Bivariate Correlational Research Notes

Chapter 8: Bivariate Correlational Research

Bivariate Correlation

• Definition of Correlation:

  • Correlation refers to the association between measured factors or variables.

• Key Consideration:

  • How many variables are being examined in bivariate correlation?

  • The focus is on 2 variables.

Interrogating Association Claims

• To assess the quality of association claims, consider the following questions:

  • Construct Validity:

  • How well was each variable measured?

  • Internal Validity:

  • Can we make a causal inference from an association?

  • Statistical Validity:

  • How well do the data support the conclusions?

  • External Validity:

  • To whom can the association be generalized?

Construct Validity

• To evaluate construct validity, ask the following:

  • How well was each of the variables measured?

  • Reliability of Measure:

  • Does the measure have good reliability?

  • Does it measure the same way each time under the same circumstances?

  • Validity of Measurement:

  • Is it measuring what it’s intended to measure?

Internal Validity

• Three criteria are essential for establishing causation:

  • Covariance:

  • Changes in one variable relate to changes in another.

  • Temporal Precedence:

  • The cause must precede the effect in time.

  • Internal Validity:

  • Control for third variable problems that may obscure causal links.

Test Yourself

• Example Case:

  • Mental illness is linked to lower socioeconomic status (SES).

  • What additional information is needed to determine whether mental illness is causing lower SES?

Statistical Validity

• When assessing statistical validity, consider the following factors:

  • Strength of the Relationship:

  • How strong is the relationship between the variables?

  • Precision of the Estimate:

  • How precise is the estimate?

  • Replicability:

  • Has it been replicated?

  • Outliers:

  • Could there be outliers affecting the association?

  • Restriction of Range:

  • Is there a restriction of range?

  • Nature of Association:

  • Is the association curvilinear?

How Strong is the Relationship?

• Effect Size:

  • Describes the strength of an association and indicates how well Y can predict X.

Effect Size Classification

• Weak Association:

  • Effect size of 0.1

• Moderate Association:

  • Effect size of 0.3

• Strong Association:

  • Effect size of 0.5 and above

• General Principle:

  • Larger effect sizes generally denote more significant effects.

How Precise is the Measurement: Confidence Intervals

• Confidence Interval:

  • Indicates the range within which we expect our measurements to fall, typically representing 95% confidence.

• Example of Car Repair Estimate:

  • Range of estimates: $200-$250 versus $200-$1500.

• Importance of Size:

  • Smaller confidence intervals indicate greater confidence in our sampling methods and measurement precision.

Has It Been Replicated?

• Multiple estimates should provide a more reliable result compared to a single estimate.

• The majority of estimates should be in agreement.

Could Outliers Be Affecting the Association?

• Outlier Definition:

  • An extreme score that is far removed from the rest of the data points.

• Considerations for Excluding Outliers:

  • Outliers may not represent the population effectively.

  • Outliers exert the most effect on correlation in smaller samples.

Is There a Restriction of Range?

• Definition:

  • A lack of a full range of scores, which can lead to a smaller apparent correlation.

  • Example:

  • Correlation A: 0.33

  • Correlation B: 0.57

Curvilinear and Inverted U-Shaped Relationships

• Correlation Coefficient:

  • A correlation coefficient of 0 indicates no linear relationship between variables.

• Visualization Importance:

  • It’s crucial to visualize your data to capture non-linear relationships.

External Validity

• Factors influencing external validity include:

  • Times:

  • People:

  • Places:

• Determining Generalizability:

  • Which factor (sampling size or sampling procedure) is more critical for external validity?

Learning Objectives

• By the end of the lecture students should be able to:

  • Determine the type of correlation (positive or negative) from examining a graph of data points.

  • Define construct validity.

  • Explain what it means for a measure to have good reliability.

  • Define and explain the three criteria for determining a causal relationship: covariance, temporal precedence, and internal validity.

  • Understand what effect size refers to and how to classify it for correlational studies.

  • Define what an outlier is and understand when it exerts the most effect on a correlation.

  • Define restriction of range and provide an example.

  • Explain what it means if a confidence interval contains zero.