Distribution
The
Distribution box contains three options:
Normal means,
Binomial proportions, and Poisson frequencies. Specify the type of quality characteristic that is being measured.
Normal means
Select
Normal means if the quality characteristic of interest is continuous and probably normally distributed.
Binomial proportions
Select
Binomial proportions if the characteristic of interest is an attribute that is distributed following the binomial distribution. For example, this setting would be applicable when designing a sampling plan to determine the proportion defective in a batch.
Poisson frequencies
Select
Poisson frequencies if the characteristic of interest is a relatively rare attribute. For example, this setting would be applicable when designing a sampling plan to determine the number of defects found in a batch.
Sample size estimation for binomial proportions and Poisson frequencies. Note that the sampling plans options in the Process Analysis module will use the normal approximation to the binomial and Poisson distributions in order to estimate required fixed sample sizes. These approximations are described in, for example, Duncan (1986), and are consistent with the approach used in quality control charting (see also Quality Control for additional details). Note that, usually, in power analysis applications in the biomedical sciences, the explicit formulas (instead of the normal approximations) are used, and those analyses may yield slightly different results. If your version of Statistica does not include the Statistica Power Analysis module, contact Statistica or visit our Web site at
http://Statistica.io/ for information about the availability of this module.
Test criterion
The
Test criterion box contains three options:
Two tailed,
One-sided (right) test, and One-sided (left) test.
Two tailed
If you select
Two tailed, the sampling plan is computed so as to detect a shift in either direction from the mean under H0.
One-sided (right) test
If you select
One-sided (right) test, the sampling plan is computed so as to detect an H1 mean that is greater than H0.
One-sided (left) test
If you select
One-sided (left) test, the sampling plan is computed so as to detect an H1 mean that is smaller than H0.
Alpha error (rejecting H0 when it is correct)
Use this box (and the accompanying microscrolls) to enter a value for the probability of erroneously rejecting H
0 when it is correct. Put another way, this value is the probability of rejecting a batch, when in fact there is nothing wrong with it. Refer also to the Introductory Overviews for more information concerning the
Alpha and
Beta error probabilities.
Beta error (rejecting H1 when it is correct). Use this box (and the accompanying microscrolls) to enter a value for the probability of erroneously rejecting H1 when it is correct. Put another way, this value is the probability of accepting a batch, when in fact it deviates from specifications by the magnitude defined under H1. Refer also to the Introductory Overviews for more information concerning the
Alpha and
Beta error probabilities.
Note: the Statistica Power Analysis program is designed to enable you to compute Statistical power and estimate required sample size while planning experiments and to evaluate experimental effects in your existing data. You will find many features in this module designed to make it possible for you to perform these calculations quickly and effectively in a wide variety of data analysis situations. For more information on purchasing this program, contact Statistica or visit our web site at
http://Statistica.io/.
Hypothesized mean for H0 (hypothesis/spec.).
Use this box (and the accompanying microscrolls) to specify the means for H
0. Note that the H
1 mean must be greater than H
0 if a right-sided test is requested (see
Test criterion, above), and H
1 must be smaller than H
0 if a left-sided test is requested. If a two-sided test criterion is requested, then Statistica assumes two equal intervals around the H
0 mean. For example, if H
1 = 5 and H
0 = 4 then, given a two-sided test criterion, the actual means under H
1 are H
1 = 5 for an upward shift and H
1 = 3 for a downward shift.
Hypothesized mean for H1 (alternative hyp.). Use this box (and the accompanying microscrolls) to specify the means for H1. See
Hypothesized mean for H0 (above) for more information.
Assumed sigma (standard deviation). Use this box (and the accompanying microscrolls) to specify the assumed standard deviation of the variable of interest. Note that
Sigma is a function of the process average if the binomial or Poisson distributions are selected; specifically, for binomial proportions, Sigma is equal to:
Sigmap = Ö{p*(1-p)/n}
where
n is the sample size.
For Poisson frequencies, Sigma is computed as:
Sigmaλ = Ö(λ)
where λ (lambda) is the average Poisson frequency.
Note: this box is only available when
Normal means is selected in the
Distribution box (see above).