chi square based measures

8/6/2019 Chi Square Based Measures

http://slidepdf.com/reader/full/chi-square-based-measures 1/19

G2

By: Likith R PrakashAshwini S Rao



` Chi-square (pronounced ³ky-square´)

` Greek notation for chi-square is G2` Quantitative measure used to determine whether a

relationship exists between two variables` Ex: Gender and the year of promotion for a sample of

employees. We want to establish whether arelationship exists between gender and year of

promotion



` Chi-square statistic first shows there is statisticalsignificance



` A test of independence assesses whether pairedobservations on two variables, expressed ina contingency table , are independent of each other

` o find out whether two or more attributes areassociated (related ) or not



` A test of goodness of fit establishes whether or not anobserved frequency distribution differs from atheoretical distribution.

` Ex: To test the hypothesis that a random sample of 100 people has been drawn from a population in which menand women are equal in frequency, the observednumber of men and women would be compared to the

theoretical frequencies of 50 men and 50 women. If there were 44 men in the sample and 56 women,then«««.



` The x2 test of homogeneity is an extension of the chi-square test of independence.

` Tests of homogeneity are designed to determine

whether two or more independent random samples aredrawn from the same population or from different

populations



` For example we may be interested in finding outwhether or not university students of various levels i.e.,undergraduate, postgraduate PhD feel the same inregard to the amount of work required by their

professors i.e., too much, right amount of work or toolittle work.

` We shall take the hypothesis that the three samplescome from the same population, i.e., the threeclassifications are homogeneous in so far as the opinionof three different groups of students about the amountof work required by their professors is concerned. Thisalso means there exists no difference in opinion amongthe three classes of people on this issue.



` Even though a chi-square test may show statisticalsignificance between two variables, the relationship

between those variables may not be substantively

important.

` Hence there are many measures of associationavailable to help evaluate the relative strength of a

statistically significant relationship



` The Phi Coefficient denoted by introduced by KarlPearson is a measure of association for two variables.

` varies from 0 to 1 or -1 (No, complete & Inverseassociation)

` The Phi coefficient is related to the chi-squarestatistic for a 2×2 nominal contingency table only.



` Cramer's V (also referred to as C ramer's phi and denotedas V or c )

` May be used with variables having 2 or more levels` Varies from 0 (no association) to 1 (complete association)` V may be viewed as a percentage of maximum possible

variation between variables` In case of 2x2 contingency table V = .



` D escribing Strength of Association` Ch aracterizations` > .5 high association` .3 to .5 moderate association` .1 to .3 low association` 0 to .1 little if any association

LEVEL OF ASSOCIATION Verbal Description COMMENTS

0.00 No RelationshipKnowing the independent variable does not reduce the number of errors in predicting the dependent variable atall.

.00 to .15 Not generally useful Not acceptable

.10 to .20 Weak Minimally acceptable

.20 to .25 Moderate Acceptable

.25 to .30 Moderately Strong

.30 to .35 Strong

.35 to .40 Very Strong

.40 to . 45 Worrisomely Strong Either an extremely good relationship or the two variables are measuring the same concept

.45 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.



` D escribing Strength of Association` Ch aracterizations` > .5 high association` .3 to .5 moderate association` .1 to .3 low association` 0 to .1 little if any association



` It is interpreted as a measure of the relative (strength)of an association between two variables.

` The coefficient will always be less than 1 and varies

according to the number of rows and columns.

Where N is total sample size



` Phi: Only when both nominal variables have exactly 2 possible values.

` C : When there are 3 or more values for each nominal

variables. (Rows = Columns)` V: Number of possible values for variables is not equal.

(Rows Columns)



Thank You

chi square based measures

Documents