Entry
Reader's guide
Entries A-Z
Subject index
Intraclass Correlation
The words intraclass correlation (ICC) refer to a set of coefficients representing the relationship between variables of the same class. Variables of the same class share a common metric and variance, which generally means that they measure the same thing. Examples include twin studies and two or more raters evaluating the same targets. ICCs are used frequently to assess the reliability of raters. The Pearson correlation coefficient usually relates measures of different classes, such as height and weight or stress and depression, and is an interclass correlation.
| Table 1 Data on Sociability of Dyads of Gay Couples | ||||||||
|---|---|---|---|---|---|---|---|---|
| Couple | Partner 1 | Partner 2 | Couple | Partner 1 | Partner 2 | Couple | Partner 1 | Partner 2 |
| 1 | 18 | 15 | 6 | 30 | 21 | 11 | 40 | 43 |
| 2 | 21 | 22 | 7 | 32 | 28 | 12 | 41 | 28 |
| 3 | 24 | 30 | 7 | 35 | 37 | 13 | 42 | 37 |
| 4 | 25 | 24 | 9 | 35 | 31 | 14 | 44 | 48 |
| 5 | 26 | 29 | 10 | 38 | 25 | 15 | 48 | 50 |
Most articles on ICC focus on the computation of different ICCs and their tests and confidence limits. This entry focuses more on the uses of several different ICCs.
The different ICCs can be distinguished along several dimensions:
- One-way or two-way designs
- Consistency of order of rankings by different judges, or agreement on the levels of the behavior being rated
- Judges as a fixed variable or as a random variable
- The reliability of individual ratings versus the reliability of mean ratings over several judges
One-Way Model
Although most ICCs involve two or more judges rating n objects, the one-way models are different. A theorist hypothesizing that twins or gay partners share roughly the same level of sociability would obtain sociability data on both members of 15 gay couples from a basic sociability index. A Pearson correlation coefficient is not appropriate for these data because the data are exchangeable within couples—there is no logical reason to identify one person as the first member of the couple and the other as the second. The design is best viewed as a one-way analysis of variance with “couple” as the independent variable and the two measurements within each couple as the observations. Possible data are presented in Table 1. With respect to the dimensions outlined previously, this is a one-way design. Partners within a couple are exchangeable, and thus a partner effect would have no meaning. Because there is no partners effect, an ICC for consistency cannot be obtained, but only an ICC can be obtained for agreement. Within a couple, partner is a fixed variable—someone's partner can not be randomly select. Finally, there is no question about averaging across partners, so the reliability of an average is not relevant. (In fact, “reliability” is not really the intent.)
Table 2 gives the expected mean squares for a one-way analysis of variance. The partner effect can not be estimated separately from random error.
If each member of a couple had nearly the same score, there would be little within-couple variance, and most of the variance in the experiment would be a result of differences between couples. If members of a dyad differed considerably, the within-couple variance would be large and predominate. A measure of the degree of relationship represents the proportion (ρ) of the variance that is between couple variance. Therefore,
The appropriate estimate for ρICC, using the obtained mean squares (MS), would be
For this sample data, the analysis of variance summary table is shown in Table 3.
...
