Chapter 1

• Statistics and Statistical thinking are fundamental tools needed for a modern society to function effectively
• The influence of science is immediately evident in nearly all areas of modern society
• Where ancient societies were predominantly supported by primitive agricultural and/or hunting techniques, modern society is characterized by a more scientific existence
• The incredible feats achieved in medicine in the last few decades are the result of modern medical science
• Scientific methods have edged their way into the decision making processes of both governments and private undertakings
• These decision making processes are founded on objectivity, critical analyses and a systematic philosophy
• Using these methods, decisions are usually only made after data have been collected and studied
• A vital aspect of modern science is the process of using empirical evidence
• Scientists conducting experiments in a laboratory and recording the observed results for further analysis are making use of an empirical process
• When analysts run opinion polls and surveys, they are engaged in collecting observations
• Observations, or empirical evidence, are crucial to scientifically based decision making
• Academics have not always appreciated the use of empirical evidence
• There have always been schools of thought that suppose knowledge can be obtained through pure reasoning alone
• Decisions are usually only made after data have been collected and studied
• Empirical evidence

  Observations made through experiments, surveys, etc.
• Studies based purely on contemplation lead to unreliable or erroneous results
• Reality can only be understood through a combination of meticulous observation and critical thinking
• Development of scientific knowledge


  • Involves human innovation, scientific intuition, and collaboration with other scientific fields
  • Empirical process with public methods and resulting data
• Statistics

  The science of extracting information from data
• Statistics is a "support science" employed to manage data
• Scientists should have at least some basic statistical knowledge to collaborate with statisticians
• Scientific journals demand that all results be statistically analysed
• Methods in Statistics


  • Methods for data collection
  • Methods to order, represent graphically and summarize data
  • Methods to draw conclusions from data
• Population

  The complete group of elements from which one would like to gain information
• Sample

  A sub-set of the population
• Statistical Inference


  Methods used to make conclusions about a population from sample data
• Probability theory forms the basis of statistical inference
• Descriptive Statistics refers to graphical and tabular methods used to summarize and order data
• Measurement involves the process of assigning a numerical value to a property of an observed element
• Valid measurements


  Measurements that lead to useful information concerning the properties being studied
• Variable


  Any property of an observed element that varies from one element to the next
• Examples of variables


  • Height of a person
  • Weight of a banana
  • Marks obtained by a student
  • Gender
• Two different types of variables are quantitative and qualitative variables
• Variables


  • Height of a person
  • Weight of a banana
  • Marks obtained by a student in an exam
  • Gender
• Variable


  Expressed in symbols like x, y, u, v to refer to the property of interest
• Discrete variable


  • Possible values are clearly distinguishable and disconnected from one another
• Discrete variables


  • Number of horses in a stable
  • Number of rooms in a residence
  • Number of homework problems a student receives daily
  • Gender of a person
• Continuous variable


  • Possible values are not clearly distinguishable, it is always possible to find another value between any two possible values
• Continuous variables


  • Surface area of the floor in residences
  • Ages of cats
  • Body mass of squirrels
  • Heights of 25-year-old men
  • Daily volume of milk used by a restaurant
  • Fuel consumption of motorcars
• Nominal scale


  Values only indicate classes or categories