Eta-squared
A variance-explained effect size for ANOVA designs. Eta-squared (η²) is the proportion of total variance in the dependent variable accounted for by an independent variable, computed as SS_effect / SS_total. Values range from 0 to 1, where 0 indicates no variance explained by the factor and 1 indicates that the factor accounts for all observed variance.
Partial Eta-squared
Partial η² (η²_p) is the dominant variant reported by SPSS and most published L2 ANOVA tables. It is defined as SS_effect / (SS_effect + SS_error), removing variance attributable to other factors from the denominator. In a one-way design η² and η²_p are identical; in factorial designs they diverge, with η²_p typically larger because the denominator excludes other systematic sources of variance. Partial values from different studies and different designs are not directly comparable, a point Larson-Hall (2016) and Field (2018) both emphasise.
Cohen's Benchmarks
Cohen (1988) suggested rough η² thresholds of 0.01 small, 0.06 medium, and 0.14 large, derived from the relationship between η² and his f index. As with Cohen's d, these are conventions for fields without empirical norms.
L2-Specific Benchmarks
Plonsky and Oswald (2014) report observed-in-the-literature distributions of η² in L2 research and recommend treating values around .06 as small, .16 as medium, and .36 as large in this field — substantially higher than Cohen's general guidelines, because typical SLA studies report inflated variance-explained estimates due to small samples and design constraints.
Cautions
η² is upwardly biased, particularly in small samples; omega-squared (ω²) and epsilon-squared (ε²) are less biased alternatives but rarely reported in applied linguistics. Reviews now recommend pairing any η² with a Confidence Interval and being explicit about whether the reported value is η² or partial η². For pairwise comparisons within a significant ANOVA, Cohen's d or Hedges' g gives more directly interpretable mean-difference information.
References
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Plonsky, L., & Oswald, F. L. (2014). How big is "big"? Interpreting effect sizes in L2 research. Language Learning, 64(4), 878–912.
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). London: Sage.
- Larson-Hall, J. (2016). A Guide to Doing Statistics in Second Language Research Using SPSS and R (2nd ed.). New York: Routledge.