- Descriptive Statistics
- Distributions
- Graphical Displays of Data
- Hypothesis Testing
- Alternative Hypotheses
- Beta
- Critical Value
- Decision Rule
- Hypothesis
- Nondirectional Hypotheses
- Nonsignificance
- Null Hypothesis
- One-Tailed Test
- p Value
- Power
- Power Analysis
- Significance Level, Concept of
- Significance Level, Interpretation and Construction
- Significance, Statistical
- Two-Tailed Test
- Type I Error
- Type II Error
- Type III Error
- Important Publications
- “Coefficient Alpha and the Internal Structure of Tests”
- “Convergent and Discriminant Validation by the Multitrait-Multimethod Matrix”
- “Meta-Analysis of Psychotherapy Outcome Studies”
- “On the Theory of Scales of Measurement”
- “Probable Error of a Mean, The”
- “Psychometric Experiments”
- “Sequential Tests of Statistical Hypotheses”
- “Technique for the Measurement of Attitudes, A”
- “Validity”
- Aptitudes and Instructional Methods
- Doctrine of Chances, The
- Logic of Scientific Discovery, The
- Nonparametric Statistics for the Behavioral Sciences
- Probabilistic Models for Some Intelligence and Attainment Tests
- Statistical Power Analysis for the Behavioral Sciences
- Teoria Statistica Delle Classi e Calcolo Delle Probabilità
- Inferential Statistics
- Association, Measures of
- Coefficient of Concordance
- Coefficient of Variation
- Coefficients of Correlation, Alienation, and Determination
- Confidence Intervals
- Margin of Error
- Nonparametric Statistics
- Odds Ratio
- Parameters
- Parametric Statistics
- Partial Correlation
- Pearson Product-Moment Correlation Coefficient
- Polychoric Correlation Coefficient
- Q-Statistic
- R2
- Randomization Tests
- Regression Coefficient
- Semipartial Correlation Coefficient
- Spearman Rank Order Correlation
- Standard Error of Estimate
- Standard Error of the Mean
- Student's t Test
- Unbiased Estimator
- Weights
- Item Response Theory
- Mathematical Concepts
- Measurement Concepts
- Organizations
- Publishing
- Qualitative Research
- Reliability of Scores
- Research Design Concepts
- Aptitude-Treatment Interaction
- Cause and Effect
- Concomitant Variable
- Confounding
- Control Group
- Interaction
- Internet-Based Research Method
- Intervention
- Matching
- Natural Experiments
- Network Analysis
- Placebo
- Replication
- Research
- Research Design Principles
- Treatment(s)
- Triangulation
- Unit of Analysis
- Yoked Control Procedure
- Research Designs
- A Priori Monte Carlo Simulation
- Action Research
- Adaptive Designs in Clinical Trials
- Applied Research
- Behavior Analysis Design
- Block Design
- Case-Only Design
- Causal-Comparative Design
- Cohort Design
- Completely Randomized Design
- Cross-Sectional Design
- Crossover Design
- Double-Blind Procedure
- Ex Post Facto Study
- Experimental Design
- Factorial Design
- Field Study
- Group-Sequential Designs in Clinical Trials
- Laboratory Experiments
- Latin Square Design
- Longitudinal Design
- Meta-Analysis
- Mixed Methods Design
- Mixed Model Design
- Monte Carlo Simulation
- Nested Factor Design
- Nonexperimental Design
- Observational Research
- Panel Design
- Partially Randomized Preference Trial Design
- Pilot Study
- Pragmatic Study
- Pre-Experimental Designs
- Pretest-Posttest Design
- Prospective Study
- Quantitative Research
- Quasi-Experimental Design
- Randomized Block Design
- Repeated Measures Design
- Response Surface Design
- Retrospective Study
- Sequential Design
- Single-Blind Study
- Single-Subject Design
- Split-Plot Factorial Design
- Thought Experiments
- Time Studies
- Time-Lag Study
- Time-Series Study
- Triple-Blind Study
- True Experimental Design
- Wennberg Design
- Within-Subjects Design
- Zelen's Randomized Consent Design
- Research Ethics
- Research Process
- Clinical Significance
- Clinical Trial
- Cross-Validation
- Data Cleaning
- Delphi Technique
- Evidence-Based Decision Making
- Exploratory Data Analysis
- Follow-Up
- Inference: Deductive and Inductive
- Last Observation Carried Forward
- Planning Research
- Primary Data Source
- Protocol
- Q Methodology
- Research Hypothesis
- Research Question
- Scientific Method
- Secondary Data Source
- Standardization
- Statistical Control
- Type III Error
- Wave
- Research Validity Issues
- Bias
- Critical Thinking
- Ecological Validity
- Experimenter Expectancy Effect
- External Validity
- File Drawer Problem
- Hawthorne Effect
- Heisenberg Effect
