[ Up ] [ Principles of neoplasia ] [ Clinicopathological staging of cancer ] [ Cancer genetics ] [ Chemotherapy ] [ Radiotherapy ] [ Malignant melanoma ] [ Skin cancers ] [ Benign skin lesions ] [ Nail disorders ] [ Benign breast disease ] [ Fibroadenoma ] [ Breast cysts ] [ Breast pain ] [ Breast sepsis ] [ Nipple discharge ] [ Gynaecomastia ] [ Breast cancer ] [ Breast reconstruction ] [ Breast screening ] [ Breast  assessment ] [ Palliative care ] [ Quality of life ] [ Informed consent ] [ The Coroner ] [ Clinical audit ] [ Statistics for surgeons ] [ Design of clinical trials ]

## Statistics for surgeons

### 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

### 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