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# How to find the sample size for two sample proportion tests with given power in R?

To find the sample size for two sample proportion tests with given power, we can use the function power.prop.test where we need to at least pass the two proportions and power.

By default the significance level will be taken as 0.05 and if we want to change it then sig.level argument will be used.

Given below are some examples with the display of significance levels.

## Example 1

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=8/20,p2=6/20,power=0.90,sig.level=0.05)

## Output

If you execute the above given snippet, it generates the following Output for the two-sample comparison of proportions power calculation −

n = 476.0072 p1 = 0.4 p2 = 0.3 sig.level = 0.05 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 2

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=18/20,p2=16/20,power=0.90,sig.level=0.05)

## Output

If you execute the above given snippet, it generates the following Output for the two-sample comparison of proportions power calculation −

n = 265.856 p1 = 0.9 p2 = 0.8 sig.level = 0.05 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 3

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=18/100,p2=16/100,power=0.90,sig.level=0.05)

## Output

If you execute the above given snippet, it generates the following Output for the two-sample comparison of proportions power calculation −

n = 7410.91 p1 = 0.18 p2 = 0.16 sig.level = 0.05 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 4

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=18/1000,p2=16/1000,power=0.90,sig.level=0.05)

## Output

n = 87792.7 p1 = 0.018 p2 = 0.016 sig.level = 0.05 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 5

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=49/100,p2=51/100,power=0.90,sig.level=0.05)

## Output

n = 13132.2 p1 = 0.49 p2 = 0.51 sig.level = 0.05 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 6

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=49/100,p2=51/100,power=0.90,sig.level=0.10)

## Output

n = 10702.93 p1 = 0.49 p2 = 0.51 sig.level = 0.1 power = 0.9 alternative = two.sided

**Note** − n is number in *each* group.

## Example 7

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=49/100,p2=51/100,power=0.95,sig.level=0.10)

## Output

n = 13525.01 p1 = 0.49 p2 = 0.51 sig.level = 0.1 power = 0.95 alternative = two.sided

**Note** − n is number in *each* group.

## Example 8

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=49/100,p2=51/100,power=0.80,sig.level=0.10)

## Output

n = 7727.15 p1 = 0.49 p2 = 0.51 sig.level = 0.1 power = 0.8 alternative = two.sided

**Note** − n is number in *each* group.

## Example 9

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=5/200,p2=5/100,power=0.80,sig.level=0.10)

## Output

n = 713.0383 p1 = 0.025 p2 = 0.05 sig.level = 0.1 power = 0.8 alternative = two.sided

**Note** − n is number in *each* group.

## Example 10

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=5/200,p2=5/100,power=0.80,sig.level=0.05)

## Output

n = 905.3658 p1 = 0.025 p2 = 0.05 sig.level = 0.05 power = 0.8 alternative = two.sided

**Note** − n is number in *each* group.

## Example 11

Use the code given below to find the sample size for two sample proportion tests −

power.prop.test(p1=5/200,p2=5/100,power=0.80,sig.level=0.05,alternative="one.sided")

## Output

n = 713.0383 p1 = 0.025 p2 = 0.05 sig.level = 0.05 power = 0.8 alternative = one.sided

**Note** − n is number in *each* group.

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