- Internal Validity
- John Henry Effect
- Mortality
- Multiple Treatment Interference
- Multivalued Treatment Effects
- Nonclassical Experimenter Effects
- Order Effects
- Placebo Effect
- Pretest Sensitization
- Random Assignment
- Reactive Arrangements
- Regression to the Mean
- Selection
- Sequence Effects
- Threats to Validity
- Validity of Research Conclusions
- Volunteer Bias
- White Noise
- Sampling
- Cluster Sampling
- Convenience Sampling
- Demographics
- Error
- Exclusion Criteria
- Experience Sampling Method
- Nonprobability Sampling
- Population
- Probability Sampling
- Proportional Sampling
- Quota Sampling
- Random Sampling
- Random Selection
- Sample
- Sample Size
- Sample Size Planning
- Sampling
- Sampling and Retention of Underrepresented Groups
- Sampling Error
- Stratified Sampling
- Systematic Sampling
- Scaling
- Software Applications
- Statistical Assumptions
- Statistical Concepts
- Autocorrelation
- Biased Estimator
- Cohen's Kappa
- Collinearity
- Correlation
- Criterion Problem
- Critical Difference
- Data Mining
- Data Snooping
- Degrees of Freedom
- Directional Hypothesis
- Disturbance Terms
- Error Rates
- Expected Value
- Fixed-Effects Models
- Inclusion Criteria
- Influence Statistics
- Influential Data Points
- Intraclass Correlation
- Latent Variable
- Likelihood Ratio Statistic
- Loglinear Models
- Main Effects
- Markov Chains
- Method Variance
- Mixed- and Random-Effects Models
- Models
- Multilevel Modeling
- Odds
- Omega Squared
- Orthogonal Comparisons
- Outlier
- Overfitting
- Pooled Variance
- Precision
- Quality Effects Model
- Random-Effects Models
- Regression Artifacts
- Regression Discontinuity
- Residuals
- Restriction of Range
- Robust
- Root Mean Square Error
- Rosenthal Effect
- Serial Correlation
- Shrinkage
- Simple Main Effects
- Simpson's Paradox
- Sums of Squares
- Statistical Procedures
- Accuracy in Parameter Estimation
- Analysis of Covariance (ANCOVA)
- Analysis of Variance (ANOVA)
- Barycentric Discriminant Analysis
- Bivariate Regression
- Bonferroni Procedure
- Bootstrapping
- Canonical Correlation Analysis
- Categorical Data Analysis
- Confirmatory Factor Analysis
- Contrast Analysis
- Descriptive Discriminant Analysis
- Discriminant Analysis
- Dummy Coding
- Effect Coding
- Estimation
- Exploratory Factor Analysis
- Greenhouse-Geisser Correction
- Hierarchical Linear Modeling
- Holm's Sequential Bonferroni Procedure
- Jackknife
- Latent Growth Modeling
- Least Squares, Methods of
- Logistic Regression
- Mean Comparisons
- Missing Data, Imputation of
- Multiple Regression
- Multivariate Analysis of Variance (MANOVA)
- Pairwise Comparisons
- Path Analysis
- Post Hoc Analysis
- Post Hoc Comparisons
- Principal Components Analysis
- Propensity Score Analysis
- Sequential Analysis
- Stepwise Regression
- Structural Equation Modeling
- Survival Analysis
- Trend Analysis
- Yates's Correction
- Statistical Tests
- Bartlett's Test
- Behrens-Fisher t′ Statistic
- Chi-Square Test
- Duncan's Multiple Range Test
- Dunnett's Test
- F Test
- Fisher's Least Significant Difference Test
- Friedman Test
- Honestly Significant Difference (HSD) Test
- Kolmogorov-Smirnov Test
- Kruskal-Wallis Test
- Mann-Whitney U Test
- Mauchly Test
- McNemar's Test
- Multiple Comparison Tests
- Newman-Keuls Test and Tukey Test
- Omnibus Tests
- Scheffé Test
- Sign Test
- t Test, Independent Samples
- t Test, One Sample
- t Test, Paired Samples
- Tukey's Honestly Significant Difference (HSD)
- Welch's t Test
- Wilcoxon Rank Sum Test
- z Test
- Theories, Laws, and Principles
- Bayes's Theorem
- Central Limit Theorem
- Classical Test Theory
- Correspondence Principle
- Critical Theory
- Falsifiability
- Game Theory
- Gauss-Markov Theorem
- Generalizability Theory
- Grounded Theory
- Item Response Theory
- Occam's Razor
- Paradigm
- Positivism
- Probability, Laws of
- Theory
- Theory of Attitude Measurement
- Weber-Fechner Law
- Types of Variables
- Validity of Scores
- Loading...
Get a 30 day FREE TRIAL
-
Watch videos from a variety of sources bringing classroom topics to life -
Read modern, diverse business cases
-
Explore hundreds of books and reference titles
Read next
More like this
Sage Recommends
We found other relevant content for you on other Sage platforms.
Have you created a personal profile? Login or create a profile so that you can save clips, playlists and searches