Sample Size for Proportions

The sample size can be defined as the number of samples that has been taken from the total size that is the total quantity. The sample size for proportion is the calculation between two similarly sized or dissimilar sized quantities. The sample size for proportion will be large when considering about various properties like the population which directs to increased accuracy in the value. A minute mistake in the calculation would collapse the entire system.

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Central limit theorem for sample size for proportions:

The theorems like central limit theorem are an important result in finding sample size for proportions which focuses on sample size. It states that the size of a sample of independent observations approaches infinity, provided data come from a distribution with finite variance, that the sampling distribution of the sample mean approaches a normal distribution.

Problems - Sample size for proportions:

Normally, a statistical report will show about 95% assurances for the correct value which can be noted as B. The B value is the error rate which decrease with the increase in the sample size (n). A statistician will calculate 955 of confidence interval which will be a constrained value. He will calculate 95% unbounded value for unknown population.

Standard difference = (p_1-p_2)/sqrt(barp(1-barp))

p1 and p2 are the proportions in two sets and = (p1 + p2)/2 is the mean of two values. This is for equally sized groups.

Example 1

Find the sample size for the two values 35% and 44% if the reduction is 9% with the low value group. Take their  power as 90%.

Solution:

Formula is,

Standard difference= (p_1-p_2)/(sqrtbarp(1-barp))

Here P1 =0.44, p2=0.35, barp  = 0.395

S, D = (0.44-0.35)/(sqrt0.395(1-0.395))

= 0.09/0.38

= 0.237

For unequally sized:

For unequal sizes, first consider the quantities as an equal one and find out the standard difference and take the value as N and then find N' with the remaining  values.

N'= (N(1+k)^2)/(4k)

Here, k is the ratio between two values.


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Example 2

Find the revised sample size for proportions where N=1200 and Take k as 2.

Solution:

Formula is

N'= (N(1+k)^2)/(4k)

= (1200(1+2))^2/(4xx2)

=1200xx9/8

=1350.