Statistics MA4114

• Statistics includes: Collecting data, Describing data, Interpreting and drawing conclusions from the data
• Why Statistics is Important

  • Data is being generated on a huge scale in almost every area of our daily lives
  • How do we extract valuable information and draw meaningful conclusions from these data?
  • Statistics is the science of learning from data
• The most popular trick in the media to sensationalise a graph is to start the vertical axis at a point that is not 0. The effect is to exaggerate trends for a more exciting look.
• Applications of Statistics


  • Weather forecasts
  • Predicating disease
  • Clinical trials
  • Sports
• Types of Studies


  • Observational Studies
  • Experimental Studies
• Types of Statistical Analysis

  • Descriptive Statistics
  • Statistical Inference
• Descriptive Statistics


  Method for organising, summarising and presenting data in an informative way
• Statistical Inference


  Methods used to draw conclusions from the data and make decisions using data that exhibit variability
• Data collected by scientists/engineers/medics etc. exhibits variability
• The variability within data can obscure the patterns within the data which are of interest to us
• Statistics is the science of distinguishing the pattern from the variability
• Example 1: Louis Pasteur's experiment in 1881

  • 24 sheep were vaccinated, and 24 sheep were not vaccinated
  • Consequently, all sheep were inoculated with anthrax and the number of sheep that died was recorded
  • No variability present, pattern is clear!
• Example 2: A company wishes to reduce the number of failures of an electronic component

  • Variability is evident, but is the difference in failure % due to mounting position (pattern) or chance (variability)
• Example 3: A medical company wants to investigate the effect of different doses of chemotherapy on tumour size in males and females

  • Is there a difference between the average tumour diameter of the two doses?
  • Do males and females respond differently to the two doses?
  • How do we know if this is a real change or is due to random variation?
• Where does variability come from?
• The aim of statistics is to discover the pattern in a data set whilst accounting for the variation in the data
• Data


  Values, facts or observations
• Statistics is the science of collecting, analysing, presenting and interpreting data
• Types of Data


  • Quantitative Data
  • Qualitative Data
• Quantitative Data


  Numeric data that indicates how much or how many
• Quantitative Data


  • height
  • mass
  • number of children
• Qualitative Data


  Normally classifications or groupings
• Qualitative Data


  • university department
  • social class
• Scales of Measurement for Quantitative Data

  • Interval Scale
  • Ratio Scale
• Interval Scale


  No true zero, can calculate the difference between two values
• Ratio Scale


  Has a unique zero point
• Types of Quantitative Data

  • Continuous
  • Discrete
• Continuous Data


  Variables can take any value in a certain range, usually measured according to some scale
• Continuous Data


  • height
  • mass
  • age
• Discrete Data


  Data only contains integer values, often counted
• Discrete Data


  • number of children
  • number of subjects
• Types of Qualitative Data

  • Nominal
  • Ordinal
• Nominal Data


  Labels/categories that are not able to be organised in a logical sequence (no ordering of categories)
• Nominal Data


  • political party
  • blood type
  • gender
• Ordinal Data


  Labels/categories that can be logically ordered or ranked
• Ordinal Data


  • size (small, medium, large)
  • school grades (A, B, C)
  • attitudes (strongly agree, agree, disagree, strongly disagree)
• Population: Entire group of objects/subjects about which information is wanted
• Sample: Any subset of a population
• Unit: Any individual member of the population
• Sampling Frame: A list or form of identification of the individuals in the population