Percentage points of the normal distribution
Henry Neave · 2002
The following notation is used in this and subsequent tables. q represents a quantile, i.e. q and the tabulated value z are related here by Prob (Z≤z)=q=Φ(z); e.g. Ф(1.9600)=q=0.975, where z=1.9600. and denote significance levels for onetailed or one-sided critical regions. Sometimes and values, corresponding to critical regions in the left-hand and right-hand tails, need to be tabulated separately; in other cases one may easily be obtained from the other. Here we have included only , since values are obtained using the symmetry of the normal distribution. Thus if a 5% critical region in the right-hand tail is required, we find the entry corresponding to and obtain Z≥1.6449. Had we required a 5% critical region in the left-hand tail it would have been Z≤−1.6449. α2 gives critical regions for twosided tests; here |Z|≥1.9600 is the critical region for the two-sided test at the α2=5% significance level. Finally, γ indicates confidence levels for confidence intervals-so a 95% confidence interval here is derived from |Z|≤1.9600. For example with a large sample X1, X2,…, Xn we know that has approximately a standard normal distribution, where and the adjusted sample standard deviation s is given by . So a 95% confidence interval for µ is derived from , which is equivalent to .