ARCH 21266126

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ARCH 2126/6126

• Session 3 Summarizing data visually

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To recap, the purpose of statistics..

• To provide insight into situations and problems
  by means of numbers
• How is this provided?
• Data are available or are collected
• Data are organized, summarized, analysed and
  results presented
• Conclusions are drawn, in context
• Whole process is often guided by critical
  appraisal of similar work already done

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Data sets

• Usually data do not come singly they come in,
  or are collected in, sets
• We collect them because we want to test some idea
  fairly against them
• E.g. we might want to test whether the stone
  artefacts from one site differ in size from stone
  artefacts from another
• For this, we measure artefact sizes
  systematically consistently

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Some issues implied by this

• Definition of data-set what belongs in it and
  what does not
• Performance of each measurement accurate and
  repeatable
• Methods of summarizing and analysing patterns in
  the data-set as whole-? visual ? numerical
• Today mainly defining data-sets, measurement
  visual summary

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What belongs in a data-set?

• We have considered it prudent to adopt the years
  1919-1925, excluding the drought year of 1926, as
  a fair standard for the future Queensland Land
  Settlement Advisory Board, 1927
• The tacit assumption that drought is an
  exceptional visitation to the inland country has
  shaped and infected public thought and official
  policy alike Francis Ratcliffe, 1937

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Making a measurement

• A variable is a measured property of a case
  measuring assigns numbers representing each
  cases value for that variable
• Variables must be exactly defined measurements
  reliably carried out
• Some variables are relatively simple but still
  need explicit specification, e.g. length
• Some are more complex and/or depend on
  non-obvious definitions, e.g. unemployment

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Measurement is never perfectly accurate but

• Our measurement of scraper length is valid, to
  the extent that it measures what it is supposed
  to measure
• Our measurement is reliable, to the extent that
  repetitions of the same measurement give the same
  result
• Our measurement is unbiased, to the extent that
  it does not tend to under-state or over-state the
  true value of the variable

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Recording a measurement

• Rare important observations deserve recording as
  insight-giving anecdotes
• But in many fields the bread butter of research
  are common observations where the issue is
  varying frequency
• Importance of a recording system
• Unsystematic recording is likely to lead to
  omissions or inconsistencies
• Limits to the benefits of precision

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Recording technology

• Pen paper still have their place
• Complex technology has its traps its
  vulnerability, your dependence
• But early, direct or automatic data entry into
  computers can bring big benefits in efficient
  use of time labour error reduction
  cross-checks
• Importance of duplicates back-ups

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How much data to collect?

• Limits to the benefit from measuring variables to
  many significant figures
• Limits to the benefit from increasing sample size
  indefinitely
• Limits to the benefit from increasing number of
  variables how many will you analyse?
• Attention to limits can save lots of time
• Limits not fixed, but depend on the situation
  under study the ideas under test

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Spreadsheets (e.g. Excel) databases (e.g.
Access)

• End point of data collection is often a matrix or
  table a column for each variable, a row for each
  case
• Often convenient to enter these into a
  spreadsheet or database (linkable, searchable)
• These can store, check, transform, calculate,
  apply conditions, select, test statistically,
  output to statpack

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Study design experiment versus observation

• How do we define? Variously but element of
  control often the key
• For practical, ethical etc. reasons, experiments
  rare in our subjects
• But experimental design important
• Dependent variable response variable under study
• Independent variable explanatory variable or
  factor

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Contexts and confounds

• Treatment a combination of specific conditions
  (levels of experimental factors)
• Extraneous variables ones not being studied but
  which may influence dependent variable thus
  part of relevant context
• Effects of different (independent or extraneous)
  variables are said to be confounded if they
  cannot be distinguished
• Good study design requires data on context

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Observational studies the risks of confounding

• Well designed experiments minimize confounding by
  appropriate choice of variables, cases and
  treatments random sequence of treatments
  random allocation of cases to groups
• Observational surveys lack this control
• Groups may be self-selected
• Differences in groups may have causes other than
  the variables under study
• But much can be done despite limitations

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Examples of presentation

• Even the simplest forms of stating findings
  numerically (percentages, averages), and the
  simplest graphical presentations, emphasize
  selected aspects
• This can be legitimate can also be misleading
  much depends on honesty clarity with which
  procedure is described
• What as a percentage of what?
• Please bring in examples yourselves

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Value of examining data visually first

• Even if you will eventually do sophisticated
  statistical testing
• Start clear and simple
• This familiarizes the researcher with the
  characteristics of the data set
• At the end of the process, it also helps the
  researcher to communicate the patterns found

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Graphical displays should

• Show the data
• Lead viewer to think about content, not graphic
  technology itself
• Avoid distorting data
• Present much info concisely coherently

• Encourage eye to compare
• Show both overview detail
• Serve clear purpose
• Be integrated with text and/or numerical
  descriptions

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Graphical depictions include

• line graphs
• bar charts
• histograms
• pie charts
• stem--leaf plots
• scatterplots
• An important principle is data density

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Line graphs

• Usually used to plot a variable against time (on
  horizontal axis)
• Shows seasons trends
• Does the graph have linear scales? A zero?
• Different scales give different impressions, e.g
  non-zero base to vertical axis, unequal units,
  log scale

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Bar charts and histograms

• Bar charts compare the values of different
  variables, often categorical
• Histograms display frequency or relative
  frequency distributions of one variable at a time
• Width of histogram bars has meaning
• Eyes respond to impressions of area symbols,
  unequal widths, pseudo-3D can give a misleading
  impression

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Pie charts

• Circular symbols divided into sections according
  to divisions of a category into sub-categories
• Pies sometimes also vary in size
• And sometimes are presented in pseudo-3D manner
• Will return to pie charts a bit later

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Stem-and-leaf plots

• A simple way of showing the pattern in a set of
  numbers
• Truncate the numbers at an appropriate point,
  write out the truncated numbers in an even
  systematic way (forming stem)
• For each number, add the amount left next to the
  truncated one (forming leaf)

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Scatterplots

• Show the distributions of two variables at once
  (i.e. bivariate data)
• If one variable is independent and one dependent,
  independent goes on horizontal axis
• Essence of any relationship between them is
  apparent visually ve or -ve, strong or weak,
  simple or complex
• This can affect future statistical testing

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Graphics can also mislead or even deliberately
deceive

• The principle should be show data variation, not
  design variation
• Perception depends on individual, experience,
  context
• Perception of circle area grows more slowly than
  its actual physical area
• Computer packages increase ease of making both
  good bad images

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So

• Beware irregular scales
• Beware symbols with changing area or volume,
  including pie charts
• Beware pseudo-3-dimensional depictions
• Beware excessively busy images which distract
  attention from the information to be conveyed

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Ed Tufte (1983) on pie charts

• The only worse design than a pie chart is
  several of them, for then the viewer is asked to
  compare quantities in spatial disarray both
  within and between pies Given their low
  data-density and failure to order numbers along a
  visual dimension, pie charts should never be
  used.

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Lie factor (effect in graphic/effect in data)
14.8 (should not be less than 0.95 or greater
than 1.05)
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5 different vertical scales 2 different
horizontal scales Lie factor 15.1
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Lie factor of 2.8 plus effects of perspective and
horizontal spacing
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The pie chart problem