Sample size
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:<math>A=t_{\alpha,v} S_{\bar {y}}\,</math> | :<math>A=t_{\alpha,v} S_{\bar {y}}\,</math> | ||
| − | :<math>A=t_{\alpha,v} \frac { | + | :<math>A=t_{\alpha,v} \frac {s}{\sqrt {n}}\rightarrow n= \frac {t^2 s^2}{A^2}\,</math> |
For sampling without replacement we have to consider a [[Lecturenotes:finit population correction|finit population correction]] and the calculation would look different. | For sampling without replacement we have to consider a [[Lecturenotes:finit population correction|finit population correction]] and the calculation would look different. | ||
Revision as of 16:07, 3 December 2008
The sample size is the number of samples drawn from a defined sample frame based on a certain inventory design. Sample size calculation is an important reqirement in forest inventory as it directly affects the cots of the sampling exersise as well as the confidence interval for the derived estimations (Kleinn 2007[1]).
The question about the required sample size can not be answered directly. But the question about what sample size is necessary to derive an estimation with a predetermined precicion and a defined width of the confidence interval generally can be answered, though this answer is an estimation too (de Vries 1986[2]).
Note:
- It is intuivly clear that the required sample size must be related to some specifications (you may ask: required for what?). This predefined specification is the desired width of the confidence interval for the estimation. The width of this interval is determined by a defined error probability \(\alpha\) and a predefined allowable error (e.g. \(\pm\)10%). Further the variability inside the population is affecting the required sample size that is necessary to meet the above specifications.
For simple random sampling the sample size can be calculated with:
\[A=t_{\alpha,v} S_{\bar {y}}\,\]
\[A=t_{\alpha,v} \frac {s}{\sqrt {n}}\rightarrow n= \frac {t^2 s^2}{A^2}\,\]
For sampling without replacement we have to consider a finit population correction and the calculation would look different.
References
- ↑ Kleinn, C. 2007. Lecture Notes for the Teaching Module Forest Inventory. Department of Forest Inventory and Remote Sensing. Fakulty of Forest Science and Forest Ecology, Georg-August-Universität Göttingen. 164 S.
- ↑ de Vries, P.G., 1986. Sampling Theorie for Forest Inventory. A Teach-Yourself Course. Springer. 399 p.
