QuantitativeAnalysis

Quantitative / Formal Methods

• objective measurement systems

• graphical methods

• statistical procedures

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

• exploratory analysis– pattern searching/recognition

– “data mining”

• evaluate strength of patterning…

“Patterning”

• patterning = departures from randomness

• strength of patterning = ?

degree of departure from randomness…

• “how likely is it that observed patterning could have occurred by chance??”

• this is a statistical question…

• “is the patterning strong enough to either require or support an explanatory argument??”

• this is usually an anthropological question…

basic vocabulary

• case• variable• data matrix• attribute

• aggregation• stratification• accuracy• precision

• 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…

cases and variables

variable 1 variable 2 variable 3 variable 4 variable 5 …case 1case 2case 3case 4case 5…

(data matrix)

• 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’

• 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

• 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)

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

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

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

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. can’t use ‘goodness of fit’ tests on nominal

data!

data coding

• presence / absence data– can use 0 / 1 (but analyze with care!)

• nominal data– OK to use integers (1, 2, 3, etc.)– but don’t subject them to arithmetic operations– don’t assume rules of numerical distance

data coding

• ordinal data– use integers…

• ratio / metric data– use integer or decimal notation– don’t record spurious levels of accuracy or

precision– note: x = 10.2 means 10.15 < x < 10.25

coding “missing data”

• MD more problematic than most realize…

• may want more than one code:1. variable state is uncertain, vs.

2. variable doesn’t apply, vs.

3. variable state is not present (not really MD)

• R gives you one coding option (“NA”)

recoding data

• can readily recode “down” the scale (ex. ratioordinal)

– 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…

data management

• three main options for electronic storage of data:

– spreadsheet– statistics package– database

• 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’

• data forms offer less versatility than spreadsheets

• organized by case & variable

• powerful analytical tools

• poor management tools

‘stat-pac’

• best option for managing complex data structures

‘database’

pottery design elements:

‘reptile eye’‘obsidian knife’‘cloud motif’ etc….

artifact # design elementsax-122 reptile eye, obsidian knife, cloudaz-01 maguey thorn, reptile eyeaa-01 jaguar paw… …

“multiple entry”

“flat-file” format

artifact # D1 D2 D3ax-122 rep obk cldaz-01 mgt repaa-01 jgp…

artifact # rep obk cld mgt jgpax-122 1 1 1 0 0az-01 1 0 0 1 0aa-01 0 0 0 0 1…

artifactsID catNum

1 ax-1222 az-013 aa-01

design element linkartID deID

1 11 21 42 12 23 5

design elementsID element abbrev

1 reptile eye rep2 obsidian knife obk3 maguey thorn mgt4 cloud cld5 jaguar paw jgp

artifacts design element linkID 1------------- artID design elementscatNum deID -------------1 ID

elementabbrev

relational database

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;

catNum abbrev

ax-22 rep

ax-22 obk

ax-22 cld

az-01 rep

az-01 obk

aa-01 jgp

“structured query language” (SQL)