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.
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.
0There 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
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
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-
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
0Finally, it should be remembered that none of
the measures of association indicate whether
a relationship is casual or not.
0BIVARIATE RELATIONSHIPS ARE STUDIES WHICH CALL
FOR DETERMINING RELATIONSHIPS BETWEEN PAIRS OF
0THE MEASURES OF ASSOCIATION IS USED WHEN ONE
WISHES TO KNOW THE STRENGTH OF RELATIONSHIP.
0GAMMA 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-TABULATED
0THE 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
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
0WHEN THERE IS NO RELATIONSHIP, THE COEFFICIENT
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
1. Bivariate Relationships
2. Relationships Between Interval Variables
3. Pearson correlation coefficient (r)
4. linear regression analysis
5. Cramer’s V