Maths for Clinicians 6

• What does distribution describe?

  • Frequency or probability of occurrence for given value
  • Describes shape of data
  • Distribution of sample used to make inferences about wider population & to generate confidence intervals
• What are probability distributions for?

  Continuous variables

  E.g, height, age- normal & skewed
• What are frequency distributions for?

  Discrete variables

  E.g, GP visits- Poisson, binomial
• What is the normal distribution?

  • Probability distribution that describes data symmetric around a mean
  • 2 parameters- mean & SD
• What is skewness?

  Measure of asymmetry of the distribution
• What is the null hypothesis?

  Outcome not associated with exposure
• What is the alternative hypothesis?

  There is an association between outcome & exposure
• How is a 95% CI made?

  Mean +- 1.96 SD
• How is a 99% CI made?

  Mean +- 2.58 SD
• How do we calculate the observed effect size?

  • Difference in data between the 2 groups
  • Use stats test to see if effect due to chance
• What is a significance level?

  Strength of evidence needed to reject null hypothesis

  Normally set to 5%

  5% = Type 1 error/alpha
• What is the standard deviation?

  Summary statistic

  Spread of variable values
• What is standard error (SE)?

  Inferential statistic

  How precise is estimate of true mean based on sample mean?

  Used to create CI

  How variable a statistic would be if study repeated (estimate)

  SE= SD/square root of n (number of observations/sample size)
• What is a type 1 error?

  Association in study

  But not in the population
• What is a type 2 error?

  No association in study

  But there is an association in the population
• What does the p value tell us?

  Strength of evidence against the null hypothesis

  The smaller the p value, the greater the evidence against the null hypothesis

  0.001= strong

  0.01= increasing strength

  0.1= weak evidence
• What does the confidence interval tell us?

  Range of values within which true difference lies- if study repeated, different effect sizes & CI would be obtained

  95% CI= In 95% replicate experiments, true value lies in the interval
• What does a smaller SE lead to?

  Smaller P value -> narrower
• What does a smaller SE mean?

  More precise