Sampling Plans - Advanced Tab
Select the Advanced tab of the Sampling Plans dialog box to access the options described here.
- 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 H0 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 H0. Note that the H1 mean must be greater than H0 if a right-sided test is requested (see
Test criterion, above), and H1 must be smaller than H0 if a left-sided test is requested. If a two-sided test criterion is requested, then Statistica assumes two equal intervals around the H0 mean. For example, if H1 = 5 and H0 = 4 then, given a two-sided test criterion, the actual means under H1 are H1 = 5 for an upward shift and H1 = 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.