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Education Courses Biomathematics

Biomathematics

Language
English
Nature
mandatory
Method of evaluation
semi-final examination
Year in the curriculum
2
Semester in the curriculum
2
Credits
3
Lectures
15
Practical lessons
30
Specialization
veterinary (English)
Documents
Documents
Allow for
  • Vet EN

Course description

The aim of this course is to prepare you for an understanding of the basic statistical methods that are useful in your major field. Concepts are introduced in an intuitive way. The relevance of the procedures is demonstrated by examples selected from a wide area of life sciences. The course uses a common-sense approach to explain basic ideas and methods. Real-life examples show how each idea or method is applied in practice.

Instructors and their email addresses:

Péter Fehérvári – [Click to see email]
Andrea Harnos – [Click to see email]
Szilvia Kövér – [Click to see email]
Zsolt Lang – [Click to see email]
Imre Sándor Piross – [Click to see email]

Abonyi-Tóth Zsolt – [Click to see email]

Recommended literature:

Wassertheil-Smoller S: Biostatistics and Epidemiology. A Primer for Health and Biomedical Professionals, Springer, 1990, 1995, 2004. (It can be borrowed from the University Library.)

Petrie A, Watson P: Statistics for Veterinary and Animal Science. 3rd edition. Wiley-Blackwell, 2013.

Course material can be reached on the e-learning site of the Biomathematics Department.

Lectures theme

1. week

Introduction. Descriptive and inferential statistics. Population and sample. Data types. Probability theory and statistics. Sample mean, median, lower and upper quartiles, range, variance, standard deviation.

2. week

Probabilities and statistics. Popper’s theory of falsification. Hypothesis testing, H0, H1. Clinical relevance and statistical significance. The p-value. Student’s t-test, Mood’s median test, Wilcoxon’s rank sum test. Components of a statistical test.

3. week

Probability theory. The notion of probability. Classical probability formula. Elementary and composite events. Relative frequency. Law of large numbers. Conditional probability and independence. Odds, logit, odds ratio and relative risk.

4. week

Random variables, probability distributions. Discrete and continuous distributions. Density function, histogram, boxplot. Symmetric, skewed, unimodal, bimodal and multimodal distributions. Binomial, Poisson and normal distribution. Central limit theorem. Expected value, population variance and standard deviation. Independence of random variables.

5. week

Hypothesis tests. One-sample, two-sample, multiple sample tests. Paired sample tests. One-sided and two-sided problems. Type I error, Type II error, power. Parametric tests: t-tests, F-test, Levene test, ANOVA. Nonparametric tests: sign test, Mood’s median test, Wilcoxon’s signed rank test, Mann-Whitney U-test, Kruskal-Wallis test.

6. week

Analysis of qualitative data: Chi-square test, Fisher’s exact test, goodness of fit test, test of independence, homogenity test. Binomial test. Multiple testing, Bonferroni-Holm correction.

7. week

Applications of probability theory in epidemiology. Theorem of total probability. Diagnostic tests. Prevalence, sensitivity, specificity, positive and negative predictive values. Bayes’ theorem. Observed and true prevalence.

8. week

Estimation. Point estimate, interval estimate. Plug-in estimate. Standard error, confidence interval. Relationship between statistical tests and confidence intervals. Equivalence tests.

9. week

Correlation, regression. Simple and multiple linear regression. Estimation of parameters. Testing hypotheses on regression. Model diagnostics.

10. week

Analysis of variance (ANOVA). One-way ANOVA. Decomposition of variance. Multi-way ANOVA. Model diagnostics.

11. week

Variance-covariance analysis (ANCOVA). Factors and covariates. Dummy variables. Interactions. Model diagnostics. Confidence bands and prediction bands.

12. week

Design of experiments. Randomised block design. Multiple testing. Bonferroni-Holm correction. Multiple comparisons. Tukey’s test, Dunnett’s test. Nonparametric or distribution-free methods.

13. week

Logistic regression. Odds ratio. Generalised linear model. The method of maximum likelihood.

Practical lessons theme

1. week

R-commander, entering data, data manipulation, descriptive statistics

2. week

Loading data. Charts.

3. week

Charts.

4. week

Binomial and Poisson distribution.

5. week

Normal distribution.

6. week

Binomial test, t-test, F-test, Levene test.

7. week

Midterm.

8. week

Contingency table, chi-square test, Fisher’s exact test.

9. week

Correlation, linear regession.

10. week

ANOVA, ANCOVA.

11. week

ANOVA, ANCOVA.

12. week

ANOVA, ANCOVA.

13. week

Midterm.

Evaluation description

General information:

  • It is obligatory to participate both on the lectures and the practicals! At most three uncertified absences from the lectures and from the practicals (altogether 3+3=6) are tolerated to obtain signature of the course and to be allowed to write the final exam. (Medical certifications are accepted.)
  • It is not allowed to change between groups during the semester.
  • The subjects of this course are statistics, and a little bit of probability theory (necessary to understand statistics).
  • The practicals will be computer assisted with the use of R commander (www.rcommander.com). Hand calculations will almost be omitted.
  • You will find the course material (lecture and practical handouts, etc.) on the university homepage.  (password: Biomath2018)
  • Recommended literature: Wassertheil-Smoller, Biostatistics and Epidemiology, A Primer for Health and Biomedical Professionals, Springer, 1990, 1995, 2004.

Short tests will be written on each practical from the subjects of the previous lecture and  practicals  32 points (no limit to pass)

Practical test: early May

32 points (≥ 16 are needed to pass)

  • Participation is obligatory on the midterm.  Absences are accepted and justified only if you provide medical certification.
  • Exercises only, similar to the ones on the practicals. No theoretical questions. Proper reporting and interpretation of the results obtained.
  • You need to achieve at least 16 points on the test to be allowed to write the final test.
  • You will have the opportunity to use one page of hand-written paper (not photocopied) as a help.
  • There’s a re-take possibility on the last practical in May provided you have not missed more than 3 practicals.

Homeworks: Maximum 10 bonus points can be collected from homeworks.

Written final test

36 points (>18 are needed to pass)

  • There will be a possibility to write the final test each week in the exam term.
  • Theoretical questions only, no exercises.

The final score is the sum of the scores of the short tests, the midterm and the final test (maximum: 100+10).

Altogether: 110 points

  •  0-50  -> 1
  • 51-61  -> 2
  • 62-72  -> 3
  • 73-83  -> 4
  • 84-110 -> 5

Exam information

(to be announced in due time)

Exam dates:

Location:

Time:

Duration: 45 minutes