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INTERVALS Statement |
Notation | Definition |
n | number of nonmissing values for a variable |
mean of variable | |
s | standard deviation of variable |
100 percentile of the standard normal distribution | |
100 percentile of the central t distribution with degrees of freedom | |
100 percentile of the noncentral t distribution with noncentrality | |
parameter and degrees of freedom | |
100 percentile of the F distribution with degrees of freedom in | |
the numerator and degrees of freedom in the denominator | |
100 percentile of the distribution with degrees of freedom. |
The values of the variable are assumed to be independent and normally distributed. The intervals are computed using the degrees of freedom as the divisor for the standard deviation s. This divisor corresponds to the default of VARDEF=DF in the PROC CAPABILITY statement. If you specify another value for the VARDEF= option, intervals are not computed.
You select the intervals to be computed with the METHODS= option. The next six sections give computational details for each of the METHODS= options.
One-sided limits are computed using the conservative approximation
Hahn (1970c) states that these approximations are satisfactory except for combinations of small n, large k, and large . Refer also to Hahn (1969 and 1970a) and Hahn and Meeker (1991).
One-sided limits are computed as
where .
Exact one-sided limits are computed as
where .
In some cases (for example, if is large), is approximated by
where and .
Hahn (1970b) states that this approximation is "poor for very small n, especially for large p and large , and is not advised for n < 8." Refer also to Hahn and Meeker (1991).
One-sided limits are computed as
One-sided limits are computed as
One-sided limits are computed as
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