Errata for A Gentle Introduction to Stata, 6th Edition

The results show that for the sample-size factor of 1.0 of our current sample size of \(N=365\), we have a power of 0.365. This means that if the percentage distribution we observed were true in the population, we would obtain a statistically significant chi-squared just \(100\times 0.365 = 36.5\%\) of the time. If these percentages represent what we consider an important or interesting gender difference (women rating their health worse than men), then we would be doomed to failure with a sample of 365. If we had a sample that was four times bigger, making \(N = 1,428\), we would have power of 0.927. Meaning that 92.7% of the time, we would get a sample of 1,428 people in which the chi-squared was significant, but the other 7.3% of the time, we would get a chi-squared that was not statistically significant.

Statisticians usually say that the power should be greater than 0.80, and in many fields, they say it should be greater than 0.90. The results of the chi2power command show that we would need 1,071 observations to have a power greater than 0.80 and 1,428 observations to have a power greater than 0.90.

The results show that for the sample-size factor of 1.0 of our current sample size of \(N=365\), we have a power of 0.527. This means that if the percentage distribution we observed were true in the population, we would obtain a statistically significant chi-squared just \(100\times 0.527 = 52.7\%\) of the time. If these percentages represent what we consider an important or interesting gender difference (women rating their health worse than men), then we would be doomed to failure with a sample of 365. If we had a sample that was four times bigger, making \(N = 1,460\), we would have power of 0.992. Meaning that 99.2% of the time, we would get a sample of 1,460 people in which the chi-squared was significant, but the other 0.8% of the time, we would get a chi-squared that was not statistically significant.

Statisticians usually say that the power should be greater than 0.80, and in many fields, they say it should be greater than 0.90. The results of the chi2power command show that we would need 730 observations to have a power greater than 0.80 and 1,095 observations to have a power greater than 0.90.