#srot

Bollen, K. A., & Long, J. S. (1993). Testing structural equation models (Vol. 154). Sage. 

Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural equation modeling, 14(3), 464-504.

Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural equation modeling, 9(2), 233-255. 

The scales of magnitude are taken from Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates (see also here). The scales of magnitude for partial ω2 are taken from Table 2.2 of Murphy and Myors (2004).There is also a table of effect size magnitudes at the back of Kotrlik JW and Williams HA (2003) here. An overview of commonly used effect sizes in psychology is given by Vacha-Haase and Thompson (2004).

Kraemer and Thiemann (1987, p.54 and 55) use the same effect size values (which they call delta) for both intra-class correlations and Pearson correlations. This implies the below rules of thumb from Cohen (1988) for magnitudes of effect sizes for Pearson correlations could also be used for intra-class correlations. It should be noted, however, that the intra-class correlation is computed from a repeated measures ANOVA whose usual effect size (given below) is partial eta-squared. In addition, Shrout and Fleiss (1979) discuss different types of intra-class correlation coefficient and how their magnitudes can differ.

The general rules of thumb given by Cohen are for eta-squared, which uses the total sum of squares in the denominator, but these would arguably apply more to partial eta-squared than to eta-squared. This is because partial eta-squared in factorial ANOVA arguably more closely approximates what eta-squared would have been for the factor had it been a one-way ANOVA and it is presumably a one-way ANOVA which gave rise to Cohen's rules of thumb.

CLICK HERE FOR Effect Sizes Table Rules of Thumb Table

References

Cohen, J. (1988) Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

Field, A. (2013) Discovering statistics using IBM SPSS Statistics. Fourth Edition. Sage:London.

Green, SB, Salkind, NJ & Akey, TM (1997). Using SPSS for Windows:Analyzing and understanding data. Upper Saddle River, NJ:

Haddock, CK, Rinkdskopf, D. & Shadish, C. (1998) Using odds ratios as effect sizes for meta-analysis of dichotomous data: A primer on methods and issues. Psychological Methods 3 339-353.

Howell, DC (2013). Statistical methods for psychology. 8th Edition. International Edition. Wadsworth:Belmont,CA.

Kotrlik, JW and Williams, HA (2003) The incorporation of effect size in information technology, learning, and performance research. Information Techology, Learning, and Performance Journal 21(1) 1-7.

Kraemer HC and Thiemann S (1987) How many subjects? Statistical power analysis in research. Sage:London. In CBSU library.

Murphy KR and Myors B (2004) Statistical power analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests (2nd ed.). Lawrence Erlbaum, Mahwah NJ. (Alternative rule s of thumb for effect sizes to those from Cohen are given here in Table 2.2).

Preacher, KJ and Kelley, K (2011) Effect size measures for mediation models: quantitative strategies for communicating indirect effects. Psychological Methods 16(2) 93-115.

Shrout, PE and Fleiss, JL (1979) Intraclass Correlations: Uses in Assessing Rater Reliability, Psychological Bulletin, 86 (2) 420-428. (A good primer showing how anova output can be used to compute ICCs).

Tabachnick, BG and Fidell, LS (2007) Using multivariate statistics. Fifth Edition. Pearson Education:London.

Vacha-Haase, T and Thompson, B (2004) How to estimate and interpret various effect ssizes. Journal of Counseling Psychology 51(4) 473-481.