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Methods focused on contrasting and combining results from different studies, in the hope of increasing precision and external validity.

-1 votes
2 answers
99 views

Why Euclidean norm was used in Z-score combination?

The formula for the Z-score combination is, $$ Z_w = \frac{\sum_{i=1}^k w_i Z_i}{\sqrt{\sum_{i=1}^k w_i^2}} $$ Euclidean norm was used as the dividend. Why isn't it absolute-value norm ($\sum |w|$)? T …
John Smith's user avatar
8 votes
2 answers
2k views

What does Φ mean? [closed]

In the documentation of METAL, a software for meta-analyzing GWAS results, Φ is in the formulas. Intermediate Statistics $Z_i = \Phi^{−1}(P_i/2) * \textrm{sign}(\Delta_i$) Overall P-value $P=2\P …
John Smith's user avatar
0 votes

Why Euclidean norm was used in Z-score combination?

Got it! I have further looked into the literature, and found that it was first described by F. M. Mosteller, and R. R. Bush in 1954 rather than Liptak, T. (1958). First, we known $$z = \frac{Δx}{SD}$$ …
John Smith's user avatar
3 votes
1 answer
48 views

How to combine p-values of weighted effects?

Suppose I know the effect of running on strength of muscle 1 and 2 and their $p$-values. These values were calculated from the same sample. Now I want to know the effect of running on the strength of …
John Smith's user avatar
4 votes
2 answers
257 views

Using sample sizes when combining z-scores

What is the theoretical justification for using the square root of the sample size as the weight when combining z-scores in a meta-analysis? Is this because the variance of the z-score is proportional …
John Smith's user avatar