This hypothesis was tested seven times in the questionnaire. Six of seven times the general direction of the hypothesis was supported but in only four of the seven was the difference statistically significant. Statistical significance by race will be stated for each figure but will be addressed later on in the result section when discussing hypothesis three (blacks and whites will have divergent opinions on every issue).

The first question asked students if blacks had the same chance as whites in the job market. Black students were more pessimistic than whites in thinking blacks did have an equal chance in obtaining jobs (see Figure 4). The result was statistically significant (p < .001) indicating blacks perceived the situation differently than whites. The line for blacks was always below the line indicating white responses. The lower line indicates a lower mean value which indicates a more pessimistic the opinion.
 

Figure 4: Blacks have same chance as whites (jobs)

 

The next question asked students how they felt about race relations in general. Even though the direction of the hypothesis was confirmed, the result was not statistically significant (p < .410) (see Figure 5). This indicates that it is possible that blacks are more pessimistic than whites but one cannot say for sure that is true.
 

Figure 5: Relations between blacks and whites

 

The third question asked students if they felt most blacks held prejudicial views against whites. Again, the general direction of the hypothesis was confirmed but the result was not statistically significant (p < .554) (see Figure 6).
 

Figure 6: Most blacks have prejudicial views against
whites

 

The fourth question reversed the conditions of the previous statement and asked if most whites held prejudicial views against blacks. The black response line was below the white response line which indicates a more pessimistic attitude for blacks (see Figure 7). The result was statistically significant (p < .001) indicating black students were more likely than white students to perceive that whites do hold prejudicial views against blacks.
 

Figure 7: Most whites have prejudicial views against
blacks

 

The fifth question asked if whites tend to feel comfortable dealing with blacks. The line for blacks was above the line for whites which for this question indicated a more pessimistic outlook for blacks regarding perceived comfortableness of whites (see Figure 8). The result was also statistically significant (p < .001).
 

Figure 8: Whites comfortable dealing with blacks

 

The sixth question asked the reverse of the previous statement and asked students if blacks tended to feel comfortable dealing with whites. This was the only question were the results were mixed (see Figure 9). At the campus level, whites were a little more pessimistic as indicated by the higher mean value. On the national level, blacks were a little more pessimistic. Overall, when combining both contexts, whites were more pessimistic than blacks. The result, however, was not statistically significant (p < .965).
 

Figure 9: Blacks comfortable dealing with whites

 

The last question asked students if overall, opportunities were fair and equal for everyone. The lines representing black responses were higher than the lines representing white responses denoting a more pessimistic opinion on the part of black students (see Figure 10). The result was also statistically significant (p < .001).
 

Figure 10: Opportunities are fair and equal

 

I would like to point out one interesting finding. Blacks appeared to be more critical of blacks' behavior than whites were of blacks' behavior. For example, black students were more likely than white students to agree with the statement that other blacks held prejudicial views against whites even if they did not express them openly (Figure 6). The mean black response was 3.23 on a scale ranging from 1 (strongly agree) to 7 (strongly disagree). Whites rated blacks more favorably with an overall mean of 3.39. Even though race was not statistically significant, the direction of the scores indicate blacks are a bit more critical of other blacks. A higher power test (larger sample size) would be needed to determine if this occurrence was actually credible or just a statistical occurrence.
 
 

Table 15: ANOVA table for blacks have prejudicial views against whites
SOURCE	df	III SS	MS	F	p value	R2
Race	1	1.572	1.572	.352	.554	.004
error A	92	410.414	4.461
D. of Proximity	2	7.751	3.875	11.444	.001 *	.111
Proximity*Race	2	.744	.372	1.098	.336	.012
error B	184	62.313	.339
Total corrected	281	483.986

* p .05 R² represents eta squared
 

The second question dealt with the perceived comfortableness of blacks toward whites and also showed the same pattern (Figure 9). At the national level, black college students rated other blacks as feeling less comfortable dealing with whites than did white college students. Blacks produced an overall mean response of 3.94 whiles white students yielded an overall score of 3.93. The scale ranged from 1 (very comfortable) to 7 (very uncomfortable). Again, the result was not statistically significant indicating one cannot say for sure blacks are more critical of other blacks (see Table 16).
 
