this presentation contains the types of correlation, uses, limitations, introduction to spearman rank correlation, and its application. a numerical is also given in the presentation

1. Correlation

2. Introduction
 In education many situations arises that involves
two or more variables. For example we have the
height and weight of 12 year old girls in 2 groups.
Now we can compute the mean and standard
deviation of height and we can do the same for
the weight but a very important question that
arises is there any relationship between height
and weight of these girls. So, to check that
relationship we have to apply some kind of
statistics. Which is known as correlation.

3. Meaning
Correlation emerges when
an educationist has to deal
with two or more variables.
In case the change in one
variable appears to be
accompanied by a change
in the other variable that two
variables are said to be
correlated and this
interdependence is called
correlation.

4.  In short we can say that correlation is the
relationship between two or more sets of
variables. The degree of relationship is
measured and described by the coefficient
correlation. Both the parametric Pearson
product moment and spearman non-
parametric method can be used to check the
correlation between two variables
 It is expressed on a range from +1 to -1,
known as the correlation coefficient.

5. Definition
 Correlation means that between two series or
groups of data there exist some connection (W.I.
King).
 Correlation analysis attempts to determine the
degree of relationship between variables (ya. Lun.
Chou)
 When the relationship is of a quantitative nature
the appropriate statistical tool for discovering and
measuring the relationship and expressing it in a
brief formula is known as correlation (Croxton and
Cowden)

6. Types of
Correlation
1.
Positive
2.
Negative
3. Zero
4.
Linear
5. Non-
Linear or
Curvilinear

7. 1. Positive Correlation
 This correlation refers to the movement of variables
in one direction. When increase or decrease in one
variable is accompanied by the increase or decrease
of another variable it is called positive correlation.
 For example increase in the hours of study leads to
an increase in attainment of marks in examination or
lesser the number of hours of study leads to lower
attainment of marks in examination.
 Another example is the relationship between the
speed and distance covered in a fixed time by an
individual.

8.  In a perfect positive correlation, expressed as +1,
an increase or decrease in one variable always
predicts the same directional change for the
second variable.
 There’s a common tendency to think that
correlation between variables means that one
causes or influences the change in the other one.
However, correlation does not imply causation.
There may be an unknown factor that influences
both variables similarly.

9. 2. Negative Correlation
 If there is an increase or decrease in one
variable and that leads to a decrease or
increase in another variable it is known as
negative correlation.
 For example sale of woolen garments depend
on the temperature of the climate sale
increases temperature decreases.

10.  A perfect negative
correlation means the
relationship that exists
between two variables
is exactly opposite all of
the time.
 The negative correlation
has a range between 0
to -1 i.e, -1 is the perfect
negative correlation

11. 3. Zero Correlation
 When there is no relationship between two
variables and the change of one situation
never affects the change of another situation
that is known as zero classroom.
 For example the relationship between the
shape of a head and intelligence of an
individual.

12. 4. Linear Correlation
 The relationship between two variables can be
explained with a straight line.
 For example if an individual has more intelligent
his performance in any field will increase.

13. 5. Non-Linear Correlation
 If an increase in one variable another variable
increases up to a certain direction and gain if that
variable decreases another variable also
decreases.
 For example rainfall relates more production to a
certain level more rainfall decreases production.

14. uses
 Correlation is used to describe the degree of relationship
between two variables.
 It is used to determine the reliability and validity of a test.
 It is used for determining statistical measures like factor
analysis.
 It predicts the dependent variable on the basis of
independent variable.
 It reminds correlation between certain traits of individuals
in a group.
 It is also widely accepted by the researchers in the field of
social science .

15. For teacher
 classroom teachers can use the correlation:
 To know the relationship between two School
subjects.
 To determine the relationship between teaching
method and achievement of student.
 To determine the reliability and validity of test.
 To determine the role of various traits and abilities
and how they correlate.

16. For Psychologist
 Psychologist can use the correlation method:
 To help in prediction on the basis of present
thoughts and activities.
 To determine the degree of relationship between
where is personality traits.
 To determine the role of heredity factories in
various psychological disorder.
 To determine the relationship between various
social thought for activities

17. Limitations of correlation
 Correlation is not and cannot be taken to imply
causation. Even if there is a very strong
association between two variables we cannot
assume that one causes the other.
 For example suppose we found a positive
correlation between watching violence on T.V.
and violent behavior in adolescence. It could be
that the cause of both these is a third
(extraneous) variable - say for example, growing
up in a violent home - and that both the watching
of T.V. and the violent behavior are the outcome
of this.

18.  Correlation does not allow us to go beyond the data that
is given. For example suppose it was found that there
was an association between time spent on homework
(1/2 hour) and number of 6 students achieving high
passes. It would not be legitimate to infer from this that
spending 1hour on homework would be likely to
generate 12 high achieving individuals.

19. Spearman Rank Difference
Method
 The Spearman’s rank coefficient of correlation is a
nonparametric measure of rank correlation (statistical
dependence of ranking between two variables).
 Named after Charles Spearman, it is often denoted by
the Greek letter ‘ρ’ (rho) and is primarily used for data
analysis.
 It measures the strength and direction of the
association between two ranked variables.

21. Steps
 Create a table from your data.
 Rank the two data sets. Ranking is achieved by giving the
ranking '1' to the biggest number in a column, '2' to the second
biggest value and so on. The smallest value in the column will
get the lowest ranking. This should be done for both sets of
measurements.
 Tied scores are given the mean (average) rank. For example,
the three tied scores of 1 euro in the example below are
ranked fifth in order of price, but occupy three positions (fifth,
sixth and seventh) in a ranking hierarchy of ten. The mean
rank in this case is calculated as (5+6+7) ÷ 3 = 6.
 Find the difference in the ranks (d): This is the difference
between the ranks of the two values on each row of the table.
The rank of the second value is subtracted from the rank of
the.
 Square the differences (d²) To remove negative values and
then sum them.

23. Merits
 It is easy to understand and easy to calculate.
 If we want to see the association between
qualitative characteristics, rank correlation
coefficient is the only formula.
 Rank correlation coefficient is the non-parametric
version of the Karl Pearson’s product moment
correlation coefficient.
 It does not require the assumption of the normality
of the population from which the sample
observations are taken.

24. Limitations
 If n >30, this formula is time consuming.
 The fact two variables correlate cannot prove
anything - only further research can actually prove
that one thing affects the other.

25. Assignment