Hi all,

I have (an imputed) GWAS that only has z-score and p-values. I want to convert z-score into beta and SE. My ultimate goal is to use log(odds ratio) with its corresponding standard error to run COJO analysis. I came across this post [Caclulate effect estimates and SE from Z scores] that describes the formula to convert z-score into SE. I tested it on a SNP whose SE I have from GWAS but answers are not matching.

```
Formula = SE = 1/ sqrt(2p(1− p)(n + z^2))
zscore = z = 0.50795203
frequency = p = 0.123274
sample size = n = 375752
```

when I run the code in R, it gives

```
> SE = 1/sqrt((2*p)*(1-p)*(n+z^2))
> SE
[1] 0.003508864
```

However, the real SE as in my GWAS is 0.0252602590 and beta is 0.012831. A snippet from my GWAS is

```
variant_id panel_variant_id chromosome position effect_allele non_effect_allele current_build frequency sample_size zscore pvalue effect_size standard_error imputation_status n_cases
rs143225517 chr1_816376_T_C_b38 chr1 816376 C T hg38 0.123274 375752 0.50795203 0.611487 0.012831 0.025260259097695255 original 59674.0
```

I am not sure where I am going wrong. Can anyone please point me in right direction?