Analytical Methods for Anthropology

1
Analytical Methods for Anthropology Archaeology

• ARCH 2126/6126
• Session 2
• Variation, variables and values

2
The purpose of statistics

• To provide insight into situations and problems
  by means of numbers
• How is this provided?
• Numerical 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

3
M. R. Dawkins

• Statistical description is the quest for
  patterns or rules which permit reduction in the
  quantity of data without undue loss of
  information. Some reduction is essential if the
  description is to be useful. One cannot publish
  ones field notebook. Clearly some data must be
  thrown away. (1974)

4
Whether categorical or metrical, the essence is
variation

• Almost always empirical research describes
  attributes of a society or culture, a site or
  artefact, an individual or population, which vary
  (or might vary) this is intrinsic to our
  interest
• Single entities may vary within a set sets of
  entities may differ on average
• How to capture this variation?

5
Characterizing variation

• Where variation is described in words or images,
  analysis may be likewise verbal or visual, and
  relatively informal
• But even where entities are simply categorized,
  they can be counted
• And where they are measured, the methods
  available for summarizing variation are
  inherently quantitative

6
Data, variables and values

• What are data? (Singular datum Plural data)
• Givens fixed points which constrain possible
  interpretations
• Variation can be more formally seen in terms of
  variables e.g. stature
• In a particular case, the variable attains a
  particular value, e.g. stature of a particular
  person may be 178 cm

7
Kinds of variables

• Variables that can be analysed numerically are of
  several different sorts
• Categorical/qualitative/nominal variables
• Ranked/ordered/ordinal variables
• Numerical/quantitative/metric variables
• Different kinds of variables allow different
  kinds of numerical analysis
• This applies to the method of description or
  measurement, not the basic property

8
Categorical/qualitative/nominal

• E.g. female/male, A/B/AB/O blood groups, marital
  or employment status, artefact types
• You can assign code numbers to these values if it
  helps you to do so e.g. in SPSS you might code
  female as 1, male as 2, missing data as 9
• But in that case it is arbitrary what numbers you
  assign, you could have assigned reversed or
  different ones, and there is no implication of a
  mathematical relationship between the values
• You might summarize by reporting the modal (most
  common) category there is no average
• All cases should normally be placed in one and
  only one category

9
Ranked/ordered/ordinal

• Any numbers assigned indicate an ordered
  relationship between the values, but not
  necessarily any more than that
• E.g. many sociological psychological
  questionnaires have an ordered range of answers
  primatologists infer dominance amongst monkeys
  these can be coded the codes indicate relative
  rank only
• Results can be reported as modes or as medians
  (middle values of a distribution)

10
Numerical/quantitative/metric

• The case most familiar to scientists, where
  numbers have a true mathematical meaning the
  variable varies along an ordered scale of equal
  units 3 is as far from 4 as 4 is from 5
• E.g. the weight of a person, the length of a
  stone artefact, the volume of a pottery vessel,
  the area of a village
• It is meaningful to calculate a mean (average) as
  well as a median or mode

11
Numerical variables may have either interval or
ratio scales

• Both have an ordered scale of equal units
• Interval scales have equal units but do not make
  multiplicative sense or have a mathematically
  meaningful zero, e.g. ºC
• Ratio scales make multiplicative sense, e.g. a 66
  kg person is twice as heavy as a 33 kg person
  and zero is meaningful
• We shall generally not need to distinguish
  between interval and ratio subtypes of numerical
  variables

12
Numerical variables may be continuous or
discontinuous

• Continuous variables are in principle infinite
  and values may fall anywhere along the scale,
  between as well as on integers e.g. weights,
  volumes, areas, angles, linear measurements
• Discontinuous variables are essentially counts
  can only be integers e.g. no. of household
  members, fingerprint ridge counts, no. of teeth
  in a mandible or artefacts in a spit
• Means can be calculated for either

13
More terminology about variables

• Frequency of any value of a variable is the
  number of times that value is found i.e. it is a
  count, an absolute number
• Relative frequency of any value is its frequency,
  expressed as a proportion of all observations
  (often a percent)

14
More terminology about variables

• Ratio the size of a number relative to another
  number
• Proportion a ratio in which the second number
  includes the first
• Percentage a proportion multiplied by 100
• Rate a ratio of the number of events to the
  number of cases at risk of experiencing that event

15
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
  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

16
Examples of presentation

• Even the simplest forms of stating findings
  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?
• Does the graph have linear scales? A zero?
• Please bring in examples yourselves