This document discusses correlation and different aspects of studying correlation. It defines correlation as the association or relationship between two variables that do not cause each other. It describes different types of correlation including positive, negative, linear, non-linear, simple, multiple and partial correlation. It also discusses various methods of studying correlation including graphic methods like scattered diagrams and correlation graphs, and algebraic methods like Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient. The document explains concepts like coefficient of determination and hypothesis testing in correlation. It emphasizes that correlation indicates association but does not necessarily imply causation between variables.

1. CORRELATION
Fahmida Rashid Swati
Assistant Professor
Department of Obstetrics & Gynecology
Chittagong Medical College
Email:dr.fahmidaswati@gmail.com

2. Independent
Variables
Dependent Variable

3. Independent
Variables
Dependent
Variable

4. 1st 3rd
2nd
Rank
Independent
Variables
Dependent Variable

5. Quantity
Independent
Variables
Dependent Variable

6. Category
Independent
Variables
Dependent Variable

7. Pollen
Asthma
Independent
Variables
Dependent Variable

8. History
1888-Francis Galton
concept of correlation.
kerl Pearson -1896
Reformulated
Correlation coefficient ’ r’
British Physiologist
E. E. Spearman in 1904,
Rank Correlation

9. Contents
•Correlation
•Types of Correlation
•Methods of Studying Correlation
•Coefficient of Correlation
•Coefficient of determination
Correlation

10. • Association or relationship between two
variables that don’t cause each other.
Correlation
The concept of
Correlation
X
Co vary --- Go Together
Y

11. Variables

12. Purpose of Correlation
Determines values of one variable are
related to another or not
Y
X

13. Independent
Variables
Dependent
Variables
Grade
depends on
Number of Study Hour
Are these two
variables Related ?

14. Types
Correlation
Positive
Negative
Zero
Linear
Non Linear
Simple
Multiple
Partial
Degree of correlation No of Variables
Linearity

15. Positive Correlation
Variables go in the SAME
direction
Direct Relationship between
two variables
Increment of one variables
also ↑ another variables
and vice versa. Dependent
Variable
Independent Variable

16. SUNLIGHT
Growth
of
Plants
Y value
increases as
X value increase
Independent Variable
Dependent
Variable
Dependent
Variable-Y
Independent Variable-X

17. Labor pain in hour- X axis
Dilatation
of
Cervix
Y-Axis
Independent Variable
Dependent
Variable
x
x
x

18. Negative Correlation
Two Variable , X and Y go
In OPPOSITE direction
The ↑ in one variable X
results in the
corresponding ↓ in the
other variables.
Dependent
Variable
Independent Variable

19. Y-Value ↓as
X-value ↑
Dependent
Variable
Independent
Variable
Dependent
Variable

20. Dependent
Variable
Independent Variable

21. Zero
• No correlation
Change of X
not associated with
change of Y
X
Y

22. Dependent
Variable
Independent Variable

23. Linear Correlation
Relationship between 2 variables are in
straight line , either upward or downward
slopping
upward
downward

24. upward
Dependent
Variable
Independent Variable

25. Non Linear/Curvilinear
Ratio of changes between two
variables -not constant
• Relationship not in straight line,
• Either upward or downward slopping curve.

26. upward slopping curve
downward slopping curve
Dependent
Variable
Dependent
Variable
Independent Variable
Independent Variable

27. Partial
• Relationship between 2 variables keeping the
other variable constant or fixed
Influence of 3rd variable
Eliminated here.

