Computing in archaeology l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 63

Computing in Archaeology PowerPoint PPT Presentation


  • 161 Views
  • Uploaded on
  • Presentation posted in: General

Computing in Archaeology. Session 11. Correlation and regression analysis. © Richard Haddlesey www.medievalarchitecture.net. Lecture aims. To introduce correlation and regression techniques. The scattergram.

Download Presentation

Computing in Archaeology

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Computing in archaeology l.jpg

Computing in Archaeology

Session 11. Correlation and regression analysis

© Richard Haddlesey www.medievalarchitecture.net


Lecture aims l.jpg

Lecture aims

  • To introduce correlation and regression techniques


The scattergram l.jpg

The scattergram

  • In correlation, we are always dealing with paired scores, and so values of the two variables taken together will be used to make a scattergram


Example l.jpg

example

  • Quantities of New Forrest pottery recovered from sites at varying distances from the kilns


Negative correlation l.jpg

Negative correlation

Here we can see that the quantity of pottery decreases as distance from the source increases


Positive correlation l.jpg

Positive correlation

Here we see that the taller a pot, the wider the rim


Curvilinear monotonic relation l.jpg

Curvilinear monotonic relation

Again the further from source, the less quantity of artefacts


Arched relationship non monotonic l.jpg

Arched relationship (non-monotonic)

Here we see the first molar increases with age and is then worn down as the animal gets older


Scattergram l.jpg

scattergram

  • This shows us that scattergrams are the most important means of studying relationships between two variables


Regression l.jpg

REGRESSION

  • Regression differs from other techniques we have looked at so far in that it is concerned not just with whether or not a relationship exists, or the strength of that relationship, but with its nature

  • In regression analysis we use an independent variable to estimate (or predict) the values of a dependent variable


Regression equation l.jpg

Regression equation

y = f(x)

  • y = y axis (in this case the dependent

  • f = function (of x)

  • x = x axis


Slide13 l.jpg

y = f(x)

y = x y = 2x y = x2


General linear equations l.jpg

General linear equations

  • y = a + bx

  • Where y is the dependent variable, x is the independent variable, and the coefficients a and b are constants, i.e. they are fixed for a given data


Therefore l.jpg

Therefore:

  • If x = 0 then the equation reduces to y = a, so a represents the point where the regression line crosses the y axis (the intercept)

  • The b constant defines the slope of gradient of the regression line

  • Thus for the pottery quantity in relation to distance from source, b represents the amount of decrease in pottery quantity from the source


Slide17 l.jpg

y = a + bx


Slide20 l.jpg

least-squares


Slide21 l.jpg

least-squares


Slide22 l.jpg

least-squares


Slide23 l.jpg

least-squares


Slide24 l.jpg

y = a + bx


Slide25 l.jpg

y = a + bx


Slide26 l.jpg

y = 102.64 – 1.8x


Slide29 l.jpg

CORRELATION


Slide30 l.jpg

CORRELATION

1 correlation coefficient


Slide31 l.jpg

CORRELATION

1 correlation coefficient

2 significance


Slide32 l.jpg

CORRELATION

  • 1 correlation coefficient

    • r

  • 2 significance


  • Slide33 l.jpg

    CORRELATION

    • 1 correlation coefficient

      • r

      • -1 to +1

  • 2 significance


  • Slide35 l.jpg

    Levels of measurement:

    • nominal – in name only

    • ordinal – forming a sequence

    • interval – a sequence with fixed distances

    • ratio – fixed distances with a datum point


    Slide36 l.jpg

    Levels of measurement:

    • nominal

    • ordinal

    • interval

    • ratio


    Slide37 l.jpg

    Levels of measurement:

    • nominal

    • ordinal

    • interval Product-Moment

    • Correlation Coefficient

    • ratio


    Slide38 l.jpg

    Levels of measurement:

    • nominal

    • ordinal Spearman’s Rank

    • Correlation Coefficient

    • interval

    • ratio


    Slide40 l.jpg

    The Product-Moment

    Correlation Coefficient


    Slide41 l.jpg

    sample – 20 bronze spearheads

    length (cm) width (cm)

    n=20


    Slide42 l.jpg

    r = nΣxy – (Σx)(Σy) g

    √[nΣx2 – (Σx)2] [nΣy2 – (Σy)2]

    length (cm) width (cm)

    n=20


    Slide43 l.jpg

    r = nΣxy – (Σx)(Σy) g

    √[nΣx2 – (Σx)2] [nΣy2 – (Σy)2]

    n=20


    Slide44 l.jpg

    r = nΣxy – (Σx)(Σy) g

    √[nΣx2 – (Σx)2] [nΣy2 – (Σy)2]

    n=20


    Slide45 l.jpg

    r = nΣxy – (Σx)(Σy) g= +0.67

    √[nΣx2 – (Σx)2] [nΣy2 – (Σy)2]

    n=20


    Slide46 l.jpg

    Test of product moment correlation coefficient


    Slide47 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0


    Slide48 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0


    Slide49 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables approximately random


    Slide50 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables approximately random

    Sample statistics needed: n and r


    Slide51 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables approximately random

    Sample statistics needed: n and r

    Test statistic: TS = r


    Slide52 l.jpg

    Test of product moment correlation coefficient

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables approximately random

    Sample statistics needed: n and r

    Test statistic: TS = r

    Table: product moment correlation coefficient table.


    Slide54 l.jpg

    n = 20


    Slide55 l.jpg

    n = 20 r = 0.67 p<0.01


    Slide56 l.jpg

    n = 20 r = 0.67 p<0.01

    length (cm) width (cm)


    Slide57 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)


    Slide58 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0


    Slide59 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0


    Slide60 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables at least ordinal


    Slide61 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables at least ordinal

    Sample statistics needed: n and rs


    Slide62 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables at least ordinal

    Sample statistics needed: n and rs

    Test statistic: TS = rs


    Slide63 l.jpg

    Spearman’s Rank Correlation Coefficient (rs)

    H0 : true correlation coefficient = 0

    H1 : true correlation coefficient ≠ 0

    Assumptions: both variables at least ordinal

    Sample statistics needed: n and rs

    Test statistic: TS = rs

    Table: Spearman’s rankcorrelation coefficient table


  • Login