Statistics analysis of varience

1. Correlation Analysis

2. Meaning
Correlation analysis is a process for establishing the relationships
between two variables.
The measure is best used in variables that demonstrate a linear
relationship between each other..
• Correlation is used to test relationships between quantitative
variables or categorical variables. In other words, it’s a measure of
how things are related. The study of how variables are correlated is
called correlation analysis.

3. Some examples of data that have a high correlation:
• Your caloric intake and your weight.
• Your eye color and your relatives’ eye colors.
• The amount of time your study and your GPA
Some examples of data that have a low correlation (or none at all):
A dog’s name and the type of dog biscuit they prefer.
Correlations are useful because if you can find out what relationship variables have,
you can make predictions about future behavior. Knowing what the future holds
is very important in the social sciences like government and healthcare. Businesses
also use these statistics for budgets and business plans.

4. The Correlation Coefficient
• A correlation coefficient is a way to put a value to the relationship.
Correlation coefficients have a value of between -1 and 1. A “0” means
there is no relationship between the variables at all, while -1 or 1
means that there is a perfect negative or positive
correlation (negative or positive correlation here refers to the type of
graph the relationship will produce).

5. • Fg.1=

8. Interpretationof “r”orcorrelation coefficients:
Between ±0.80to ±0.99 High correlation
Between ±0.60to ±0.79 Moderately high correlation
Between ±0.40to ±0.59 Moderately correlation
Between ±0.20to ±0.39 Low correlation
Between ±0.01to±0.19 Negligible correlation

9. Pearson’s Coefficient
Correlation
• Karl Pearson’s coefficient of correlation is an extensively used
mathematical method in which the numerical representation is applied
to measure the level of relation between linearly related variables. The
coefficient of correlation is expressed by “r”.

10. 1. Find the Karl Pearson’s coefficient of correlation of the given data.
X: 2,3,4,5,6,7,8
Y: 4,7,8,9,10,14,18

11. Spearman’s Rank Correlation
• While calculating the correlation coefficient or product-moment correlation
coefficient, it is assumed that both characteristics are measurable. But, in reality,
some characteristics are not measurable. For example, the qualities of individuals
are not measurable. Instead, they can be ranked based on their qualities. In such
cases, rank correlation is used to determine the relationship between two
characteristics.
• This technique to find the correlation between the ranks of two series.

12. • Following are the