Bivariate Relationships

0These are studies which call for determining relationships between pairs of variable , such as intervention and effects or inputs or outputs.

0The appropriate analytic technique for examining bivariate relationship is defined by the variables whether they are nominal, ordinal, or interval.

0When one is to examine relationship between two nominal variables, the chi-square should be applied to the cross-tabulated variables so as to find out whether significant relationship exists between two variables.

0If the relationship does exist and the researcher wishes to know the strength of relationship, then the “measure of association” is to be used.

0For the nominal variables, one of the best measures of association is the Cramer’s V which is derived by using the chi-square value.

LEVEL OF ASSOCIATION Verbal Description COMMENTS

0.00 No Relationship Knowing the independent variable does not help in predicting the dependent variable.

.00 to .15 Very Weak Not generally acceptable

.15 to .20  Weak  Minimally acceptable

.20 to .25 Moderate  Acceptable

.25 to .30 Moderately Strong  Desirable

.30 to .35 Strong  Very Desirable

.35 to .40 Very Strong Extremely Desirable

.40 to .50 Worrisomely Strong Either an extremely good relationship or the two variables are measuring the same concept

.50 to .99 Redundant The two variables are probably measuring the same concept.

1.00 Perfect Relationship.  If we the know the independent variable, we can perfectly predict the dependent variable. 

GAMMA0There are various measures of association which

can be used in examining the relationship between the cross-tabulated ordinal variables. One of the simplest to calculate is gamma. However, there is NO significance test for gamma. Some researchers resort to using the chi-square test to find out whether the relationship between variables is significant.

0This test is not sensitive to the ordinality of the data and, therefore, does not provide a true test of the significance of gamma.

0In examining the relationship between variables distinguished as independent and dependent, linear regression analysis may be used.

0For this, the measure of association is the zero-order-regression coefficient. This measure indicates the average amount of change in the dependent variable in relation to the unit of change in the independent variable.

Relationships Between Interval Variables

0can be studied with or without cross-tabulation.0If interval variables are cross-tabulated, the nature

of the relationship will become apparent and the values of gamma or Cramer’s V can be assessed.

0If interval variables are not cross-tabulated, the most common measure relationship is the Pearson correlation coefficient (r) the statistical significance of which can be assessed by the use of t-test.

Linear Relationship 0Can be measured by either the correlation

coefficient or by the regression coefficient. In such relationship, the value of one variable rises or declines in direct proportion to rises or declines in the value of the other variable.

0These two coefficients (correlation coefficient and the regression coefficient) are not sensitive to non-linear relationships where high values of one variable are associated with both high and low value of another variable.

0It should be that all the measures of association above, except for the regression coefficient and Cramer’s V range from -1.oo (a perfect negative relationship) to +1.00 (a perfect positive relationship).

0When there is no relationship, the coefficient is 0.00.

0Finally, it should be remembered that none of the measures of association indicate whether a relationship is casual or not.

SUMMARY o.O

0BIVARIATE RELATIONSHIPS ARE STUDIES WHICH CALL FOR DETERMINING RELATIONSHIPS BETWEEN PAIRS OF VARIABLE.

0THE MEASURES OF ASSOCIATION IS USED WHEN ONE WISHES TO KNOW THE STRENGTH OF RELATIONSHIP.

0CRAMER’S V0GAMMA IS THE TEST THAT IS NOT SENSITIVE TO THE

ORDINALITY OF THE DATA.0RELATIONSHIPS BETWEEN INTERVAL VARIABLES CAN

BE STUDIED WITH OR WITHOUT CROSS-TABULATION.0PEARSON CORRELATION COEFFICIENT (r)

0INTERVAL VARIABLES ARE NOT CROSS-TABULATED0THE STATISTICAL SIGNIFICANCE OF WHICH CAN BE

ASSESSED BY THE USE OF T-TEST.

0LINEAR REGRESSION ANALYSIS MAYBE USED IN EXAMINING THE RELATIONSHIP BETWEEN VARIABLES DISTINGUISHED AS INDEPENDENT AND DEPENDENT.

0ZERO-ORDER-REGRESSION COEFFICIENT INDICATES THE AVERAGE AMOUNT OF CHANGE IN THE DEPENDENT VARIABLE IN RELATION TO THE UNIT OF CHANGE IN THE INDEPENDENT VARIABLE.

0LINEAR RELATIONSHIP CAN BE MEASURED BY EITHER THE CORRELATION COEFFICIENT OR BY THE REGRESSION COEFFICIENT. VALUE OF THE OTHER VARIABLE.

0WHEN THERE IS NO RELATIONSHIP, THE COEFFICIENT IS 0.00.

QUESTIONS \(^.^)/

1. This are studies which call for determining relationships between pairs of variable.

2. It can be studied with or without cross-tabulation.3. If interval variables are not cross-tabulated, the

most common measure relationship is the ___________________.

4. In examining the relationship between variables distinguished as independent and dependent, ___________________ may be used.

5. One of the best measures of association for the nominal variables, which is derived by using the chi-square value.

Answers c:

1. Bivariate Relationships2. Relationships Between Interval Variables3. Pearson correlation coefficient (r)4. linear regression analysis5. Cramer’s V

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