This tests the relationship between the variables of educational attainment (degree) and perceptions of life being interesting or dull (life) in the GSS database.
- H0, the null hypothesis = Greater educational attainment does not affect on perceptions of life being interesting or dull.
- Ha, the alternative hypothesis = Greater educational attainment has a positive effect on perceptions of life being interesting or dull.
|Value||df||Asymp. Sig. (2-sided)|
|N of Valid Cases||927|
|a. 2 cells (13.3%) have expected count less than 5. The minimum expected count is 2.86.|
At 8 df, the p < 001 yielded by the calculation (Table 1 alongside) shows that attitude profiles differ significantly from the expected distribution of absolute numbers. There is less than 1 chance in a thousand that such differences in life profiles could have occurred by chance alone. Hence, one concludes that education affect on opinions about life.
This then begs the question: what is the direction of the effect? The associated bar chart (Figure 1 overleaf) and a recasting of the absolute numbers to reveal proportions excited or bored within educational attainment subsamples (Table 2 overleaf) demonstrate that higher educational attainment is associated with an increased likelihood of finding one’s life stimulating.
|Respondent’s highest degree * IS LIFE EXCITING OR DULL Crosstabulation|
|Percent||IS LIFE EXCITING OR DULL|
|Less than HS||31.7||57.9||10.4||100.0|
This stands to reason. First, greater education expands one’s horizons and fosters awareness of a richer variety of interests and avocations.
Secondly, in an example of indirect effects, the better-educated gain entrée to “knowledge” jobs and more diverse career paths. Naturally, this stimulates greater excitement and aspirations about their prospects in life.
Likelihood of Dual-Income Couples
This is a test to find out the extent to which the married couples are simultaneously employed, the data being the GSS variables husband and wife.
- H0, the null hypothesis = Husbands and wives do not differ for having full-time employment.
- Ha, the alternative hypothesis = Husbands and wives differ in having full-time employment.
|wife works full time – husband works full time||Negative Differencesa||177|
|a. wife works full time < husband works full time|
|b. wife works full time > husband works full time|
|c. wife works full time = husband works full time|
For two-thirds of the couples (67% or 478 in the GSS sample of 710, see Table 3 alongside), the question of full-time employment for both husband and wife held.
By way of completing the picture, we see that the next biggest sub-group (25%) was for couples where only the husband boasted full-time employment. The balance (8%) consisted of couples where, in contrast, only the wife worked full-time.
|wife works full time – husband works full time|
|Asymp. Sig. (2-tailed)||.000|
|a. Sign Test|
If the null hypothesis were true, the p-value should be 0.50. This means that if chance alone were at work, half the differences in the population would be positive (successes) and the other half negative (failures).
As it happens, the calculated two-tailed significance value, p < 001 (Table 4) suggests that, if there were no difference in employment status between spouses, such a result as that depicted in Table 3 has less than one in a thousand survey re-sampling runs of ever occurring. Hence, we reject the null hypothesis and conclude there are altogether many instances when only one of the couples works full-time.
Hours Worked by Gender
From the same GSSFT database, the analysis proceeds to whether men and women differ for hours worked. This involves the variable hrs1.
- H0, the null hypothesis = Males and females do not differ for hours worked.
- Ha, the alternative hypothesis = Males and females differ in hours worked.
|Respondent’s Sex||N||Mean Rank||Sum of Ranks|
|Number of hours worked last week||Male||792||852.94||675526.50|
The Mann-Whitney is employed because of the assumption that the distribution of work hours is skewed to the left because a substantial number of workers in the population work only part-time.
|Number of hours worked last week|
|Asymp. Sig. (2-tailed)||.000|
|a. Grouping Variable: Respondent’s Sex|
The obtained z score (-10.24, see Table 6 alongside) for the comparison of the summed ranks is high enough that p < 0.001. The difference in the underlying distributions of hours worked by men and women is statistically significant.
That women work about 10% fewer hours than men, on average, is very likely a function not of choice but accessible career choices. Adult females may enjoy and even be financially successful at, say, part-time “Avon lady” kind of work. In their child-rearing years, the demands of home and hearth can also take time away from work.
Gaps in Clerical Compensation by Gender and Race
Yet a fourth analysis investigates whether clerical-level pay at the time of the survey (variable salnow) differs across four sub-groups of the compound variable sex race for ethnicity within gender. The task involved evaluating the results of both non-parametric and parametric analyses.
- H0, the null hypothesis = there are no differences among the means of the samples (for the ANOVA) or their medians (in the case of the non-parametric test).
- Ha, the alternative hypothesis = there is a difference among the means or medians of the four sub-samples.
|SEX & RACE CLASSIFICATION||N||Mean Rank|
|CURRENT SALARY||WHITE MALES||194||329.23|
The median ranks reveal that white male clerks typically earn more than minority men in the same job. The latter appear to rank second (this needs to be qualified by later findings). White female clerks typically rank third while minority women seem the most disadvantaged.
Based on the right-tail significance value (p < 0.001, Table 8 overleaf) indicating that the probability of the differences between the data sets occurring by chance is extremely low, one rejects the HO and accepts the alternative that there are meaningful variations in clerical pay by sex and race.
|a. Kruskal Wallis Test|
|b. Grouping Variable: SEX & RACE CLASSIFICATION|
Granting an assumption that the clerical pay data is equally distributed, an ANOVA can be done. The outcome affirms that the differences in mean pay across the groups can hardly be attributed to chance variation (p also < 0.001, Table 9 below).
|Sum of Squares||df||Mean Square||F||Sig.|
|CURRENT SALARY |
|(I) SEX & RACE CLASSIFICATION||(J) SEX & RACE CLASSIFICATION||Mean Difference (I-J)||Std. Error||Sig.||95% Confidence Interval|
|Lower Bound||Upper Bound|
|WHITE MALES||MINORITY MALES||4891.727*||850.965||.000||2637.12||7146.34|
|MINORITY MALES||WHITE MALES||-4891.727*||850.965||.000||-7146.34||-2637.12|
|WHITE FEMALES||WHITE MALES||-7107.449*||614.521||.000||-8735.60||-5479.29|
|MINORITY FEMALES||WHITE MALES||-8565.165*||1025.109||.000||-11281.16||-5849.17|
|*. The mean difference is significant at the 0.05 level.|
Not unexpectedly, the results of the Bonferroni posthoc group comparisons demonstrate that:
- White male clerks typically earn better pay than all other gender and race groups. All the tests of significance show p < 0.001.
- Minority males do make less than their White counterparts do (p < 0.001) but more than their “sisters” (p < 0.05) in the clerical ranks.
- Both White and minority females earn less than white male clerks (p < 0.001). The former are as disadvantaged as minority clerks of any gender (p > 0.05). Minority women, in turn, areas worse off than other females and minority men (p < 0.05 in each case).
One, therefore, concludes that all other things equal, race and gender combine to create discriminatory, albeit perhaps unintentional, pay disparities for minorities and women.