 

Table 16: ANOVA table for blacks comfortable dealing with whites
SOURCE	df	III SS	MS	F	p value	R2
Race	1	.005	.005	.00	.965	.001
error A	91	253.393	2.785
D. of Proximity	1	8.803	8.803	20.315	.001 *	.182
Proximity*Race	1	.029	.029	.067	.797	.001
error B	91	39.433	.433
Total corrected	185	301.898

* p .05 R² represents eta squared
 

In summary, the results illustrated that white students were generally more optimistic than black students but not necessarily optimistic about the situation. In other words, both groups felt pessimistic about the situation overall, but whites in general were less pessimistic than blacks. The direction of the responses in six of the seven questions confirmed the hypothesis but only with four of those questions were the differences statistically significant.
 

This hypothesis was also tested seven times in the questionnaire. All seven times, the data confirmed the hypothesis that degree of proximity does play a role in perception. Regardless of the issue, the more abstract, distant context (national level) was always judged more harshly than the concrete, close context (local level). The combined mean scores of each racial group would consistently increase (or decrease depending on the question) as the degree of proximity moved from close and concrete to distant and abstract. If one looks at Figure 4-10 again, one observes the lines for both racial groups continue in one direction as the context goes from the most concrete environment (campus or city) to the most abstract environment (state or national). The questionnaire contained three questions where subjects had to compare two contexts (campus or city to the entire nation) while the other four questions utilized more than two contexts. In all seven cases, the variable degree of proximity yielded a statistically significant main effect.

It is easy to determine where the differences are if there are only two contexts to compare (i.e. campus versus nation) but one needs further analysis if there are more than two present. The questionnaire contained four questions where respondents had rate three or more contexts:

1) Relations in general between blacks and whites
2) Most blacks have prejudicial views against whites
3) Most whites have prejudicial views against blacks
4) Overall, opportunities fair and equal for everyone

These questions asked students to rate their campus, the city and the entire nation. Only one question, relations in general between blacks and whites, utilized a fourth context, the state. This was done because the question from the original survey utilized the same range of contexts. Post hoc tests are used when one needs to determine if three or more groupings differ from each other. Using Tukey's Studentized Range test (HSD), for the last three questions, showed that all three contexts were statistically different from each other. In other words, the mean value for the campus was statistically different from the value for the city which was different from the national value (see appendix B, Tables 29,32 and 39). The difference between each context was statistically significant indicating student perceived differences in perceptions at the campus level to the city level to the national level.

When subjects were asked to judge race relations in general between their campus, city, state and the entire nation, statistically significant differences were only found between the campus context and the state and national contexts controlling for race. The other comparisons were not significantly different in terms of mean differences (see Table 17).
 
 

Table 17: Tukey's post-hoc test for differences in degree of proximity regarding general relations between blacks and whites
	mean diff.	D. of Proximity	Mean
U.S. vs. state	.02	U.S.	4.61
U.S. vs. city	.35	state	4.59
U.S. vs. campus	.54 *	city	4.26
		campus	4.07
state vs. city	.33
state vs. campus	.52 *
city vs. campus	.19	HSD = .42

* honestly significant difference (HSD): alpha=.05, df=270, MSE=1.464, N=92
Scale: 1=excellent, 7=very poor
 

As pointed out in Chapter III, a result can be statistically significant but not substantively important. This project utilized R² to try and help answer the relevancy question. When using categorical data, R² is measured as eta squared. Eta squared operates in the same way as R² and is the proportion of the total variance in the dependent variable explained by the independent categorical variable. In the seven examples analyzed, eta squared ranged from .044 (race relations question) to .263 (whites feel comfortable). In other words, the variable degree of proximity provided between 4 percent and 26 percent of the total variance depending on the question. For example, when addressing the question, do blacks have as good a chance as whites to get any kind of job for which they are qualified, it produced a statistically significant main effect of degree of proximity but yielded an eta squared of .046 (see Table 18). One usually wants a high eta squared but in the social sciences, that is hard to obtain.
 
 

Table 18: ANOVA table for blacks have as good a chance (jobs)
SOURCE	df	III SS	MS	F	p value	R2
Race	1	62.144	62.144	22.456	.001 *	.198
error A	91	251.834	2.767
D. of Proximity	1	1.373	1.373	4.394	.039 *	.046
Proximity*Race	1	.513	.513	1.641	.203	.018
error B	91	28.433	.312
Total corrected	185	343.978

* p .05 R² represents eta squared
 

So, although the result is statistically significant, one might be too hasty in concluding degree of proximity as a major factor in forming one's perception of how good a chance blacks have in the job market.

