3: Estimating Correlations

Question 1

______ is a statistical measure that quantifies the magnitude or strength of a relationship or difference between variables in a research study. It provides a standardized way to express the practical significance of a finding, independent of sample size. Effect size is particularly useful because it allows researchers to assess the real-world impact or importance of their results.

There are different types of ______ measures, depending on the nature of the analysis:

1. Hedges’ g: This is similar to Cohen’s d but is often used when dealing with small sample sizes.
2. Relative Risk (in epidemiology): This measures the likelihood of an event occurring in one group compared to another.
3. R-squared (in regression analysis): This indicates the proportion of variance in the dependent variable that can be explained by the independent variable(s).
4. Phi coefficient (in 2x2 contingency tables): This measures the strength of association between two categorical variables.
5. Odds ratio (in logistic regression): This is used in logistic regression to express the odds of an event occurring in one group compared to another.
6. Eta-squared (η²) and Omega-squared (ω²) (in ANOVA): These are used in analysis of variance (ANOVA) to quantify the proportion of variance in the dependent variable that is attributable to the independent variable(s).
7. Correlation coefficient (e.g., Pearson’s r): This measures the strength and direction of association between two continuous variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship, +1 indicates a perfect positive relationship, and 0 indicates no relationship.
8. Cohen’s d (for comparing means): This is commonly used in studies comparing the means of two groups. It quantifies the difference between the means in terms of standard deviation units.

Answer 1

Effect size

Question 2

Two most commonly used measures of effect size:

Answer 2

Cohen’s d and Pearson r

Question 3

It is used to characterize the differences in means between experimental groups.

Answer 3

Cohen’s d

Question 4

The correlation coefficient, typically used to characterize the degree to which one variable can be predicted from another.

Answer 4

Pearson’s r

Question 5

Cohen’s standards is a nonsensical but widely used interpretation of effect size. What are the set r values for small, medium, and large effects?

Answer 5

.10, .30, and .50

Question 6

It is a statistical measure used in meta-analysis, specifically for studies that involve binary outcomes (events that can occur or not occur). It quantifies the effect size by estimating the probability of success (or occurrence) in each group being compared.

It is particularly useful when dealing with proportions, percentages, or probabilities. It provides a way to express the effect size in a more interpretable and intuitive manner compared to other effect size measures.

For example, in a meta-analysis comparing the effectiveness of two treatments in curing a specific condition, it would estimate the probability of successful treatment for each group, allowing for a clearer understanding of the effect size in terms of probabilities. This can be especially useful in clinical and medical research.

Answer 6

Binomial Effect Size Display (BESD)

Question 7

______ Analysis:

1. Experimental Design:

a. Randomized Controlled Trials (RCTs): Participants are randomly assigned to different experimental conditions, allowing researchers to make causal inferences about the effects of the independent variable.

b. Quasi-Experimental Designs: Similar to RCTs, but lack complete randomization. Researchers use pre-existing groups or conditions and apply interventions.

2. Observational Studies:

a. Longitudinal Studies: Observe participants over an extended period, making it possible to assess causal relationships over time.

b. Cross-Sectional Studies: Observe participants at a single point in time, making it harder to establish causation.

3. Instrumental Variables (IV) Analysis:

a. Used when randomization is not possible. It involves identifying an “instrumental variable” that is correlated with the independent variable of interest but is not directly related to the dependent variable.

Answer 7

Causal

Question 8

____ Analysis:

1. Simplex Models:
   A basic form of path analysis that examines the direct relationships between variables in a linear model.
2. Recursive Models:
   A type of path analysis where variables are organized in a causal sequence, and the model assumes that causality flows in one direction.
3. Non-Recursive Models:
   These models allow for feedback loops, meaning variables can influence each other in a circular manner.
4. Mediation Models:
   Examines the process or mechanism through which an independent variable affects a dependent variable by including one or more mediator variables in the model.
5. Moderation Models:
   Tests whether the relationship between an independent variable and a dependent variable varies depending on the level of a third variable (the moderator).
6. Latent Variable Models:
   Involves the use of latent variables (unobserved constructs) and their relationships in a model.

Answer 8

Path

Question 9

Steps to _____:

a. Data Collection: Gather the data on the variables you want to analyze. Ensure the data is complete and representative of the population or sample.

b. Data Cleaning: Check for outliers, missing values, and potential errors. Clean the data to ensure accuracy in the analysis.

c. Choose the Appropriate Correlation Coefficient: Select the correlation coefficient based on the type of variables you have and the nature of the relationship you want to explore.

d. Compute the Correlation: Use statistical software like SPSS, R, Excel, or specialized tools to calculate the correlation coefficient.

e. Interpret the Correlation: Understand the value of the correlation coefficient. Positive values indicate a positive relationship, negative values indicate a negative relationship, and values closer to 0 indicate weaker correlations.

f. Significance Testing: Determine if the correlation is statistically significant. This helps assess whether the observed relationship is likely to exist in the population.

Answer 9

Estimate Correlations

Question 10

_____ Results:

1. Magnitude: The closer the correlation coefficient is to -1 or +1, the stronger the relationship.
2. Direction: Positive correlations imply that as one variable increases, the other tends to increase as well. Negative correlations indicate that as one variable increases, the other tends to decrease.
3. Statistical Significance: A correlation is statistically significant if the p-value is below a predetermined significance level (usually 0.05).
4. Scatterplot Visualization: Creating a scatterplot of the data can provide a visual representation of the relationship between variables.

Answer 10

Interpreting Correlation

Question 11

_____:

Correlation assumes a linear relationship between variables. Non-linear relationships may not be accurately captured.

Outliers can have a significant impact on correlation coefficients. It’s important to identify and address outliers appropriately.

Correlation does not imply causation. Establishing causation requires additional evidence and study design.

Answer 11

Assumptions and Considerations