HUBS M2 Biostats

• When we have a question we can use biostats to answer
• Population

  group of things we want to investigate
• Sample

  a small subset/ group of the population
• Percentage

  100 x no. with characteristic / total number
• Proportion

  no. with characteristic / total number
• Catergorical variable

  variable with limited options eg blood types
• continuous variable

  a large range of numbers eg height
• mean

  sum of characteristics / total number
• Large sample = smaller range and standard deviation
• larger spread = larger standard deviation
• standard deviation

  common way of measuring variability of spread
• Errors (2 types)

  1. Make answers more uncertain = more variability
  2. move away from the truth = wrong answers/ bias
  3. cant avoid 1, can avoid 2 by taking samples of whole population
• Continuous variable

  Population described by: mean and standard deviation

  sample described by: mean and standard deviation

  sampling distribution described by: sampling distribution

  is centred on: population mean and standard deviation of sampling distribution
• Binary variable

  Population described by: proportion

  sample described by: proportion

  sampling distribution described by: sampling distribution

  is centred on: population proportion and standard error
• Standard error

  variability/ standard deviation of sampling distribution
• Normal distribution

  • bell shaped curve
  • if we have mean and standard deviation we can draw shape
  • 95% of the sample mean lies w/i 1.96 SE of population mean
• Scatter plots and regression lines

  regression lines --> y-mx+c
• One sample

  • use 1 smaple to infer back to population
  • mean or proportion will be best guess of population mean
  • sample standard deviation is best guess of population
• Standard error

  • if sample >30 then sampling distribution will be normal
• Calculating Standard error

  $SE=$$s/square root(n)$

  S= standard deviation

  n= sample size
• Precision

  takes into account variability in sample and sample size
• 95% confidence interval

  "we are 95% confident that the [population parameter] for the population is between [L] and [U]."
• 95% confidence interval

  x̅ ± 1.96 ✗ SE

  x= sample mean

  means if we repeated that 95% of intervals would contain true population mean

  + = upper limit. -= lower confidence interval
• Box plot

  1. (left hand end of box) 25th percentile - 25% below this point
  2. (Line in box) median- 50% above 50% below
  3. (RHS end of box) 75th percentile - 75% below this point

  
• CI - confidence interval

  shows estimated proportion

  calculate proportion +-19.6 x SE

  works out precision
• How to research

  1. make assumption
  2. collect sample
  3. work out if assumption was true
  4. compare sample to hypothesis
  5. make a conclusion
• Make sure the question asked is important to understand

  eg lime scooter danger vs lime scooter deaths