The problem of relevance was illustrated in the debate regarding the book, the Bell Curve, where the researchers found race accounted for 10 percent of the variance. Is this enough of a proportion to cause a national stir? If so, how do these results from this project compare? It would seem that if 80 to 90 percent of the variability is left unexplained, more work should be done to find what variables account for the unexplained variance.

This hypothesis utilized every question analyzed in the questionnaire and the results were mixed. Sometimes race was statistically significant while other times it was not. A striking pattern developed when both racial groups had to rate themselves as well as the other group. When both black and white students were asked to rate other whites, there was always at least a 0.8 point differential in the white scores from the black scores (see Table 19). However, when both groups were asked to rate blacks, white and black responses were very similar. For example, the two racial groups did not differ much when asked to rate if blacks held prejudicial views against whites.
 
 

Table 19: Racial differences/similarities in attitudinal ratings
	means
	whites	blacks	difference
whites prejudice	3.24	2.41	.83
whites comfortable	3.69	4.69	1.0
blacks prejudice	3.39	3.23	.16
blacks comfortable	3.72	3.71	.01

scale for prejudice: 1=str. agree, 7=str. disagree
scale for comfortable: 1=very comfortable, 7=very uncomfortable
 

When whites and blacks had to rate other whites, the differences were statistically significant. For example, using the question do most whites hold prejudicial views against most blacks, the ANOVA table yielded a statistically significant main effect of race (see Table 20). In that example, degree of proximity not race seemed to be the more important variable. The eta squared for degree of proximity was 19 percent versus race which was 13 percent. Yet, when students were asked to rate if blacks held prejudicial views against whites, race as a main effect was not statistically significant (p < .554) (see Table 15). That table produced an eta square for race of only .4 percent.
 
 

Table 20: ANOVA table for whites have prejudicial views against blacks
SOURCE	df	III SS	MS	F	p value	R2
Race	1	46.348	46.348	14.122	.001 *	.133
error A	92	301.936	3.282
D. of Proximity	2	18.829	9.415	21.835	.001 *	.192
Proximity*Race	2	2.106	1.053	2.442	.090	.026
error B	184	79.334	.431
Total corrected	281	448.284

* p .05 R² represents eta squared
 

Four of the questions yielded statistically significant main effects of race while three questions did not. The four questions which yielded statistically significant differences were:

1) In this city, do you think blacks have as good a chance as white people to get any kind of job for which they are qualified or don't they have as good a chance? And in the United States? (see Table 18)

2) Most whites on this campus have prejudiced views about blacks, even if they do not express them openly? In this city? In the country? (see Table 20)

3) Generally speaking at this campus, would you say white people tend to feel very comfortable dealing with black people or tend to feel very uncomfortable dealing with blacks? And in the country? (see table 33)

4) Overall, opportunities are fair and equal for everyone here on this campus? In this city? In the country? (see Table 36)

The questions that did not produce statistically significant results were:

1) Generally speaking, do you think relations between blacks and whites on this campus are: (excellent - poor)? In the city? In the state? In the country? (see Table 26)

2) Most blacks on this campus have prejudiced views about whites, even if they do not express them openly? In this city? In the country? (see Table 15)

3) Generally speaking at this campus, would you say black people tend to feel very comfortable dealing with white people or tend to feel very uncomfortable dealing with whites? And in the country? (see Table 16)
 

The four questions yielding significant differences between the races shared some similarities. These questions were based on issues of fairness or ratings of whites while the non-significant results dealt with questions dealing with ratings of blacks or general issues. So depending on the questions, whites and blacks do seem to have divergent opinions while with other questions, they do not.

Finally, for the seven questions analyzed, eta squared for race ranged from .001 (blacks comfortable dealing with whites) to .198 (blacks have as good a chance as whites for jobs) (see Table 21). In other words, the variable race provided between less than 1 percent to a high of 20 percent of the total variance depending on the question. When comparing the relevance of race and context, only one time (for the question do blacks have as good a chance as whites for jobs) did the R² of race exceed the R² of context. That indicates for most questions, context explained a larger proportion of the total variance than race.
 
