# elementary statistics for foresters

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Elementary statistics for foresters Lecture 5 Socrates/Erasmus Program @ WAU Spring semester 2005/2006

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Elementary statistics for foresters. Lecture 5 Socrates/Erasmus Program @ WAU Spring semester 2005/2006. Statistical tests. Statistical tests. Why using tests? Statistical hypotheses Errors in tests Test of significance Examples of tests. Why do we use tests?. We work with samples - PowerPoint PPT Presentation

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• Elementary statistics for forestersLecture 5

Socrates/Erasmus Program @ WAUSpring semester 2005/2006

• Statistical tests

• Statistical testsWhy using tests?Statistical hypothesesErrors in testsTest of significanceExamples of tests

• Why do we use tests?We work with samplesWe want to know about populationsSample = uncertaintySo: we need a tool to be able to answer questions about population based on results from the sampleSome examples...

• Statistical hypothesesHypothesis: it is a statement about parameters or variable distribution of populationHypothesis refers to a parameter parametric hypothesisHypothesis refers to a distribution non-parametric hypothesis

• Parametric hypothesesThey are usually written as a short equation, e.g.

= 441 = 21 = 2

• Non-parametric hypothesesUsually written as a sentence, such as e.g.the distribution of the x variable in the population follows the normal distributionsamples were drawn from populations having the same distributions...Used not only exactly for distributions

• Statistical hypothesesNull hypothesis a hypothesis being tested during the testing procedureAlternative hypothesis a reserve hypothesis used when the null hypothesis is not trueThese hypotheses can be both: parametric and non-parametric.

• Statistical hypothesesH0: = 44H0: 1 = 2H0: the distribution of the x" variable follows the normal distribution

• Statistical hypothesesH1: 44H1: 1 2H1: the distribution of the x" variable doesnt follow the normal distribution

• Errors in testsThe hypothesis can be: true or falseThe result of the test can be: accept or reject the null hypothesisAll possible cases are:H0 is true, test accepts the hypothesisH0 is true, test rejects the hypothesisH0 is false, test accepts the hypothesisH0 is false, test rejects the hypothesis

• Errors in testIn two cases we have a bad scenario:H0 is true, test rejects the hypothesisH0 is false, test accepts the hypothesisIn these cases we have an error in using a statistical testAll cases can be shown in the table:

• Errors in tests

• Errors in tests

• How to avoid errors?test construction: use only tests rejecting hypotheses or saying that this is not enough to reject it. By doing so you can avoid type II errors,choose small significance level.

(Test of significance)

• Test of significance schemeformulate H0 and H1,sample the population(s),calculate a statistics for a given test (such statistics is also a variable having it's distribution if the null hypothesis is true),compare the calculated statistics with a critical value of the statistics for a given significance levelreject the null hypothesis is rejected or state, that "we can't reject the null hypothesis for a given significance level

• Test of significance in practiceWhen using any statistical software the end of the test is different.Instead of comparison of calculated test statistics with its theoretical value for a given significance level p-value (critical significance level) is calculated.This will be discussed in details during the practical exercises.

• Examples of tests

• Tests for the arythmetic mean(s)

• Tests for proportions

• Tests for variances

• Goodness-of-fit tests

• Thank you!