Introduction Scatter Plots Linear relationships ...

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Overview

Introduction
Scatter Plots
Linear relationships
Curvilinear Relationship
Correlation of Dichotomies
Interpretation

CORRELATION Correlation Coefficients: Quantitatively describe
the strength and direction of a relationship
Ajin Jayan Thomas (PT) between 2 variables

Introduction Range from -1 to +1
-1 = perfect negative correlation
Purpose: Evaluate the relationship between two 0 = no relationship between the variables
variables +1 = perfect positive correlation
If research question is: “Is group A diff from B”
or “Does the treatment cause this outcome”- 1
then Statistical test of Group Differences
If research question is : “what is the
relationship between a and b” or “Does a
increase with b”- Then Correlation

CORRELATIONAL ANALYSIS 15-07-2011

DESIGN NON PARAMETRIC PARAMETRIC SCATTER PLOTS

One group – 2 sets of Spearman Rank Pearson product Each point/dot represents the intersection of a pair
scores Order correlation moment coefficient of of related observations

coefficent correlation Strength of Linear Association

One group – 3 or Kendall’s Coefficnet
more set of scores of Concordance

Dichotomies Phi coefficent
Point Biserial Coefficent
Rank Biseral Coefficent

Direction of Association

Positive Correlation : as the x Negative Correlation: as the x
variable increases so does the y variable increases, the y
variable decreases
variable

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Linear Vs Curvilinear Relationship Linear Relationship- r

r Association

0.00 to 0.25 Little or No relationship

0.25 to 0.50 Fair degree of relationship

0.50 to 0.75 Moderate to good

Above 0..75 Good

These should not be used as strict cut off points

Pearsons Product Moment Correlation Spearman Rank Order Correlation
Coefficient- Paramentric Coefficent Test (Rho)- Nonparametric

RESULTS FROM Subj Result from Calculations
EXPERIMENT experiment
SUBJ CALCULATIONS
VARIABLE A VARIABLE B
A×B A2 B2 Variable Variable Rank A Rank B d d2
AB (A-B) (A-B)2

df=N-2

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Curvilinear relationships The Correlation Matrix

Correlation Coefficent: ETA Cor relati ons

Interpretation of eta is same as r but eta can only be AGE HEIGHT WEIGHT SMWD BMI
positive ie from 0.00 to +1.00 .880* * .034
AGE Pearson Correlation 1 .967* * .808* * .000 .885
Example: 20 20
Relationship between Age Sig. (2-tailed) .000 .000 .870* * .065
and Strength .000 .785
N 20 20 20 20 20
Correlation of Dichotomies .884* * .577**
HEIGHT Pearson Correlation .967** 1 .852** .000 .008
Dichotomy: Nominal variable which can take only 20 20
2 values Sig. (2-tailed) .000 .000 1 .331
Eg: Male/Female, Yes/No response on Survey .154
Usually 1 or 0 is assigned to the 2 variables N 20 20 20 20 20
Phi Coefficent is calculated when both X and Y .331 1
are dichotomous. WEIGHT Pearson Correlation .808** .852* * 1 .154
A contingency table is formed. 20
Sig. (2-tailed) .000 .000 20

N 20 20 20

SMWD Pearson Correlation .880** .870* * .884* *

Sig. (2-tailed) .000 .000 .000

N 20 20 20

BMI Pearson Correlation .034 .065 .577**

Sig. (2-tailed) .885 .785 .008

N 20 20 20

**. Correlation is signif icant at the 0.01 lev el (2-tailed).

Association of success in motor and verbal skills

n=60 MOTOR SKILLS

FAIL PASS TOT
0 1 AL

VERBAL SKILLS FAIL A B 33 A+B
08 25

PASS C D 27 C+D
1 20 7

28 32 60
A+C B+D

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Point Biserial Correlation Rank Biserial Correlation

Interpreting Correlation Coefficents Factors Influencing the Generalization
of Correlation Coefficients
Based on COVARIANCE- if a change in x causes
a change in y,then x and y are said to COVARY Range of test values: Generalization of
Correlation coefficents do not compare variables should be limited to the range of
between the differences in the variables, you values that have been used to obtain the
will have to use for example a t test for that correlation
purpose Restricting the range of scores: Include as wide
Correlation does not mean that 2 variables a range of values as possible
have a causation relationship, x causes y or vice In a valid correlation the variables should be
versa independent of each other.

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