Types of data
- Before data analysis can be performed need to identify type of data presented
- Data can be quantitative or categorical
- Quantitative and continuous - e.g. height, weight, blood pressure
- Quantitative and discrete - e.g. number of children
- Categorical and ordinal - e.g. Grade of tumour
- Categorical and nominal - e.g. Male / female, blood group
Description of quantitative data
- Data can be described by a 'measure of location'
- Median = mid point. 50% of variables above and 50% of
variables below
- Mode = most common variable
- Mean = the average i.e. the sum of variable divided by the number
- Data can also be described by a 'measure of variation'
- Range = distribution between maximum and minimum value
- Interquartile range = distribution between first and third quartile
- Standard deviation = distribution around mean in a 'normally' distributed population
The Normal distribution
A skewed distribution
Calculation of sample size
- Sample size needed to test a hypothesis depends on four factors
- Expected difference in means between the two groups
- Variability of the data
- Power of the study = probability that any difference is real (usually 90%)
- Level of significance accepted (usually 5%)
Type I and Type II errors
- Type I error = rejection of null hypothesis when it is in fact true
- No difference is present between the samples
- The statistical method used identified a difference
- Type II error = rejection of null hypothesis when difference between groups exists
- A difference is present between the samples
- The statistical method used failed to identify it
Choice of statistical test
- Prior to analysing data need to define the hypothesis being tested
- If no hypothesis proposed then no statistical test can be selected
- Also need to decide whether matched, paired or independent
- Also need to define input and output variables
- Both variable can be categorical or quantitative
Statistical tests for paired or matched observations
| Variable |
Test |
| Nominal |
McNemar |
| Ordinal |
Wilcoxon |
| Quantitative (non-normal) |
Wilcoxon |
| Quantitative (normal) |
Paired t-test |
Choice of statistical test for independent observations and categorical outcome variables.
Input variables are listed in first column.
|
Nominal |
Categorical |
Ordinal |
| Nominal |
Chi-squared or Fisher's
|
Chi-squared |
Chi-squared or Mann Whitney |
| Categorical |
Chi-squared |
Chi-squared |
Kruskal-Wallis |
| Ordinal |
Mann-Whitney |
|
Spearman rank |
| Quantitative - discrete |
Logistic regression |
|
|
| Quantitative - non-normal |
Logistic regression |
|
|
| Quantitative - normal |
Logistic regression |
|
|
Choice of statistical test for independent observations and quantitative outcome variables.
Input variables are listed in first column.
|
Quantitative - discrete |
Quantitative - non-normal |
Quantitative - normal |
| Nominal |
Mann-Whitney |
Mann-Whitney or log-rank |
Student's t-test |
| Categorical |
Kruskal-Wallis |
Kruskal-Wallis |
ANOVA |
| Ordinal |
Spearman rank |
Spearman rank |
Spearman rank or linear regression |
| Quantitative -discrete |
Spearman rank |
Spearman rank |
Spearman rank or linear regression |
| Quantitative - non-normal |
|
Pearson or Spearmen rank |
Pearson or Spearman rank |
| Quantitative - normal |
|
Linear regression |
Linear regression |
Bibliography
Whitely E, Ball J. Statistics review 1: presenting and summarising data. Crit Care
2002; 6: 66-71.
Whitely E, Ball J. Statistics review 2: samples and populations. Crit Care 2002;
6: 143-148.
Whitely E, Ball J. Statistics review 3: hypothesis testing and p values. Crit Care
2002; 6: 222-225.
Whitely E, Ball J. Statistics review 4: sample size calculation. Crit Care 2002;
6: 335-341.
Whitely E, Ball J. Statistics review 5: comparison of means. Crit Care 2002;
6: 424-428.
Whitely E, Ball J. Statistics review 6: non-parametric methods. Crit Care 2002;
6: 509-513 |