28. Taking out the effect
of economic state
Mother Child

29. Multiple
• The relationship among 3 or more variables at
the same time.
Fetal Growth
Nutrition
Preeclampsia
Smoking

30. Method of
Studying
Correlation
Graphic
Scattered
Diagram
Correlation
Graph
Algebraic
Karl Pearson
Coefficient
Spearman’s
Rank
Coefficient
Collect Data → Compile data

31. Graphic

32. Scattered Diagram Method
Each points of Graph
represents a
combination value - Xi
& Yi
One of the simplest ways of diagrammatic
representation of the quantitative bi-variate.
55 Inch
10 Yr
Dependent
Variable
Independent Variable

33. Positive
relationship
between hours of
study & Grades
• Points are represented
by dots .
• By convention,
Independent variable(IV)
plotted on
horizontal X-axis.
Dependent Variable(DV)
plotted on Vertical Y-axis
X
Y
The closer the point lie to a
straight line , the stronger the
linear relationship

34. Two information
• Nature &
Strength
Pattern of
Relationship

36. Advantage:
•First Steps in investigating relationship between
two variables.
•Simple & Non mathematical
•Not influenced by size of extreme values
Disadvantage:
Can not adopt an exact degree of
correlation

37. Correlation Graph
Independent Variable

38. Algebraic
-Correlation Analysis
Correlation Coefficient
Karl Pearson
Coefficient
Spearman’s
Rank
Coefficient
Coefficient of Determination

39. Means for examining the relationship between
two variables systematically
It measures co-variation, not causation
Correlation analysis
Before conducting Correlation Analysis, always
should create a two-way scatter Plot
Existence of linear relationship between X & Y
determined Via scatter Plot

40. Two-way Scatter Plot

41. A measure of the strength & direction of a linear
relationship between two variables.
Correlation Coefficient
Strength of
Relationship
Direction of
relationship
Size indicates
strength
(values closer to -1
or +1 indicate
greater strength)
-ive =
inverse
/indirect
relation
+ive
same
direction/direct
relation

42. Correlation Coefficient
Computed from sample data
‘r’
p (rho)
‘r’ has no unit

43. In Perfect +ive linear
relationship r is +1
Range of Correlation Coefficient
In Strong +ive linear
relationship r close to +1
-1 to +1
In Perfect -ive linear
relationship r is -1
In Strong -ive linear
relationship r close to -1
In Nonlinear relationship
r close to ‘0’
In Weak/No relationship
r close to ‘0’

45. Interpretation of Value of ‘r’
Larger absolute value of r –stronger relationship

47. Importance of Correlation analysis
Used to derive degree/strength & direction of
relationship between 2 variables.
Useful in presenting average relationship between
2 variables.
Use to ↓ range of uncertainty in matter of
prediction.

49. Step 1: Kind of Scale

50. Ranked Order Scale

51. Continuous Scale

52. Categorical Scale

53. Combination of 3 Scale

54. Formula
N - Number of Paired Data
X - Independent Variable
Y - Dependent Variable

55. Correlation between Age and Blood Pressure
X-Age
Y-Blood Pressure
XY- Age X BP
X2-Age 2
Y2- BP2
With Formula:
r = .897
X Y XY X2 Y2
Suggests a strong +ive
relationship between
age & blood pressure

56. Association Between
Height & Weight
Association between Likert
Scale on work satisfaction
and work output
Two continuous Variables
Pearson
Linear Relationship
One continuous and One
categorical
Variable(Ordinal)/Ranked
order scale
Spearman
Step 2 &3:
Decide And Calculate Correlation Coefficient:

57. Interval /Ratio
Measure
Most
Popular
Normally
distributed
linear
relationship
Quantitative
variable

58. Gives precise numerical value of degree of
linear relationship between two variable.
Measures strength and direction of
linear relationship between two
variables.
A ‘r’ = 0.9 (+/-) - very strong Association
‘r’- value has nothing to do with 90% CI

59. • Not need to know
exact formulas.
• Not need to be able
to do by hand.

60. Non parametric
statistical Measure
Non Normal
distribution &
ordinal scale
Used to study
strength of
association
between two
ranked variable
Observed value
qualitative/
quantitative
converted to Rank

61. • r= Rank correlation Coefficient
• D= Difference between ranks(R1-R2)
• N= Number of paired observations
• In case of r -1 ≤ R ≤ +1
• The sum of the total Rank difference is
always equal to Zero ,i.e.ED=0
• Not need to know
exact formulas.
• Not need to be
able to do by
hand.

