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Correlation Analysis

- Topics
- Scatterplot
- Pearson product-moment correlation coefficient
- Coefficient of Determination ( R2)
- Testing the significance of r
- Other correlation coefficients

Correlation defined

Correlation is the degree of relationship that exists between two variables. Correlation however does not imply “causation” but merely implies that the two variables under study is “associated” in some way.

This association is measured as “coefficient” of correlation denoted as “r”. The most common of which is the Pearson product-moment correlation coefficient, or "Pearson's correlation coefficient"

Interpreting “strength” of correlation coefficient

From the previous value of r ( = 0.9960) the strength of relationship

Between “age” and “years of management experience” is “very high”

Other interpretations of Pearson’s r

- Coefficient of Determination ( r2 )
- there are cases wherein the verbal interpretation of r may not be enough to answer the requirements for further analysis of the data presented. The coefficient of determination ( r2 ) is used to show the percentage of the variations of the dependent variable y that can be attributed to the independent variable x , the rest is attributable to chance.

Previous example: if r = 0.9960 (“very high” )

then r2 = 0.9921 ( 99 .21 % of variation in y is due to x )

therefore 1 - r2 = 0.79% ( less than 1 % is due to chance)

Testing the significance of r

Solution:

Step1 : H0there is no significant relationship between age and years of

management experience

Ha : there is significant relationship between age and years of

management experience

Step2 : df= (n-1) = (30-1)= 29, t (two tailed, 1%, 29)= ± 2.756

Step3 : t test

Step4: Decision: Reject Ho

Step5: there is a significant relationship between age and years of

management experience

Find the coefficient r

Coefficient of Determination ( r2 ) = 0.6776

1 - r2 = 0.3223

therefore 32.23% is due to

chance variation

High (negative) correlation

Testing the significance of r

Solution:

Step1 : H0there is no significant relationship between year and malnutrition rate

Ha : there is significant relationship between year and malnutrition rate

Step2 : df= (n-1) = (8-1)= 7, t (two tailed, 1%, 7)= ± 3.499

Step3 : t test

Step4: Decision: Reject Ho

Step5: there is a significant relationship between year and

malnutrition rate

Review exercise : Knowledge test(x) and skills test ( y)

A training program requires the measurement of knowledge and skills gained . Find/ complete the following

1) Scatterplot of the data.( provided)

2) compute for the correlation coefficient.

3) coefficient of determination

4) test if r is significant.

Submit thru [email protected] not later than Wednesday, October 2, 2013.

Other correlation coefficients

It can be observed from the two previous examples that the values of x and y are both scale/interval values and uses Pearson's correlation coefficient r.

Pearson’s r is specific only for this level of measurement and the assumption that the relationship described is “linear” in nature may not be fully applicable for other cases.

This necessitates the use of other “derived” measures of correlation, the discussion of which will be further explored independently from the core discussions included in this presentation.

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