Effect size and eta squared |
James Dean Brown University of Hawai'i at Manoa |
Source | SS | df | MS | F | p | eta2 | Power |
Anxiety | 0.08 | 1 | 0.08 | 0.02 | 0.90 | 0.0012 | 0.05 |
Tension | 2.08 | 1 | 2.08 | 0.38 | 0.55 | 0.0324 | 0.09 |
Anxiety x Tension | 18.75 | 1 | 18.75 | 3.46 | 0.10 | 0.2919 | 0.37 |
Error | 43.33 | 8 | 5.42 | 0.6745 | |||
Total | 64.24 | 12 |
[ p. 38 ]
Anxiety | Tension | M | SD | N |
1 | 1 | 8.67 | 3.06 | 3 |
2 | 7.00 | 2.65 | 3 | |
2 | 1 | 6.00 | 2.00 | 3 |
2 | 9.33 | 1.16 | 3 |
[ p. 39 ]
Thus there is a strong pattern but it is not consistent across Anxiety 1 and 2 conditions (if it were consistent, the lines would be parallel). Thus, even with a non-significant interaction (where p = .10), the eta2 value of .2919 drew our attention to an important interaction effect that is revealing in itself, and which may help to understand why there were no significant main effects for Tension or Anxiety (i.e., because the interaction cancels out any such differences)."One problem with eta2 is that the magnitude of eta2 for each particular effect depends to some degree on the significance and number of other effects in the design" |
[ p. 40 ]
Source | SS | df | MS | F | p |
Between Subjects | |||||
Prompt Set | 158.372 | 9 | 17.597 | 9.703 | 0.00 |
Error | 3068.553 | 1692 | 1.814 | ||
Within Subjects | |||||
Topic Type | 0.344 | 1 | 0.344 | 0.194 | 0.66 |
Prompt Set by Topic Type | 137.572 | 9 | 15.286 | 8.611 | 0.00 |
Error | 3003.548 | 1692 | 1.775 |
Source | SS | df | MS | F | p | Partial eta2 |
Between Subjects | ||||||
Prompt Set | 158.372 | 9 | 17.597 | 9.703 | 0.00 | 0.0490 |
ErrorBS | 3068.553 | 1692 | 1.814 | |||
Within Subjects | ||||||
Topic Type | 0.344 | 1 | 0.344 | 0.194 | 0.66 | 0.0490 |
Prompt Set by Topic Type | 137.572 | 9 | 15.286 | 8.611 | 0.00 | 0.0438 |
ErrorWS | 3003.548 | 1692 | 1.775 |
[ p. 41 ]
These partial eta2 values are easy to calculate. Simply divide the SS for each effect by the SS of that effect plus the SS for the error associated with that effect. The results will be as follows:"Reporting the traditional ANOVA source table (with SS, df, MS, F, and p) and discussing the associated significance levels isn't the end of the study; it's just the beginning . . ." |
[ p. 42 ]
Brown, J. D. (2007). Statistics Corner. Questions and answers about language testing statistics: Sample size and power. Shiken: JALT Testing & Evaluation SIG Newsletter, 11(1), 31-35. Also retrieved from the World Wide Web at http://jalt.org/test/bro_25.htmWhere to Submit Questions: |
Please submit questions for this column to the following address: |
JD Brown Department of Second Language Studies University of Hawai'i at Manoa 1890 East-West Road Honolulu, HI 96822 USA |
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