62. •If Spearman Correlation Coefficient is -
0.108 & p is 0.117
•Compared values against Spearman
Table
•Value 0.117 < 0.364 (P = 0.05.)
•Here P is > 0.05
Inference:
There is no significant
association between hours of
TV watched/week & IQ

63. • ‘r’ and rs similar Meaning
• Difference is :

65. Coefficient of Determination(CoD)
Used for interpretation of correlation &
comparing 2 or More correlation coefficient
Square of Correlation Coefficient i.e. r2
Explain % of variation in dependent variable Y that can be
explained in terms of independent variable X.
If r=0.8 , r2= 0.64,
It implies that 64% of total variations in Y occurs due to X.
The remaining 34% variation occurs due to external
factors.

66. So, CoD = r2=
Total Variance
Explained variance

67. If Pearson r = -0.5
r2= 0.25
Expression:
1/4th or 25% of variability in GPA scores
accounted by depression
(remaining 75% of variability is other factors,
habits, ability, motivation, courses studied , etc)
Correlation of Depression with GPA
grade:

68. If ‘r’ = 0.5 r2 = 0.25
If ‘r’ = 0.7 r2 = 0.49
r2 tells us that -
r = 0.7 accounts for about 2 fold
variability relative to r= 0.5
While ‘r’ = 0.5 Vs 0.7
might not look so different in terms
of strength.
0.49
0.25

69. Correlation Hypothesis Testing:
Step1:Identify Population, distribution and
assumption
Step 2:State null
Hypothesis and Research
Hypothesis
Step 3: Determine
Characteristics of
comparison distribution
Step 4: Determine The
critical Value
Step5: Calculate The
test Statistic(t)
Step 6: Make a decision

70. ‘Correlation’
does not imply
‘Causality’

71. Causation:
Cause & Effect Relation
Correlation :
•Interdependency among
Variables for correlating 2
phenomenon.
•Should have cause-effect
relationship &
Otherwise can not be
correlated .
Two variables vary in
such away that
movement in one
accompanied by
movement in other.
Causation always implies
correlation
but
correlation does not
necessarily implies
causation.

72. With large sample , even a small correlation can
be statistically significant
Correlation measure association not
causation.
Correlation assumes linear relationship.
Take Home Massage :
Statistically significant correlation may not be
practically significant.
A low correlation is still a low correlation

73. Values between -1 & +1 measure strength &
direction of the relationship
In simple linear Correlation Coefficient –
variables normally distributed.
In Spearman’s Rank Correlation Coefficient –
variables doesn’t follow normal distribution.

74. সম্পর্ক গুল ো কর্মন অদ্ভু ত!
কর্ছু কর্ছু সম্পলর্ক র কর্োন নোম হয় নো।
কতোমোর র্োন্নোয় আমোর ক োখ কিলে উলে
কতোমোর র্থোয় সব ি
ু ল ছুটি নতু ন পলথ।
বৃকিলত হোত ধলর কিেলত ইলে হয়
ইলে হয় কতোমোর পোাঁ লে কথলর্ র্কর কবশ্ব কর্ েয় ।
মুলেো মুলেো খুকের আড়োল কতোমোয়
হোকরলয় কে োর খুব িয় হয়!
Dependent Variable - আমি
Independent Variable – ত
ু মি
Qualitative Variable –
ততোিোর -কথো—কোন্নো
আিোর -বৃমি তেজো – মবশ্ব জয়- খুমি- েয়
CC: Spearman Correlation
Coefficient
Hypothesis–
Null- ততোিোর কথোর সোথথ আিোর খুিীর
তকোন সম্পক
ক নোই।
Alternate- ততোিোর কথোর সোথথ আিোর
খুিীর সম্পক
ক আথে ।

76. Choosing the
‘right Method’ for the data
is the key statistical expertise one
need to have .

77. Do we need to know the formulas?
• Not need to know
exact formulas.
• Not need to be able
to do correlation &
regression by hand.
•Need to understand
concept behind them
& general statistical
concepts to use the
formula.

78. Relationship between immediate postpartum umbilical cord pH,
fetal distress and neonatal outcome
Correlation of biological parameters with placental parameters
and pregnancy outcomes in pre-eclamptic women