Confidence limits of the mean for small samples

As the sample size gets smaller, s becomes less reliable as an estimate of o. This can be seen by again treating each column of the results in Table 2.2 as a sample of size five. The standard deviations of the 10 columns are 0.009, 0.015, 0.026, 0.021, 0.013, 0.019, 0.013, 0.017, 0.010 and 0.018. We see that the largest value of s is nearly three times the size of the smallest. To allow for this, equation (2.8) must be modified. 

For small samples, the confidence limits of the mean are given by 

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