1. Georgi Iskrov, MBA, MPH, PhD Department of Social Medicine
SMME I 2017/2018 Final exam
Georgi Iskrov, MBA, MPH, PhD
Department of Social Medicine

2. Layout 30 min 40 min SMME I Final Exam: Entry test in Bioethics
Entry test in Biostatistics
______________________
1 case for statistical analysis and interpretation
1 bioethical case for comment and discussion
1 theory question from the bioethics questionnaire
Oral discussion
30 min
40 min

3. Resources

4. Do not forget
List of formulas
Calculator
Student book

5. Population vs Sample Population Parameters μ, σ, σ2
Sample / Statistics
x, s, s2

6. Descriptive vs Inferential statistics
Population
Parameters
Sampling
From population to sample
Sample
Statistics
From sample to population
Inferential statistics 6

7. Sampling Stages of sampling: Defining target population
Determining sampling size
Selecting a sampling method
Properties of a good sample:
Random selection
Representativeness by structure
Representativeness by number of cases

8. Sample size calculation
Generally, the sample size for any study depends on:
Acceptable level of confidence;
Expected effect size and absolute error of precision;
Underlying scatter in the population;
Power of the study.
High power
Large sample size
Large effect
Little scatter
Low power
Small sample size
Small effect
Lots of scatter

9. Levels of measurement

10. Graphical summaries Variable Graph Statistics One qualitative
Bar chart
Pie chart
Frequency table
Relative frequency table
Proportion
Two qualitative
Side-by-side bar chart
Segmented bar chart
Two-way table
Difference in proportions
One quantitative
Dotplot
Histogram
Boxplot
Measures of central tendency
Measures of spread
Other: five number summary, percentiles, distribution shape
One quantitative by one qualitative
Side-by-side boxplots
Stacked dotplots
Statistics broken down by group
Difference in means
Two quantitative
Scatterplot
Correlation

11. Central tendency and spread
Central tendency: Mean, mode and median
Spread: Range, interquartile range, standard deviation
Mistakes:
Focusing on only the mean and ignoring the variability
Standard deviation and standard error of the mean
Variation and variance
What is best to use in different scenarios?
Symmetrical data: mean and standard deviation
Skewed data: median and interquartile range

12. Rule of 3-sigma When data are approximately normally distributed:
approximately 68% of the data lie within one SD of the mean;
approximately 95% of the data lie within two SDs of the mean;
approximately 99% of the data lie within three SDs of the mean.

13. Normal (Gaussian) distribution
Central limit theorem:
Create a population with a known distribution that is not normal;
Randomly select many samples of equal size from that population;
Tabulate the means of these samples and graph the frequency distribution.
Central limit theorem states that if your samples are large enough, the distribution of the means will approximate a normal distribution even if the population is not Gaussian.
Mistakes:
Normal vs common (or disease free);
Few biological distributions are exactly normal.

14. Outliers
Values that lie very far away from the other values in the data set.

15. Confidence interval for the population mean
Population mean: point estimate vs interval estimate
Standard error of the mean – how close the sample mean is likely to be to the population mean.
Assumptions: a random representative sample, independent observations, the population is normally distributed (at least approximately).
Confidence interval depends on: sample mean, standard deviation, sample size, degree of confidence.
Mistakes:
95% of the values lie within the 95% CI;
A 95% CI covers the mean ± 2 SD.

16. Hypothesis testing The general idea of hypothesis testing involves:
Making an initial assumption;
Collecting evidence (data);
Based on the available evidence (data), deciding whether to reject or not reject the initial assumption.
Every hypothesis test — regardless of the population parameter involved — requires the above three steps.

17. Hypothesis testing Decision: Reject null hypothesis
Do not reject null hypothesis
Null hypothesis is true
Type I error
No error
Null hypothesis is false
Type II error

18. Level of significance
Level of significance (α) – the threshold for declaring if a result is significant. If the null hypothesis is true, α is the probability of rejecting the null hypothesis.
α is decided as part of the research design, while P-value is computed from data.
α = 0.05 is most commonly used.
Small α value reduces the chance of Type I error, but increases the chance of Type II error.
Trade-off based on the consequences of Type I (false-positive) and Type II (false-negative) errors.

19. Power
Power – the probability of rejecting a false null hypothesis. Statistical power is inversely related to β or the probability of making a Type II error (power is equal to 1 – β).
Power depends on the sample size, variability, significance level and hypothetical effect size.
You need a larger sample when you are looking for a small effect and when the standard deviation is large.

20. Choosing a statistical test
Choice of a statistical test depends on:
Level of measurement for the dependent and independent variables;
Number of groups or dependent measures;
Number of units of observation;
Type of distribution;
The population parameter of interest (mean, variance, differences between means and/or variances).

22. Parametric and non-parametric tests
Parametric test – the variable we have measured in the sample is normally distributed in the population to which we plan to generalize our findings
Non-parametric test – distribution free, no assumption about the distribution of the variable in the population

23. Parametric and non-parametric tests
Type of test
Non-parametric
Parametric
Scale
Nominal
Ordinal
Ordinal, Interval, Ratio
1 group
χ2 goodness of fit test
Wilcoxon signed rank test
1-sample t-test
2 unrelated groups
χ2 test
Mann–Whitney U test
2-sample t-test
2 related groups
McNemar test
Paired t-test
K unrelated groups
Kruskal–Wallis H test
ANOVA
K related groups
Friedman matched samples test
ANOVA with repeated measurements

24. Normality test
Normality tests are used to determine if a data set is modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
In descriptive statistics terms, a normality test measures a goodness of fit of a normal model to the data – if the fit is poor then the data are not well modeled in that respect by a normal distribution, without making a judgment on any underlying variable.
In frequentist statistics statistical hypothesis testing, data are tested against the null hypothesis that it is normally distributed.

25. Chi-square test limitations
No categories should be less than 1
No more than 1/5 of the expected categories should be less than 5
To correct for this, can collect larger samples or combine your data for the smaller expected categories until their combined value is 5 or more
Yates Correction*
When there is only 1 degree of freedom, regular chi-test should not be used
Apply the Yates correction by subtracting 0.5 from the absolute value of each calculated O-E term, then continue as usual with the new corrected values

26. Association is not causation.
Beware!
Association is not causation.
The observed association between two variables might be due to the action of a third, unobserved variable.

27. Fisher exact test This test is only available for 2 x 2 tables.
For small n, the probability can be computed exactly by counting all possible tables that can be constructed based on the marginal frequencies. Thus, the Fisher exact test computes the exact probability under the null hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven.