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# How to find the sample size for t test in R?

To find the sample size for t test, we can use pwr.t.test function of pwr package, wherever we can pass the arguments for alternative hypothesis such as one-sided or two-sided, significance level, power of the test and difference for two samples.

Check out the below examples to understand how it works.

## Example 1

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.80,d=1,sig.level=0.05,alternative="two.sided")

## Output

If you execute the above given code, it generates the following Output for the two-sample t test power calculation −

n = 16.71472 d = 1 sig.level = 0.05 power = 0.8 alternative = two.sided

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

## Example 2

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.90,d=1,sig.level=0.05,alternative="two.sided")

## Output

If you execute the above given code, it generates the following Output for the two-sample t test power calculation −

n = 22.02109 d = 1 sig.level = 0.05 power = 0.9 alternative = two.sided

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

## Example 3

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.90,d=1.24,sig.level=0.05,alternative="two.sided")

## Output

If you execute the above given code, it generates the following Output for the two-sample t test power calculation −

n = 14.69768 d = 1.24 sig.level = 0.05 power = 0.9 alternative = two.sided

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

## Example 4

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.90,d=1.24,sig.level=0.01,alternative="two.sided")

## Output

n = 21.08 d = 1.24 sig.level = 0.01 power = 0.9 alternative = two.sided

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

## Example 5

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.80,d=1.24,sig.level=0.10,alternative="two.sided")

## Output

n = 8.80455 d = 1.24 sig.level = 0.1 power = 0.8 alternative = two.sided

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

## Example 6

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.85,d=1.24,sig.level=0.10,alternative="two.sided")

## Output

n = 10.10416 d = 1.24 sig.level = 0.1 power = 0.85 alternative = two.sided

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

## Example 7

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.90,d=2,sig.level=0.10,alternative="two.sided")

## Output

n = 5.130901 d = 2 sig.level = 0.1 power = 0.9 alternative = two.sided

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

## Example 8

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.95,d=2,sig.level=0.10,alternative="two.sided")

## Output

n = 6.231837 d = 2 sig.level = 0.1 power = 0.95 alternative = two.sided

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

## Example 9

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.95,d=2,sig.level=0.05,alternative="two.sided")

## Output

n = 7.608958 d = 2 sig.level = 0.05 power = 0.95 alternative = two.sided

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

## Example 10

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.80,d=0.78,sig.level=0.05,alternative="two.sided")

## Output

n = 26.79675 d = 0.78 sig.level = 0.05 power = 0.8 alternative = two.sided

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

## Example 11

Consider the following code to find sample size for t test −

library("pwr") pwr.t.test(power=0.80,d=1.5,sig.level=0.05,alternative="two.sided")

## Output

n = 8.060321 d = 1.5 sig.level = 0.05 power = 0.8 alternative = two.sided

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

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