How to find the power of t test in R?

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

Check out the below examples to understand how it works.

Example 1

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=100,d=1,sig.level=0.05,type="two.sample",alternative="two.sided")

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

   n = 100
   d = 1
sig.level = 0.05
   power = 0.9999998
alternative = two.sided

Note − n is number in *each* group.

Example 2

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=50,d=1,sig.level=0.05,type="two.sample",alternative="two.sided")

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

   n = 50
   d = 1
sig.level = 0.05
   power = 0.9986074
alternative = two.sided

Note − n is number in *each* group.

Example 3

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=50,d=1.24,sig.level=0.05,type="two.sample",alternative="two.sided")

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

   n = 50
   d = 1.24
sig.level = 0.05
   power = 0.9999853
alternative = two.sided

Note − n is number in *each* group.

Example 4

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=50,d=1.24,sig.level=0.01,type="two.sample",alternative="two.sided")

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

   n = 50
   d = 1.24
sig.level = 0.01
   power = 0.9997823
alternative = two.sided

Note − n is number in *each* group.

Example 5

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=50,d=1.24,sig.level=0.10,type="two.sample",alternative="two.sided")

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

   n = 50
   d = 1.24
sig.level = 0.1
   power = 0.9999968
alternative = two.sided

Note − n is number in *each* group.

Example 6

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=500,d=1.24,sig.level=0.10,type="two.sample",alternative="two.sided")

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

   n = 500
   d = 1.24
sig.level = 0.1
   power = 1
alternative = two.sided

Note − n is number in *each* group.

Example 7

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=500,d=12,sig.level=0.10,type="two.sample",alternative="two.sided")

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

   n = 500
   d = 12
sig.level = 0.1
   power = 1
alternative = two.sided

Note − n is number in *each* group.

Example 8

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=25,d=12,sig.level=0.10,type="two.sample",alternative="two.sided")

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

   n = 25
   d = 12
sig.level = 0.1
   power = 1
alternative = two.sided

Note − n is number in *each* group.

Example 9

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=25,d=2,sig.level=0.05,type="two.sample",alternative="two.sided")

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

   n = 25
   d = 2
sig.level = 0.05
   power = 0.9999997
alternative = two.sided

Note − n is number in *each* group.

Example 10

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=20,d=0,sig.level=0.05,type="one.sample",alternative="two.sided")

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

   n = 20
   d = 0
sig.level = 0.05
   power = 0.05
alternative = two.sided

Example 11

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=20,d=0.78,sig.level=0.05,type="one.sample",alternative="two.sided")

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

   n = 20
   d = 0.78
sig.level = 0.05
   power = 0.9110511
alternative = two.sided

Example 12

To find the power of t test in R, use the code given below −

library("pwr")
pwr.t.test(n=20,d=1.5,sig.level=0.05,type="one.sample",alternative="two.sided")

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

   n = 20
   d = 1.5
sig.level = 0.05
   power = 0.9999941
alternative = two.sided