KIndependence DemonstratedH:u<0Suppose we are interested in the relationship betweengender and attending college.If there is no relationship between gender andattending college and 4o% of our total sample attend贝college, we would expect 4o% of the males in oursample to attend college and 40% of the females toBo:μ=0attend college.If there is a relationship between gender andattending college, we would expect a higherproportion of one group to attend college than theother group, e.g. 60% to 20%
Independence Demonstrated Suppose we are interested in the relationship between gender and attending college. ✓ If there is no relationship between gender and attending college and 40% of our total sample attend college, we would expect 40% of the males in our sample to attend college and 40% of the females to attend college. ✓ If there is a relationship between gender and attending college, we would expect a higher proportion of one group to attend college than the other group, e.g. 60% to 20%
KDisplaying Independent and DependentRelationshipsH<0When group membership makesWhenthe variablesarea difference,the dependentindependent,theproportioninrelationshipisindicatedbyonebothgroupsisclosetothegroup having a higher proportionsame size asthe proportionthan the proportion for the totalforthetotal samplesample.WeIndependentRelationshipDependentRelationshipbetweenGenderandCollegebetweenGenderandCollegeBo:=o100%100%80%80%60%60%60%40%40%40%40%40%40%20%20%20%0%0%MalesFemalesTotalMalesFemalesTotalC
Displaying Independent and Dependent Relationships Independent Relationship between Gender and College 40% 40% 40% 0% 20% 40% 60% 80% 100% Poportion Attending College Males Females Total Dependent Relationship between Gender and College 60% 20% 40% 0% 20% 40% 60% 80% 100% Poportion Attending College Males Females Total When the variables are independent, the proportion in both groups is close to the same size as the proportion for the total sample. When group membership makes a difference, the dependent relationship is indicated by one group having a higher proportion than the proportion for the total sample
KIndependent and Dependent VariablesH:u<0The two variables in a chi-square test of independenceAeach play a specific role.Tv The group variable is also known as theindependentvariable because it has an influence on the testevariable.Bo:μ=0v The test variable is also known as the dependent2variable because its value is believed to bedependent on the value of the group variableThe chi-square test of independence is a test of theinfluence or impact that a subject's value on one variablehas on the same subject's value for a second variable.3
Independent and Dependent Variables ➢ The two variables in a chi-square test of independence each play a specific role. ✓ The group variable is also known as the independent variable because it has an influence on the test variable. ✓ The test variable is also known as the dependent variable because its value is believed to be dependent on the value of the group variable. ➢ The chi-square test of independence is a test of the influence or impact that a subject’s value on one variable has on the same subject’s value for a second variable
KChi square distribution0observed frequencydf= 2df = 3eoax=(-)2df = 4HExpected frequencyBo:2681012041416n/2ExpectedfrequencyarecomputedasThis formula compute howif there is no difference between thethe pattern of observedfrequency differs from thegroups, i.e. both groups have thepattern of expectedsameproportion.frequency
Chi square distribution − = E O E 2 2 ( ) Expected frequency observed frequency Expected frequency are computed as if there is no difference between the groups, i.e. both groups have the same proportion. This formula compute how the pattern of observed frequency differs from the pattern of expected frequency
KChi square distribution:u<0df=2df =3haiqeqordYTdf = 4iSBo:μ=06810021216414x21. Chi-square distribution is a nonsymmetrical distribution2. Chi-square distributions are determined by degree of freedomC
2. Chi-square distributions are determined by degree of freedom Chi square distribution 1. Chi-square distribution is a nonsymmetrical distribution