How to calculate the effect size if the chi-square value crosses the total sample size?
For example, the d value for phi coefficient value of 0.999 is 44.6878 and 1 or greater than 1 is showing infinitive. Then how do continue with the process?
can anyone give the answer?
Thanking You
Please see the link below
https://www.campbellcollaboration.org/escalc/html/EffectSizeCalculator-SMD16.php
Hello Vinu,
First, do note that correlation statistics (quantified as r, phi, rho, eta-squared, etc.) are perfectly acceptable ES metrics.
If you're asking, how to convert a correlation = |1| to the ES metric of Cohen's d, the value is indeterminate (as your query implies). In this scenario, I'd substitute a value such as .99 or .999, and go from there.
If you're asking, how does one obtain a phi value > 1 from a chi-square test of independence, then I believe the answer is, it's not from an ordinary contingency table application of chi-square, but rather something else. Using a 2 x 2 table as an example, you can show that the maximum possible chi-square = N (which implies a phi coefficient of |1|).
Good luck with your work.
Thank You David Morse for the clarity.
I am a beginner in the meta-analysis, the actual issue is chi-square goodness of fit value of 2049.274 for the alternatives hardly improved- 79, moderately improved- 284 and drastically improved- 158 in a total sample of 1944. I have calculated effect size using φ = √(X2 / n), but it is only valid for 2X2 (a table with exactly two rows and two columns).
Can you suggest any other method to find the effect size for this particular problem?
Is it possible to do a meta-analysis of these similar data?
Hello again Vinu,
Goodness-of-fit tests are really, "badness of fit" tests, in that large chi-squared values imply poor correspondence of observations to hypothesized values. Moreover, they are sensitive to sample size, such that as N increases, the statistical power of such tests (to detect departures from the hypothesized values) increases as well. If this is for checking some assumptions, then treating it as an ES isn't typical or particularly informative to most inquiries. If what you're trying to aggregate is, say, model-data fit for SEM model studies, I'd stay far away from the chi-square test and instead favor an indicator that was independent of N, such as RMSR.
If you could explain more fully: (a) the specific goal of the meta-analysis; (b) what role the G-O-F test is intended to fulfill in that quest; and (c) give an example or two of study outcomes that are consistent with the specific goal, I'd wager you would get a lot more focused response.
Good luck with your work.
Hi Dr Vinu Vijayakumar . I hope the following link could help you:
https://www.mtholyoke.edu/courses/etownsle/qr/Chi%20square%20limitations.htm
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