Exam topics for the oral examination - biostatistics (1st semester)

Topics of the final examination from biostatistics, 2012.
1. Data description.
Types of data, displaying data (bar chart, histogram, mean-SD chart, box plot, scatter plot).
2. The basics of probability theory.
Experiments, events, operations with events, the concept of probability, rules of probability calculus in
special cases.
3. Random variables I.
Definition of a random variable, discrete random variables, distribution of a discrete random variable,
some important discrete distributions (discrete uniform, binomial and Poisson distribution).
4. Random variables II.
Definition of a random variable, distribution of a continuous random variable. Properties of the density
function, examples. The histogram.
5. Population and sample characteristics.
Definitions, examples, measures of central tendency and variability and their properties.
6. The normal distribution.
The normal distribution, the standard normal distribution and their properties. z-scores,
standardization. The central limit theorem.
7. Statistical estimation.
Statistical estimation, confidence interval. The definition and meaning of the confidence interval,
confidence level. Confidence interval for a population mean . The standard error of mean.
8. Hypothesis testing.
The definition of a hypothesis, the aim and steps of hypothesis testing, null-and alternative hypothesis,
significance level, decision about statistical significance, statistical errors.
9. One sample t-test
The aim, null hypothesis and assumption of the one sample t-test, decision rules. A t-test for paired
differences: the experimental design, null and alternative hypothesis, decision rules.
10. Comparison of the mean values of two independent populations
The aim, null hypothesis and assumptions of the two sample t-tests. Experimental design, decision
rules depending on equality of variances. Testing equality of variances: F-test.
11. Comparison of the mean values of several independent populations (ANOVA)
The aim, null hypothesis and assumptions of one-way ANOVA, ANOVA table, pair wise
comparisons.
12. Correlation and regression
Pearson's correlation coefficient, its formula, properties, meaning. The significance of the correlation
coefficient (null hypothesis, decision rule, significance).
13. Linear regression analysis.
The equation of the regression line, the principle of least squares Tsignificance of the regression
coefficients. The coefficient of determination, regression using transformations.
14. Nonparametric tests
General meaning and use of nonparametric tests, preparing rans, tests for paired and independent
samples. The rank correlation coefficient and its significance.
15. Chi-square test for independence
Contingency table, observed and expected frequencies, degrees of freedom, the chi-square test,
assumptions. Special case: a 2x2 table. Fisher’s exact test.
16. Diagnostic tests.
General aim of diagnostic tests. Sensitivity, specifity, positive and negative values, examples. The
ROC curve. predictive Measures meaning and use of nonparametric tests, preparing rans, tests for
paired and independent samples. The rank correlation coefficient and its significance.
17. Survival analyis
Characteristics of prospective and retrospective studies. Censored data, life tables, Kaplan-Meier
analysis. Propertiesof the plot of a survival function.
The exam will consist of one whole topic and of 1 simple problem to be solved by manual calculation (use
of simple calculator is permitted). A formula sheet will be given and can be used during the exam, which can
be also downloaded from the Coospace.
Core topics (without this knowledge the exam is failed independently of other knowledge):
Calculation of the mean, median and standard deviation of (a few) given numbers
Null- and alternative hypotheses
Evaluation of significance using statistical tables
Evaluation of significance using p-values
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Problems
Probability
1. If we roll a dice, there are 6 possible outcomes. If X represents the value of the outcome, find the
following probabilities: a) P(X=1); b) P(X>1); c) P(1

t
Ed
aV
JS
tD
decr
Equal variances assumed
Equal variances not
assumed
Independent Samples Test
Levene's Test f or
Equality of Variances
t-test for Equality of Means
95% Confidence
Interv al of the
Mean Std. Error Dif f erence
F Sig. t df Sig. (2-tailed) Dif f erence Dif f erence Lower Upper
4.351 .051 1.634 19 .119 5.27273 3.22667 -1.48077 12.02622
1.604 15.591 .129 5.27273 3.28782 -1.71204 12.25749
Based on these results, decide whether the treatment was effective or not. Explain your decision
(=0.05).
Name of the test………….
Null hypothesis………….. Alternative hypothesis…………………..
Assumptions……………..
Result of the test
Decision about the variances……………
Test statistic, degrees of freedom, p-value………
Decision……………..Interpretation………………….
3. In a study examining eating habits of secondary school girls, the body weights were measured in two
Hungarian cities, in Szeged and in Debrecen. The results are in the following table:
The means were compared using two - sample t-test .
What is the null hypothesis of this test ....................................................................................
.....................................................................................................................................................
Find the difference in means: .....................................................
The t-value was t=1.502.
Find the value of degrees of freedom ...............................
The p-value was p=0.136
Is there a significant difference between the two populations mean at 5% level. ....................
Correlation
1. Based on 5 pairs of data, The coefficient of correlation is r=0.7. Is this correlation significant at 5%
level
Null and alternative hypothesis:………………….
t-value of the correlation:......................... Degrees of freedom:...................................
Decision (t-value in the table t 3,0.05 =3.182) …………………..
Chi-square tests
1. The following table shows the results of placebo and aspirin in an experiment, with the number of people
in each treatment group who did and did not develop thromboses. Decide whether the aspirin had or
had not effect on thrombus formation.
Developed thrombi Free of thrombi
Placebo 10 5
Aspirin 10 20
Find the value of the test statistic, and give your conclusion. (alfa=0.05, 2 table =3.84)
Nullhipothesys ……………………Assumption ………………………………
Test statistic: ……………………..
Degrees os freedom: ……………………
Decision about the significance: …………………..: ………………………..
Interpretation: ………………….
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2. Two medicines are being compared regarding a particular side effect, 60 similar patients are split
randomly into two groups, one on each drug. The results are presented in the following table:
Side effects no side effects
Drug A 10 20
Drug B 5 25
Are drug type and side effects independent Find the value of the test statistic, and give your conclusion.
(alfa=0.05, 2 table =3.84)
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