STAT1600

• Statistics is a collection of procedures and principles for gathering data and analyzing information in order to help people make decisions when faced with uncertainty
• Examples


  • Does Aspirin reduce heart attack rates?
  • Does the Internet increase loneliness and depression?
• Observation


  An individual entity in a study
• Variable


  A characteristic that may differ among individuals
• Sample data


  Data collected from a subset of a larger population
• Population data


  Data collected when all individuals in a population are measured
• Statistic


  A summary measure of sample data
• Parameter


  A summary measure of population data
• Categorical variable


  Raw data consists of group or category names that don't necessarily have a logical ordering
• Ordinal variable


  Categorical variables for which the categories have a logical ordering
• Quantitative variable


  Raw data consists of numerical values taken on each individual
• Graphical summaries are used to visually display the data
• Graphical summaries


  • Frequency Table
  • Pie Chart
  • Bar Chart
  • Box Plot
  • Side-by-Side Box Plot
  • Stem-and-Leaf Plot
  • Dot Plot
  • Histogram
• Frequency table


  Used for categorical variables
• Box plot and histogram

  Used for quantitative variables
• Side-by-side box plot


  Used for the combination of 1 quantitative variable and 1 categorical variable
• A frequency table shows the number and percentage of observations in each category
• Rounding errors can occur when calculating percentages in a frequency table
• A frequency table can be used to compare the distribution of a variable between two or more groups
• A pie chart and bar chart are used to display the distribution of a single categorical variable
• A bar chart is used to display the distribution of two or more categorical variables
• Box plot


  Covers the middle 50% of the data, shows the median, and identifies outliers
• Side-by-side box plot


  Displays two single box plots on the same graph to compare different groups
• Stem-and-leaf plot


  Shows every individual data value, good for sorting the data
• Dot plot


  Places a dot above the number line at each observation's data value
• Histogram


  Illustrates the shape of the distribution of a quantitative variable
• Histograms and bar charts are different - histograms show the distribution of a quantitative variable, while bar charts show the distribution of a categorical variable
• Box plots, stem-and-leaf plots, dot plots, and histograms are all useful for organizing and visualizing quantitative data, but each has its own strengths and weaknesses
• Data


  With a sufficient sample size, it can be used to judge shape
• Dot plot


  • Can present all individual data values
  • Easy to create
• Histogram


  • Excellent for judging the shape of a data set with moderate or large sample sizes
  • Flexible in choosing number as well as the width of the intervals for the display
  • Between 6 and 15 intervals usually gives a good picture of the shape
• Statistics can be misleading if not presented appropriately
• Same data can appear very differently when graphed
• Misleading graphs


  • Bar diagrams showing the number of men and women who scored in the top half of the history exam
• Putting a break in the vertical axis results in an incorrect proportional relationship
• Frequency distribution


  The pattern of the distribution of scores over the range of possible values
• Shapes of frequency distributions

  • J-shaped
  • Positively skewed
  • Negatively skewed
  • Rectangular
  • Bimodal
  • Bell-shaped
• Bell-shaped distribution


  • Most individuals are clumped around the center
  • The greater the distance a value is from the center, the fewer individuals have that value
• A special case of bell-shaped distribution is called a normal distribution or normal curve
• Bell-shaped distribution


  • Histogram of wives' heights in a representative sample of 199 married British couples