Hello Sundus,

Is your intended purpose to evaluate the collective/aggregate probability of the set of 10 study results? If so, you could:

1. Convert the chi-square of each individual study to a phi coefficient, and estimate a weighted average for the correlation (r or phi) between lung status and smoking status, along with confidence intervals for both the individual studies and the weighted average correlation. A lot of freely available meta-analytic programs can help with this. Here is a link that describes a number of them: https://toptipbio.com/free-meta-analysis-software/

2. Use Fisher's method for combining independent outcomes (sometimes included in meta-analysis software, but pretty simple to evaluate on its own). For each study, take the natural logarithm (ln) of the probability (p-value) from testing the observed chi-square for the study. Sum across studies, then multiply by -2.

e.g., -2 * sum(ln(p))

Then, to test whether the aggregate probability is significant, treat this value as a chi-square with 2 * k df, where k is the number of study values combined. Using Excel, you can compute the tail probability of prob>chi-square via: =1 - chisq.dist(chi_value, df_value, TRUE).

If all you wanted to do was to pool all of the 2 x 2 table frequencies into a single table to determine an "overall, weighted" chi-square, you could do that as well. However, that won't give you any insight as to how variable results were from study to study.

There's lots of freely available software for computing chi-square other than the example in your included screen display.

Finally, a minor semantics correction; it appears you have 1 IV (with two levels) and 1 DV (with two levels). This type of data table is frequently called a "2 x 2" table.

Good luck with your work.

David Morse Thank you, for such an elaborate answer and correction about levels of variables.

Like David Morse, I think you have ten 2x2 tables, one for each study, and you want to estimate the pooled effect of smoking status on type of cancer. Old school epidemiologists would use the Mantel-Haenzel method to do that, but logistic regression gives virtually identical results--and so does standard meta-analysis.

What software do you have access to through your university?

Can you share the data?

@Bruce Weaver, Thanks. You are right.

Logistic Regression solved the matter.

Using CMA.