Can I take the p-value from a probability table for a modified z-score, just like a z-score? I have a question regarding the modified Z-score, can I use this score in a Z-probability table, i.e. the p-value from a modified z-score?
where:
z-score = (xi - μ)/σ
(the z-score probability can be obtained from links)
modified z-score = 0.6745(xi - median(x))/median(|xi-median(x)|)
i can use modified z-score to get its probability from the same table
 A: It is worth noting that, with modern computers, we never (ever) have to use z-scores for sample statistics instead of t-scores even for large sample sizes, for which these two scores are quite close.
The z-score is used only when one knows the true standard deviation (or variance) of the random variable (not of the sample), which happens either if one is God or when one generates the random sample on a computer.
If the random variable is normally distributed, empirically (in a Monte Carlo simulation) you may approximate (and compare it with what you might get in the z-score or t-score table) that p-value with the following function in R.
modified_t_score_p_value <- function(modified_t_score, sample_size, simulation_size) {
    coef <- qnorm(0.75)
    sample <- matrix(rnorm(sample_size * simulation_size), nrow=simulation_size)
    medians <- apply(sample, 1, median)
    diff <- sample - medians
    sample <- coef * diff / median(abs(diff))
    print(paste0('p-value of modified sample z-score: ', mean(modified_t_score > sample)))
    print(paste0('p-value of real t-score: ', pt(modified_t_score, sample_size-1)))
    print(paste0('p-value of real z-score: ', pnorm(modified_t_score)))
}
modified_t_score_p_value(-2.0, 10, 100000)

Output
[1] "p-value of modified sample z-score: 0.039845"
[1] "p-value of real t-score: 0.0382764118853505"
[1] "p-value of real z-score: 0.0227501319481792"

