Statistical comparison of 3 biochemical tests and a PCR

#1
Hello guys, I don't know if I'm doing this right and need some thoughts

So my thesis goes like this - I have 73 samples of enteroccoci. I had to test them all using 3 different biochemical tests and a mollecular method - PCR, which should provide the results that are closest to true

My objectives are - 1. To check the P value between the tests themselves and 2. with the molecular method

Here's what I tried so far - I don't know if I done it correctly or if I'm even taking the right path

I counted how many of the biochemical test samples provided true answers (showed the same species of enterococcus as the PCR) (pic attached)

Test A got 46/76 samples right
Test B got 72/76 samples right

I checked what test would fit here and tried doing the two proportions Z test (am I right to use that in this case?)

Trying to compare the two biochemical test results I had formed a hypothesis:
H0: two proportions are the same
H1: two proportions are not the same

I dug up the formula:
1542908057019.png
p1=0.605; p2=0.947;n1=n2=72; p=(42+72)/152=0.756

and if I did the math right I got z=4.90886

So... Did I do anything right and what can I do with the number? I entered it at https://www.socscistatistics.com/pvalues/normaldistribution.aspx and it gave me "The P-Value is < .00001.
The result is significant at p < .05.". Can I safely say that null hypothesis is rejected and continue doing that with the other tests?

Thanks for any and all the help in advance
 

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#2
Hi Skalas,

I can say I understand your table.

It seems you are using the correct statistic.
I think they have also a direct calculator on the same website: https://www.socscistatistics.com/tests/ztest/Default2.aspx

Please notice, when you use several tests you need to take a lower significant level, otherwise randomly one of them may become "significant" while it isn't really significant. (type I error (rejecting a correct H0) will be bigger than significant level of a single test: 1-(1-alpha)^n

n number of statistical tests (in your case pairs)
 
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