Example of Power and Sample Size for 1-Sample t

An economist wants to determine whether the monthly energy cost for families has changed from the previous year, when the mean cost per month was $200.

Before collecting the data for a 1-sample t-test, the economist uses a power and sample size calculation to determine how large the sample must be to obtain a power of 90% (0.9). Any difference of at least $100 in either direction is considered to be meaningful and the estimated standard deviation is $150.

  1. Choose Stat > Power and Sample Size > 1-Sample t.
  2. In Differences, enter 100.
  3. In Power values, enter 0.9.
  4. In Standard deviation, enter 150.
  5. Click OK.

Interpret the results

To detect a difference of 100 with a power of 0.9, the economist needs to collect a sample of 26 observations. This is an obtainable sample size, so the economist continues with the data collection and the 1-sample t-test.

Power and Sample Size

1-Sample t Test Testing mean = null (versus ≠ null) Calculating power for mean = null + difference α = 0.05 Assumed standard deviation = 150
Results Sample Target Difference Size Power Actual Power 100 26 0.9 0.904254