Sample size calculated from Power Analysis One-Mean t-test is different from the one from Process Analysis Sampling plan with Normal-Means distribution
Article ID: KB0080562
Updated On:
| Products | Versions |
|---|---|
| Spotfire Statistica | 13.0 and higher |
Description
With the same parameters (e.g., mean, standard deviation, alpha, beta), the sample size calculated from Power Analysis module with One-Mean t-test, differs from the one calculated from Process Analysis Sampling plan module with Normal-Means distribution. The former is always slightly larger than the latter. Why?
In below example, with the same parameters, One-mean t-test under Power analysis module gives a rounded value of 265 for sample size, while Process Analysis sampling plan with Normal means distribution gives a rounded value of 263 for sample size. The former is larger than the latter by a difference of 2.
One Mean t-test under Power Analysis module:
Process Analysis Sampling Plan with Normal-means distribution:
In below example, with the same parameters, One-mean t-test under Power analysis module gives a rounded value of 265 for sample size, while Process Analysis sampling plan with Normal means distribution gives a rounded value of 263 for sample size. The former is larger than the latter by a difference of 2.
One Mean t-test under Power Analysis module:
Process Analysis Sampling Plan with Normal-means distribution:
Issue/Introduction
Why sample size calculated from Power Analysis One-Mean t-test is different from the one from Process Analysis Sampling plan with Normal-Means distribution?
Environment
Windows
Resolution
The two sample sizes calculated differ a bit for below reason:
One-Mean t-test under Power Analysis assumes that samples are randomly drawn from an infinitely large population where the mean and standard deviation are unknown. The Power analysis is based on the t-statistic and thus t-distribution which estimates the population standard deviation from sample standard deviation. The "sigma" under One-Mean t-test Power analysis, refers to the Population standard deviation estimated from sample standard deviation. There would be a 'penalty' or trade-off for using sample standard deviation to estimate large Population standard deviation, resulting in a bit lower power or more sample size. Therefore, t-test under Power analysis module would give a slightly more conservative answer.
The Process Analysis sampling plan is comparing the mean of a batch industry process samples to a specific value. It is based on the z-statistic and thus normal distribution where the standard deviation is assumed known. The target mean and "sigma" in this module are assumed known from previous quality control research or process runs.
But since the sample standard deviation is consistent and the t-statistic converges in distribution to the N(0,1), you get similar answers, with t-test power analysis giving a slight larger sample size.
Here is a link for example Process analysis sampling plan for your reference.
One-Mean t-test under Power Analysis assumes that samples are randomly drawn from an infinitely large population where the mean and standard deviation are unknown. The Power analysis is based on the t-statistic and thus t-distribution which estimates the population standard deviation from sample standard deviation. The "sigma" under One-Mean t-test Power analysis, refers to the Population standard deviation estimated from sample standard deviation. There would be a 'penalty' or trade-off for using sample standard deviation to estimate large Population standard deviation, resulting in a bit lower power or more sample size. Therefore, t-test under Power analysis module would give a slightly more conservative answer.
The Process Analysis sampling plan is comparing the mean of a batch industry process samples to a specific value. It is based on the z-statistic and thus normal distribution where the standard deviation is assumed known. The target mean and "sigma" in this module are assumed known from previous quality control research or process runs.
But since the sample standard deviation is consistent and the t-statistic converges in distribution to the N(0,1), you get similar answers, with t-test power analysis giving a slight larger sample size.
Here is a link for example Process analysis sampling plan for your reference.
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