Slide 1 : The Scores of 120 persons
Slide 2 : MEASURES OF CENTRALL TENDENCY Mean
Median
Mode
Geometric Mean
Harmonic Mean MEASURES OF DISPERSION Range
Quartile Deviation
Mean Deviation
Standard Deviation
Coefficient of Variation Average (X) = 20
Average (Y) = 20 SD (X) = 0.00
SD (Y) = 7.07
Slide 3 : Correlation is a characteristic that is found between two variables, which shows a sort of relationship between them
Treatment and Response, Income and Saving, Height and Weight, are certain pairs of characteristics that exhibit relationship.
The relationship could be linear or non linear and can be observed from statistical data.
Correlation Coefficient is a measure of linear relationship between two variables and denoted by r, known as Pearson’s Product Moment Formula Correlation Analysis
Correlation Analysis : Correlation Analysis It is also known as simple correlation coefficient
It is required that both the variables should be on a scale (measurements) rather than an ordinary scale (categorical)
The value of r between two variables X and Y could be anywhere between –1 and +1
A positive value indicates a positive relationship. We say X and Y are in sympathy with each other
A negative value indicates negative relationship
Slide 5 : If r = +1 we say the relationship is positive and perfectly linear
If r = -1 the relationship is negative and perfectly linear
Higher the magnitude stronger is the relationship
The Correlation Coefficient could be sometimes spurious and becomes nonsense. Spurious or real?
Slide 6 : The square of r is used as a measure of the strength of linear relationship between X and Y.
Suppose r = 0.80 it indicates a positive relationship, apparently high but explains (0.80)2 = 0.64 and the meaning is that about 64% of the variation between the variables can be explained by one variable about the other.
Remaining 36% is not accounted for! Is it good?
Slide 7 : Care in use Correlation Coefficient is a wrong tool to use when the relationship is known to be week or not a linear one
The observed Correlation Coefficient could be an observation by chance.
So it needs a statistical test of hypothesis
The Student’s t-test is applied to check significance
Correlation Coefficient however does not indicate a cause and effect relationship
Slide 8 : Correlation Coefficient r
r ranges from +1 to -1
r = +1 a perfect positive linear relationship
r = -1 a perfect negative linear relationship
r = 0 indicates no correlation
Strength of Linear Association : Strength of Linear Association
Slide 10 : Other Strengths of Association
Slide 11 : Selected Values of r and r 2 Selected values of r and r 2 % %
r r accounted for not accounted for 2 .10 .01 1% 99%
.20 .04 4% 96%
.30 .09 9% 91%
.40 .16 16% 84%
.50 .25 25% 75%
.60 .36 35% 64%
.70 .49 49% 51%
.80 .64 64% 36%
.90 .81 81% 19%
1.00 1.00 100% 0% 2
Slide 12 : Scatter diagram
Slide 13 : Scatter diagram
Slide 14 : SOME INTERESTING RELATIONSHIPS!!! Increasing trend
Positive Relation
r = 0.699 No clear trend
Possibly no relation
r = 0. 084
Slide 15 : No linear relationship? There is no specific trend in this case!
Specific Example : Specific Example For seven random summer days, a person recorded the temperature and their water consumption, during a three-hour period spent outside.
Correlation : Correlation Correlation
A measure of association between two numerical variables.
Example (positive correlation)
Typically, in the summer as the temperature increases people are thirstier.
Example : Example
Slide 19 : Reading Correlation Matrix r = -.904 p = .013 -- Probability of getting a correlation this size by sheer chance. Reject Ho if p = .05. sample size r (4) = -.904, p?.05
Slide 20 : Correlation Does Not Mean Causation High correlation
Hen’s crow and the rising of the sun
Hen does not cause the sun to rise.
Teachers’ salaries and the consumption of liquor
Slide 21 : Limitations of Correlation linearity:
can’t describe non-linear relationships
e.g., relation between anxiety & performance
truncation of range:
underestimate stength of relationship if you can’t see full range of x value
no proof of causation
third variable problem:
directionality: can’t be sure which way causality “flows”
Slide 22 : Questions ???
Slide 23 :