simple question about Z score and P value in R

[tujchl]

Hi
I have a list and I calculate Z score and P value in R as below
Z.score=(0.52-mean(data))/sd(data)
P.value=2*pnorm(-abs(Z.score))
and P.value is 0.028 (0.52 is in my list "data")

but I reverse data and do it in R as below again:
Z.score=(1/0.52-mean(1/data))/sd(1/data)
P.value=2*pnorm(-abs(Z.score))
and P.value is 1.5e-05

My question is that in my understanding the outcome of these two methods is the same. but now it seems different.
can you tell me the reason?

[blancha]

I think that by doing the reciprocal transformation, you are drastically changing the distribution shape, hence the drastically different Z scores and p-values.

The reciprocal transformation preserves the order of the values, but drastically alters the distribution of the values.

[tujchl]

Hi blancha
thank you for your replying. your replying helps me a lot.
just three further questions
1. I check mean and sd of my data before and after reciprocal transformation. I found that the sd is the same and mean is reciprocal before and after reciprocal transformation. are they evidence to prove your hypothese?
2. do I have chance to get the same pvalue after some kinds of handling? here I want both of them are 1.5e-05
3. can I use 1.5e-05 here to prove my value is significant against the distribution?

[blancha]

Sorry, I made a small mistake in my previous answer. I wish I could edit it.
The reciprocal transformation obviously reverses the order of the values.

1. The standard deviation of the distribution of a set of random numbers after the reciprocal transformation is different. Nor is the mean after transformation the reciprocal of the mean before distribution.

2. There are transformations that will not affect the shape of the distribution, such as multiplying each value by a constant or adding or subtracting a constant from each value. There are transformations that will affect the shape of the distributions, such as the logarithmic or the square root transformation, but to a much lesser extent than the reciprocal transformation. The logarithmic transformation is commonly used to make highly skewed distributions less skewed.

3. The reciprocal transformation is the least commonly used. I don't know what your rationale is for picking this transformation, so I can't comment on whether it is appropriate in your case.

I'm not a statistician. I just use statistics in my work so you may get better answers from a statistician.