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# How to calculate the sample size?

/* Population size: 29.477.792
/* Parametros:
N                 P       Q      P*Q     Z_95%   Z2_95%     E_ 5%     E2_5%
29477792    0,5     0,5      0,25    1,9600     3,8416       0,05       0,0025

/* Formula  :   n =     N*(p*q)*Z2 / (p*q)*Z2 + (N-1)*E2  */

How can I do a program to calculate the sample size, according to this formula ???

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Solution
‎03-06-2018 07:59 AM
Super User
Posts: 13,583

## Re: How to calculate the sample size?

```data want;
n=29477792;
p= 0.5;
q= 0.5;
pq = p*q;
z_95 = 1.96;
z2_95 = 3.8416;
e_5 = .05;
e2_5 = 0.0025;
nwant = n*pq*z2_95/pq*z2_95 +(n-1)*e2_5;
run;```

But I think you need to verify your "formula".

Note I use . instead of , as that is the NLS setting for my system. You should be able to reverse things easy enough.

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Solution
‎03-06-2018 07:59 AM
Super User
Posts: 13,583

## Re: How to calculate the sample size?

```data want;
n=29477792;
p= 0.5;
q= 0.5;
pq = p*q;
z_95 = 1.96;
z2_95 = 3.8416;
e_5 = .05;
e2_5 = 0.0025;
nwant = n*pq*z2_95/pq*z2_95 +(n-1)*e2_5;
run;```

But I think you need to verify your "formula".

Note I use . instead of , as that is the NLS setting for my system. You should be able to reverse things easy enough.

New Contributor
Posts: 3

## Re: How to calculate the sample size?

Hi, Thank you so much!

It's worked.

data want;
n=10000;
p=0.5;
q=0.5;
pq = p*q;
z_95 = 1.96;
z2_95 = 3.8416;
e_5 = 0.05;
e2_5 = 0.0025;
nwant = (n*pq*z2_95) / ((pq*z2_95) + ((n-1)*e2_5));
run;

Contributor
Posts: 21

## Re: How to calculate the sample size?

Yea I agree I think you need to verify your formula. I think what you are trying to do is:

n = N*X / (X + N – 1),

where,

X = Z(α/2)^2 ­*p*(1-p) / MOE^2,

and Zα/2 is the critical value of the Normal distribution at α/2 (e.g. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), MOE is the margin of error, p is the sample proportion, and N is the population size.  Note that a Finite Population Correction has been applied to the sample size formula.

I think it would look something like this

n=(N*((Z^2 ­*p*(1-p)) / MOE^2))  /  (((Z^2 ­*p*(1-p)) / MOE^2)+N+1)

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New Contributor
Posts: 3

## Re: How to calculate the sample size?

Thank you. Thank you.

You really  helped me.

you're so right. that's the 'exact format' of formula.

before,I guess that I didn't express right.