknesses – Cannot assess causality – Third-variable problem – Directionality problem – Low internal validity Gravetter | Forzano, Research Methods Behavioral Sciences, 6th Edition. © 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Outliers o An extreme or highly unusual score A score that is highly deviant from the rest of the data o Can have big impact on correlation coefficient Online outliers inflate correlation coefficient Offline outliers attenuate correlation coefficient Copyright @ Wan Wang  Outliers and Sample Size r =.37 r =.49 r =.26 r =.15 Copyright @ Wan Wang  Outliers o How to detect? Scores + or – 3 Standard Deviations (SDs) from the mean Or Median Absolute Deviation (MAD) (Leys et al., 2013) o How to handle? (report in manuscript) Remove from the dataset before inferential statistical analysis Keep in the dataset and recode with values equal to that of 3SDs from the mean Preferences of handling outliers may differ Must take some actions to deal with Copyright @ Wan Wang outliers  Restriction of Range (Restricted Range) o When sample under study does not include the full range of the variables o Sample is relatively homogenous for one of the variables. o The apparent association between the variables can be greatly reduced. Copyright @ Wan Wang  Restriction of Range o Recruit more people r =.33 o Statistical correction r =.57 Copyright @ Wan Wang  Learning Check o Which of the following is true of restriction of range? A. We should inspect the possibility of restriction of range if a weak correlation is observed. B. It is likely to occur if both variables have high variability. C. It overestimates the actual correlation. D. It is likely to occur in large samples. Copyright @ Wan Wang  Curvilinear Association o The relationship between two variables isn’t a straight line. r = 0 o In contrast, linear association can be described by a straight line. Copyright @ Wan Wang  Learning Check o Data shows that performance increases with arousal up to a point, but beyond that, performance decreases while arousal increases. Which type of relationship is this? A. zero B. curvilinear C. positive D. negative Copyright © Wan Wang