Quantitative Analysis

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QuantitativeAnalysis
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Quantitative / Formal Methods

• objective measurement systems
• graphical methods
• statistical procedures

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why bother?

• description
• esp. of populations
• ex average height of people in room
• inference
• describe populations on the basis of samples
• test hypothesis about populations
• estimate levels of uncertainty associated with
  inferential description

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• exploratory analysis
• pattern searching/recognition
• data mining
• evaluate strength of patterning

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Patterning

• patterning departures from randomness
• strength of patterning ?
• ? degree of departure from randomness

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• how likely is it that observed patterning could
  have occurred by chance??
• this is a statistical question

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• is the patterning strong enough to either
  require or support an explanatory argument??
• this is usually an anthropological question

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basic vocabulary

• case
• variable
• data matrix
• attribute

• aggregation
• stratification
• accuracy
• precision

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• case
• equivalent to record
• something about which we want to make/record
  observations
• variable
• kinds of observations we want to make/record
• measurements of variability among cases

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cases and variables
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• attribute
• the intersection between cases and variables
• i.e., an observation about a specific case with
  reference to a specific variable
• ex.
• elk
• strongly agree
• plain-ware
• also called value, or variable state

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• aggregation
• grouping cases, usually on the basis of a shared
  attribute
• spatial proximity, temporal proximity
• gender of interment associated with grave lots
• stratification
• dividing cases into sub-groups
• usually to carry out parallel analyses that
  relate to different control conditions

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• accuracy
• an expression of the closeness between a measured
  (or computed) value and the true value
• frequently confused with precision
• precision
• has to do with replicability
• the closeness of repeated measures to the same
  value (not necessarily the true value)

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scales of measurement

• presence / absence data
• simply whether or not the case exhibits a
  specific state
• nominal data
• contrasting groups, usually mutually exclusive
• sometimes referred to as discrete or
  categorical data

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scales of measurement

• ordinal data
• a logical order or ranking exists among the
  various categories
• no assumptions implied about the measurement
  space occupied by categories
• ratio data
• also metric, continuous
• has a non-arbitrary zero
• can meaningfully compare measurements as ratios

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scales of measurement

• interval data
• distances between categories of measurement are
  fixed and even (unlike ordinal data)
• scale lacks a non-arbitrary zero (unlike ratio
  data)
• count data
• derived from nominal data
• really a kind of ratio data created by aggregation

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Drennan

• distinctions are inconsistent and not too
  important
• measurements vs. categories
• measurements quantities measured along a scale
• categories /- equivalent to nominal data
• counts discrete enumeration
• but, confusion does occur
• ex. cant use goodness of fit tests on nominal
  data!

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data coding

• presence / absence data
• can use 0 / 1 (but analyze with care!)
• nominal data
• OK to use integers (1, 2, 3, etc.)
• but dont subject them to arithmetic operations
• dont assume rules of numerical distance

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data coding

• ordinal data
• use integers
• ratio / metric data
• use integer or decimal notation
• dont record spurious levels of accuracy or
  precision
• note x 10.2 means 10.15 lt x lt 10.25

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coding missing data

• MD more problematic than most realize
• may want more than one code
• variable state is uncertain, vs.
• variable doesnt apply, vs.
• variable state is not present (not really MD)
• R gives you one coding option (NA)

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recoding data

• can readily recode down the scale (ex.
  ratio?ordinal)
• implies a loss of information and a probably
  wasted recording effort
• reporting apparently dubious counts as
  presence/absence data is not a good idea
• moving up the scale means redoing lab work

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data management

• three main options for electronic storage of
  data
• spreadsheet
• statistics package
• database

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• organized by cells
• no restrictions on cell content
• most useful for short-term manipulation of small
  datasets
• poor for long-term storage of complex
  datastructures

spreadsheet
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• data forms offer less versatility than
  spreadsheets
• organized by case variable
• powerful analytical tools
• poor management tools

stat-pac
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• best option for managing complex data structures

database
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pottery design elementsreptile eyeobsidian
knifecloud motif etc.
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multiple entry
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flat-file format
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relational database
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structured query language (SQL)
SELECT artifacts.catNum, design
elements.abbrevFROM design elements INNER
JOIN (artifacts INNER JOIN design element link
ON artifacts.ID design element link.artID)
ON design elements.ID design element
link.deID