Measures of Association 776 Do you strongly agree,somewhat agree,somewhat disagree or strongly disagree that a majority of jobs are best done by men? Responses to this question could be expected to vary considerably for dif ferent types of respondents.It might be expected,for example,that older people,with more traditional views concerning women's and men's roles, would agree with this view.On the other hand,younger respondents might be expected to have views which are more consistent with similar job roles for the two sexes.This expectation is examined in this example. Table 11.5 gives a cross classification of age and opinion concerning whether a majority of jobs are best done by men.Age has been classi- fied into three categories,'less than 40,'40 to 54,'and 55 and over.'The first entry in each cell of the table is the observed number of cases,and the second entry in each cell is the expected number of cases.The x2 statistic, along with o2 and o are given at the bottom of the table. Again the value of 2 is very small,so it might seem as if there is no relationship between the two variables,age and opinion.But o=0.2247, indicating that there is some relationship between the two variables.While the relationship is not close to 1,it is considerably greater than 0,indicating that for different ages,there are considerably different opinions. By examining the differences between the observed and expected num- bers of cases,the pattern of the relationship between age and opinion can be determined.These differences are greatest for the youngest and the old- est age groups.For ages under 40,there are considerably fewer observed respondents than the number of respondents expected to agree under the hypothesis of no relationship between the two variables.In contrast,for the 55 and over age group,there are more observed than expected respondents who agree.What these results show is that younger respondents tend to disagree that the majority of jobs are best done by men,older respondents tend to agree,and the middle age group falls between these two.The x2 statistic and support the view that there is a relationship between age and opinion,with more egalitarian views concerning male and female job roles among younger than among older respondents. The measures of association o and o2 cannot have a value less than zero, since the minimum value for x2 is zero.If there is no relationship between the two variables,so that x2=0,then =2=0.If the chi square value is small,o will also be relatively small.When the chi square statistic is large,indicating a strong relationship between the two variables,then o willMeasures of Association 776 Do you strongly agree, somewhat agree, somewhat disagree or strongly disagree that a majority of jobs are best done by men? Responses to this question could be expected to vary considerably for dif￾ferent types of respondents. It might be expected, for example, that older people, with more traditional views concerning women’s and men’s roles, would agree with this view. On the other hand, younger respondents might be expected to have views which are more consistent with similar job roles for the two sexes. This expectation is examined in this example. Table 11.5 gives a cross classification of age and opinion concerning whether a majority of jobs are best done by men. Age has been classi- fied into three categories, ‘less than 40,’ ‘40 to 54,’ and ‘55 and over.’ The first entry in each cell of the table is the observed number of cases, and the second entry in each cell is the expected number of cases. The χ 2 statistic, along with φ 2 and φ are given at the bottom of the table. Again the value of φ 2 is very small, so it might seem as if there is no relationship between the two variables, age and opinion. But φ = 0.2247, indicating that there is some relationship between the two variables. While the relationship is not close to 1, it is considerably greater than 0, indicating that for different ages, there are considerably different opinions. By examining the differences between the observed and expected num￾bers of cases, the pattern of the relationship between age and opinion can be determined. These differences are greatest for the youngest and the old￾est age groups. For ages under 40, there are considerably fewer observed respondents than the number of respondents expected to agree under the hypothesis of no relationship between the two variables. In contrast, for the 55 and over age group, there are more observed than expected respondents who agree. What these results show is that younger respondents tend to disagree that the majority of jobs are best done by men, older respondents tend to agree, and the middle age group falls between these two. The χ 2 statistic and φ support the view that there is a relationship between age and opinion, with more egalitarian views concerning male and female job roles among younger than among older respondents. The measures of association φ and φ 2 cannot have a value less than zero, since the minimum value for χ 2 is zero. If there is no relationship between the two variables, so that χ 2 = 0, then φ = φ 2 = 0. If the chi square value is small, φ will also be relatively small. When the chi square statistic is large, indicating a strong relationship between the two variables, then φ will