Quantitative Analysis

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 (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 < 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. 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…

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….

“multiple entry”

“flat-file” format

relational database

SELECT artifacts.catNum, [design elements].abbrev FROM [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; “structured query language” (SQL)