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Content
E-learning modules statistics..................................................................................................................1
1. Introduction....................................................................................................................................2
Types of variables...........................................................................................................................2
2. Descriptive statistics.......................................................................................................................3
Frequency table..............................................................................................................................3
Measures of location......................................................................................................................4
Measures of variation.....................................................................................................................4
Graphs............................................................................................................................................5
3. Probability......................................................................................................................................6
Classical definition..........................................................................................................................6
Rules...............................................................................................................................................6
The use of probabilities in the medical world.................................................................................7
4. Probability distributions.................................................................................................................8
Binominal distribution....................................................................................................................8
Normal distributions.......................................................................................................................8
5. Estimation and confidence intervals.............................................................................................10
The 95% confidence interval for a proportion..............................................................................10
The 95% confidence interval for the difference between two means..........................................11
Relative risk..................................................................................................................................11
Odds ratio.....................................................................................................................................12
6. Hypothesis testing........................................................................................................................13
Type I and type II errors................................................................................................................14
7. Independent t-test and one-way ANOVA.....................................................................................14
The t-distribution..........................................................................................................................14
The t-test for two independent groups........................................................................................15
One-way ANOVA...........................................................................................................................17
8. Pearson’s Chi-square and Fisher’s exact test................................................................................19
Pearson’s Chi-square....................................................................................................................19
Fisher’s exact test.........................................................................................................................20
Degrees of freedom in a crosstabulation......................................................................................21
9.Non-parametric tests for independent groups..............................................................................22
Wilcoxon Ranksum test................................................................................................................22
, Mann-Whitney U test...................................................................................................................22
Kruskall-Wallis test.......................................................................................................................22
10. Statistical tests for paired observations......................................................................................24
The paired t-test...........................................................................................................................24
The sign test.................................................................................................................................24
Wilcoxon signed rank test.............................................................................................................25
McNemar’s test............................................................................................................................26
11. Correlation..................................................................................................................................27
The covariance..............................................................................................................................27
Pearson’s correlation coefficient..................................................................................................28
Spearman’s correlation coefficient...............................................................................................29
12. When to use which test?............................................................................................................29
Paired groups................................................................................................................................29
Unpaired groups...........................................................................................................................29
1. Introduction
Types of variables
Quantative data: numerical data
2
, - Discrete: only certain values are possible
E.g. 1,2,3,4,5,etc. children per household
- Continuous: all values are possible
E.g. height or weight
Qualitative data: catergorical data
- Nominal: there is no logical order
E.g. marital status: married, widowed, single, divorced
- Ordinal: values have a logical order
E.g. socio-economic status: low, medium, high
- Binary/dichotomous: there are only two categories
E.g. married: yes/no
2. Descriptive statistics
Frequency table
To give an overview of categorical data
3
, Not useful for continuous data!
Measures of location
n
The mean:
∑ Xi
i=1
μ=
n
Works best for symmetrical data in skewed data the mean is influenced by
extreme values
Median: the middle of the observed values
Works best for skewed data
Mode: the value with the highest frequency
Measures of variation
Range: difference between highest and lowest value
Interquartile range: difference between both quartiles IQR=Q 3−Q1
The median is used
Deviation: difference between each value and the mean
4
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