3' Describing a Sample

1
3. Describing a Sample

• Reading RB pp50-70 R 77-82
• 3.1 Graphical representations
• Suppose that you survey origins of 100 patients
  (N.Ireland1, Irish Rep.2 etc. as above)
• The raw data might be as follows 1 1 2 1 1
  1 3 1 1 4 3 1 1 1 1 2 2 1 1 1
• Raw data doesn't usually give people a good
  "picture" of the sample. Instead the data can be
  presented in one of several graphical forms.
• Categorical data
• bar chart pie chart frequency table
• Interval and ratio data
• histogram dot-plot

2
3.1 Graphical representations

• In the examples below suppose that there were 128
  in the sample and of these 42 patients were from
  N. Ireland, 30 from Irish Rep., 22 from Britain,
  8 from the EC and 26 from non-EC countries.
• Bar chart
• the categories are listed along the bottom and
  the height of each bar represents the number in
  that category

3
3.1 Graphical representations

• Pie chart
• Disc is divided between categories, size of slice
  represents number in category
• Note there are 360o in a circle. To calculate
  the angle for e.g. N.Ireland, you multiply 360 by
  the fraction of the sample that were from N.
  Ireland (Angle(NI) 3600 (42 / 128) 1180)

4
3.1 Graphical representations

• Frequency Table (also called a tabulation)
  (Tally)
• Simply a table giving the frequency (i.e. how
  many were in that category) and, if desired, the
  percentage.

5
3.1 Graphical representations

• Histogram
• If dealing with continuous data, we break the
  data into classes (i.e. ranges or intervals). For
  example, if you survey ages of 160 patients, we
  might break the data into classes
• 18-22
• 22-26
• 26-30
• 30-34
• 34-38
• 38-42
• 42-46
• Height of each bar represents number in each
  interval. Centre the bar on the midpoint of the
  interval. Class boundaries are at the sides of
  bars

6
3.1 Graphical representations

• Dot Plot
• A dot-plot is similar to a histogram except the
  bar is made of dots. Number of dots number of
  data of that value.
• It is easier to show a larger number of intervals
  or even a continuous range of whole numbers with
  a dot plot, e.g. the following dot plots show
  data for heart rate (beats per minute).
• ------------------------ beats
• 68 74 80 86 92

7
3.2 Shapes of the graph

• If we drew a histogram for a population using
  very small intervals we would get something like
  a line graph.
• The shape of a graph can be symmetric and
  bell-shaped. Often a graph is skewed. Less
  commonly a graph may be not bell-shaped but
  instead have several "humps".
• A graph representing length of stay in hospital
  for women giving birth is skewed to the right
• A graph representing weight of patients in a
  special clinic for eating disorders can be
  bell-shaped

8
3.2 Shapes of the graph

• The symmetric bell-shape is very common and so
  populations with such a graph are said to be from
  a Normal or Gaussian distribution, e.g. the
  number of arrivals at casualty in any day might
  be described as from a normal distribution since
  it would be bell-shaped and (reasonably)
  symmetric.
• Of course if a sample is big enough, its graph
  will be the same shape as the (underlying)
  population and so a sample might be described as
  being normal.
• Some statistical tests can only be used if the
  population is known (or can be assumed) to be
  normal.