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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

The Normal distribution

The normal distribution

A skewed distribution

A skewed distibution

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

 

 
 

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