I've been looking for a method to calculate the effect size for data of tactical behavior, which is measured by counting the frequency of actions in tactical principles. The omega squares (w2) is used to calculate effect size in desings without repeated measures. Do you know another method to calculate it?
Why not use the Mantel-Haenzel odds ratio for 2x2xk tables? Effect size,w (or sometimes called phi) are problematic for fixed margins. For a 1:1 cases to controls design, the maximum possible phi is 1/3 if the probability of the outcome of interest is 10%. The problem gets even worse for rarer events.
The strength of the association between the two unrelated nominal variables in a chi-square test of independence can be established by squaring the relevant association coefficient: the phi coefficient for 2x2 designs, Cramer’s V for multi-condition designs, or the contingency coefficient (Cramer C) for either type of design.
However, the chi-square test of independence is not applicable to related independent variables, such as repeated measures designs. Tests for related samples are applicable only to one-variable designs, in which the dependent variable is a binary category (eg. yes/no). The McNemar Change test and Sign Test are each applicable to two-condition comparisons of related samples, while the Cochran Q test is applicable to multiple-condition comparisons of related samples.
There are also three coefficients not directly related to the chi-square test which indicate the strength of the relationship between two nominal variables: the tetrachoric correlation coefficient (which assesses the relationship between two dichotomous nominal variables with an underlying quantitative distribution); and the uncertainty and lambda association coefficients (which are asymmetric, i.e. each produce 3 coefficients). Lastly, loglinear analysis is a chi-square-related test for assessing the strength of the relationship between multiple nominal variables.
Follow the link please.... it is in page 260-263
http://books.google.com.bd/books?id=QId2AgAAQBAJ&pg=PA260&lpg=PA260&dq=effect+size+in+mcnemar%27s+test&source=bl&ots=dj2En4QViL&sig=c0hxLJ2WKkpEXUhgEuSx2ZY3WM0&hl=en&sa=X&ei=7T_RU97XHYz18QWD1oKACQ&ved=0CFcQ6AEwCDgK#v=onepage&q=effect%20size%20in%20mcnemar's%20test&f=false
Chi square is the most commonly used test in Inferential statististics and can be used to test Effect Size. effect Size can be used to perform Power analysis.
There are serious problems with using the chi-square coefficient as an effect size measure. In theory, it is bounded by [-1, 1] but the maximum correlations are only possible for equal marginal probabilities. Note that w, phi and the chi-square coefficient are identical for 2x2 tables. I published the following paper where we discuss these and other issues.
If you have two time points, McNemar's test is a possibility and there are two possible effect sizes. McNemar's is an exact binomial test (the chi-square test given is an approximate test) with test statistic P=b/(b+c). Cohen proposed effect sizes for proportions of g=P-0.5 and values of 0.05, 0.15 and 0.25 as small, medium and large.
You can also use the odds ratio from McNemar's test. This comes about by representing unique combinations as a 2x2x4 table and computing the Mantel-Haenszel summary odds ratio. The results simplify to OR=b/c and the results from our paper are equivalent for this situation. So, recommendations of 1.22, 1.86 and 3.00 for small, medium and large can be used.
The recommendations given in the link arise from converting the correlation phi to an odds ratio from a 2x2 table where each marginal probability is 0.5. This is probably OK for one of the margins as it corresponds to a 1:1 case-control allocation (or 1:1 treatment to placebo). However, it also means the outcome of interest has prevalence 0.5. To put it bluntly, this means half of patients need to die, when the outcome is mortality, to achieve this range of odds ratios.
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0058777
Thanks everyone. Is it possible to perform these calculations on SPSS software? I usually perform chi-square tests in there, but I couldn't find a comand to check the effect size (for partial eta square, in ANOVA designs, this is relatively simple).
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Techniques
- Meta-Analysis