1 / 17

Elementary statistics for foresters

Lecture 4 Socrates/Erasmus Program @ WAU Spring semester 2006/2007. Elementary statistics for foresters. Statistical estimation. Estimation. Inferential statistics Drawing conclusion about population based on sample Drawing conclusion about parameter based on estimator

rosalia-woriega
Télécharger la présentation

Elementary statistics for foresters

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 4 Socrates/Erasmus Program @ WAU Spring semester 2006/2007 Elementary statistics for foresters

  2. Statistical estimation

  3. Estimation • Inferential statistics • Drawing conclusion about population based on sample • Drawing conclusion about parameter based on estimator • Using an estimator to assess the value of the parameter

  4. Estimator • Statistics from the sample used to figure out about population parameter • First of all: unbiased (means: not giving a sistematic error)‏ • E(Tn) = Θ • E(Tn) - Θ = b(Tn) <- bias • Effective • Having the lowest possible variance • Other properties

  5. Estimation • Estimation can be done using two basic techniques: • Point estimation • Parameter = Estimator • Confidence interval • Building the interval where we expect the parameter with a given probability

  6. Estimation – basic concepts • Sample mean • Sample mean distribution • Standard error of the sample mean • Significance level and confidence level

  7. Estimation – an example • Sample data (population): density of wood • Arithmetic mean: 498,76 kg/m3 • Standard deviation: 52,77 kg/m3

  8. Estimation – an example • Let's draw 10 000 samples of 10 elements each from our population • Let's calculate arithmetic mean for each sample • Mean of means: 498,43 kg/m3 – it's VERY close to the true mean

  9. Estimation – an example Estimation – an example • The histogram of 10 000 means is the normal distribution, so we can use the theory of the normal distribution to arithmetic mean from ANY sample • Standard deviation of 10 000 means: 16,25 kg/m3 <- it is smaller than the standiard deviation in our population • Standard deviation of sample means is called STANDARD ERROR

  10. Estimation – an example Estimation – an example • Standard error depends on sample size • If sample size = population size: standard error = 0 • If sample size = 1: standard error = standard deciation of the population • Any other sample size: standard error = standard deviation of populations / square root of the sample size

  11. Estimation – an example Estimation – an example • From the normal distribution theory: • Probability, that the true mean is between arithmetic mean +/- one standard error = 0,68 • Probability, that the true mean is between arithmetic mean +/- two standard errors = 0,95 • Probability, that the true mean is between arithmetic mean +/- three standard errors = 0,997

  12. Estimation – an example Estimation – an example • This probability is referred to as confidence level (beta)‏ • 1 – beta = alpha <- significance level (the probability of error)‏

  13. Sample size determination • Closely connected to the estimation process • The equation derived directly from the confidence interval formulae

More Related