TESTS OF CORRELATION

Correlation vs Regression

The two most common methods to describe the relationship between two quantitative variables ( x and y) are linear correlation and linear regressionLinear correlation is a statistic that measures the STRENGTH of a bivariate association while linear regression is a prediction equation that estimates the value of y for any given x

Questions that can be answered by Correlation:

Is there a relationship between IQ and Grade point average?

Is there a relationship between the size of the family and educational attainment of the father?

Questions that can be answered by Regression:

What change will occur in ones blood pressure after one reduces salt intake?

What would be an infants predicted birth weight for a mother possessing a known prepregnancy weight?

What would be the predicted grade of student in college algebra given her/his grade in Highschool math?

Test of Hypothesis

Null Hypothesis (Ho) : There is no relationship between/among variables

Alternative Hypothesis (Ha) : There is relationship between/among variables

When we accept Ho

It means that the difference is due to

* Sampling Fluctuations

* Chance Occurrence

* Correlation obtained is applicable only on the sample and not be concluded/applied on the population

When we reject Ho

We say that the sample results are significant. The correlation obtained can be applied to the actual population

The result obtained is NOT by mere chance or sampling variation

Interpretation of alpha (a) and p-value

Level of significance of .05 means that in repeated sampling from a given population of interest, the probability of obtaining sample results similar to the one presently observed is 95% and the probability of obtaining different sample results is 5%

Significance of a certain level alpha means that the results due to plain chance or sampling error is equal or less than alpha

A p-value of .005 means that the probability of committing the error of rejecting a true null hypothesis is 0.5% and the the probability that the said error is not committed by the researcher is 99.5%

1. PHI COEFFICIENT

Determines the degree of relationship between two variables which are both nominal dichotomous

2x2 table

Example. Finding the correlation between the hypothetical data on voters' sex (male=1, female=0) and preference for president (male prex=1, female prex=0)

Test of Hypothesis

Ho: there is no relationship between gender and preference for presidentHa: there is relationship between gender and preference for presidentComputed:2.58 tabulated: 1.96Decision: Reject HoConclusion: At 5% level of sig, it can be concluded that there is relationship between gender and preference for president. A female voter is most likely to prefer a male president, and a male voter is most likely to prefer a female president.r=-0.81, remarks = very strong relationshipCoefficient of determination = 0.67 or 67% of the preference for president can be attributed to ones gender

PHI-CORRELATION (At the back of Page 90)

Determine correlation of a. gender and watching basketball A and K)b. Draw a 2x2 table at the back of page 90,write summarized valuesc. conduct test of hypothesis

Ho: There is no relationship between gender and likeness to watch basketballHa: There is relationship between genderand likeness to watch basketballcomputed: tabulated: decision:conclusion:r = interpretation=

r2=interpretation=

3. Pearson Product-Moment

Commonly used test of correlation

Pearson moment correlation ( r )

Coefficient of Determination ( r2 ), determines the variation of the variables attributed by the other variable

PEARSON PRODUCT (Page 103)

Determine correlation of the ff:1. math grade and english grade (H and I)2. Height and arm span ( D and E)3. Neck circumference and waist line (F and G)

Conduct test of hypothesisHo:Ha:Computed: Tabulated: Decision:Conclusion:r= remarks:r2 = interpretation:

2. POINT-BISERIAL CORRELATION

Dichotomous measure will be in the form of arbitrary code nos. like 1 and 0

Used for 2 variables- interval/ratio and nominal dichotomous

Point biserial correlation ( r ), Coefficient of Determination ( r2 ), determines the variation of the variables attributed by the other variable

POINT BISERIAL (Page 105)

Determine correlation between1. Gender and Height (A and D)2. Cup of rice and Weight (B and C)3. Gender and Math grade (A and I)

Conduct test of hypothesisHo:Ha:Computed: Tabulated: Decision:Conclusion:r= remarks:r2 = interpretation:

4. SIMPLE LINEAR REGRESSION

This method can be used on predicting values of the dependent variable

The variable that is used to make the prediction is called the predictor variable; the variable about which the prediction is made is called the criterion variable

Only when a correlation of 0.50 or higher is obtained can individual predictions that are reasonable accurate for most purposes be made

LINEAR REGRESSION (Page 113)

Determine regression equation of :1.math grade (y) and hrs. of study (x)2. english grade (y) and hrs. of study (x)

Result of Pearson Moment Correlation

Result of Linear Regression:
y = 6.77 + 3.907 x

VotersGenderResult

A10

B10

C10

D11

E10

F01

G01

H01

I01

J01