Opinto-opas

Objective

The student is able to apply basic rules of probability in simple applications. The student can list the most important discrete and continuous distributions and can apply them in problems of environmental engineering. The student can explain the meaning of a confidence interval and can apply it in statistical reasoning. The student recognizes the most common statistical tests and can apply them in problems of environmental engineering. The student is able to apply the principle of least squares in regression analysis, and he or she can interpret output of regression analysis software. The student can use selected programs in statistical analyses.

Content

1. Different concepts of probability, and basic rules for calculating probabilities.
2. Random variables and their most common distributions
3. Laws of error propagation and estimation of measurement uncertainty.
4. Graphical representation of statistical data.
5. The idea of Monte Carlo simulation.
6. Confidence intervals and statistical reasoning using confidence intervals and the idea of statistical process control (SPC) in environmental monitoring.
7. Statistical tests and their applications in environmental engineering.
8. Regression analysis and its applications in environmental engineering.
9. Using programs for statistical analyses.

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

1. The student can calculate probabilities for simple combinations of given events.
2. The student recognizes binomial, Poisson and normal distributions, and he or she can apply the rules of thumb of the normal distribution in estimating normal probabilities.
3. The student can approximate the standard measurement uncertainty of simple formulae of measurement results.
4. The student can plot histograms and scatter plots of statistical data.
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6. The student can calculate confidence intervals for expected values and for variances in environmental applications.
7. The student can make the correct conclusion of a statistical test at given level of significance when the null hypothesis and the p-value are given.
8. The student can apply linear regression of one variable in environmental applications.
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Assessment criteria, good (3)

1. The student can calculate simple conditional probabilities.
2. The student can apply binomial and Poisson distributions in simple environmental applications.
3. The student can approximate the standard measurement uncertainty in typical calculations appearing in environmental engineering.
4. The student can use programs for visualizing statistical data.
5. The student can use Monte Carlo simulation in uncertainty estimation.
6. The student can calculate confidence intervals for differences of expected values.
7. The student can form statistical hypotheses and apply t- and F-tests in simple environmental applications.
8. The student can apply multiple linear regression in environmental applications.
9. The student can use programsl in elementary statistical analyses., The student can use programs instatistical tests, and in regression analyses.

Assessment criteria, excellent (5)

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2. The student can apply binomial, Poisson and normal distributions in environmental applications.
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6. The student can calculate confidence intervals for linear combinations of expected values.
7. The student can apply t- and F-tests in environmental applications.
8. The student can transform originally nonlinear models of environmental applications into linear regression form.
9. The student can write can simple scripts or functions for selected program.

Assessment criteria, approved/failed

1. Opiskelija osaa laskea todennäköisyyksiä yksinkertaisille tapahtumakombinaatioille.
2. Opiskelija tunnistaa binomi-, Poisson- ja normaalijakauman ja osaa soveltaa normaalijakauman nyrkkisääntöjä normaalisti jakautuneiden suureiden todennäköisyyksien arvioinnissa.
3. Opiskelija osaa arvioida yksikertaisiin laskulausekkeisiin perustuvien suureiden standardimittausepävarmuuksia.
4. Opiskelija osaa tehdä tilastodatan pohjalta histogrammeja ja xy-kaavioita.
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6. Opiskelija osaa laskea luottamusvälejä odotusarvoille ja variansseille ympäristöteknisissä sovelluksissa.
7. Opiskelija tehdä oikean johtopäätöksen tilastollisesta testistä, kun sen hypoteesit ja p-arvo on annettu.
8. Opiskelija osaa soveltaa lineaarista regressioanalyysia ympäristöteknissä sovellutuksissa
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