 

Table 21: Comparison of effect sizes between race and degree of proximity
	eta squared
Questions:	Race	Proximity
blacks have same chance as whites for any kind of job	.198	.046
race relations in general between blacks & whites	.008	.044
most blacks hold prejudice views against whites	.004	.111
most whites hold prejudice views against blacks	.133	.192
whites feel comfortable dealing with blacks	.160	.263
blacks feel comfortable dealing with whites	.001	.182
overall, opportunities fair & equal	.120	.261

 

The last aspect analyzed within the questionnaire concerned the estimations of the racial percentages of each group using different degrees of proximity. A story in the Washington Post indicated that for all people there was a "fundamental ignorance about numbers" (Gladwell 1995:7-8). He also observed that whites dramatically overestimated the percentage of blacks in the United States. That experiment was replicated in this project and expanded to include different degrees of proximity. There were three unusual occurrences that emerged from the data. First, blacks and whites underestimated the true percentage of whites in every context. Whites, however, always provided a lower mean estimate than black students (see Table 22). Second, blacks and whites overestimated the true percentage of blacks in every context, but whites always had a higher mean estimate than blacks. Third, differences in white and black perceptions were only statistically significant when students estimated the percentage of blacks at all contexts or when students estimated the percentage of whites on campus.
 
 

Table 22: Mean estimates of the racial population by race and degree of proximity
		University		City		N. Carolina		US
		%WH	%BL	%WH	%BL	%WH	%BL	%WH	%BL
White	mean	67.1 *	29.5	58.2	39.0	60.8	36.4	58.0	35.7
	SE	1.82	1.81	1.40	1.42	1.40	1.53	1.57	1.76
	N	57	57	57	57	56	56	57	57
Black	mean	74.2	19.2	60.5	32.8	63.6	28.2	59.9	28.2
	SE	2.68	2.47	2.82	2.90	2.70	2.40	2.79	2.28
	N	34	35	34	34	34	35	35	35
Total	mean	69.7	25.6	59.0	36.7	61.9	33.2	58.7	32.9
	SE	1.55	1.55	1.36	1.43	1.34	1.38	1.43	1.44
	N	91	92	91	91	90	91	92	92
True %		79	16	63	35	74	22	73	12

* note: percentages indicate the mean response, not the percent who answered a particular way. i.e. the average white response for the question what percent of this campus is white was 67%
 

% University white F (1,89) = 5.148         R² = .055     p = .026 *
% University black F (1,90) = 11.734     R² = .115     p = .001 *
% city white F (1,89) = .677                     R² = .008     p = .413
% city black F (1,89) = 4.607                 R² = .049     p = .035 *
% N. Carolina white F (1,88) = 1.071     R² = .012     p = .303
% N. Carolina black F (1,89) = 9.241     R² = .094     p = .003 *
% US white F (1,90) = .420                     R² = .005     p = .519
% US black F (1,90) = 6.809                 R² = .070     p = .011 *

R² represents eta squared * p .05

Sources for true percentages:
University:     Office of Institutional Research, 1997
City:             Chamber of Commerce, 1996
State:         Current Population Survey Data on North Carolina, 1996
U.S.:         U.S. Census Bureau, 1997

The pattern observed with the population estimates is the opposite of what occurred when analyzing the seven previous questions. Previously, black and white students provided similar responses when rating the perceptions of blacks but diverged when asked to rate whites (see Table 18). Here, both racial groups converged when estimating the percentage of whites but diverged when estimating the black population. Statistical differences between white and black responses were observed when students had to estimate the black population but there was no statistically significant racial difference when students estimated the white population, except at the campus level (see Table 23).
 
 

Table 23: Difference/similarities in estimations of racial populations
		white	black	mean diff.
% white	campus	67.1	74.2	7.1 *
	city	58.2	60.5	2.3
	state	60.8	63.6	2.8
	U.S.	58.0	59.9	1.9
% black	campus	29.5	19.2	10.3 *
	city	39.0	32.8	6.2 *
	state	36.4	28.2	8.2 *
	U.S.	35.7	28.2	7.5 *

* statistically significant difference (p .05)
 

Each subject was also asked to rate how confident they felt with their overall estimates. The scale ranged from 1 (very confident) to 7 (not confident at all). The mean response for all subjects was 4.58. When one separated it by race, whites produced a mean of 4.79 while blacks yielded a mean of 4.23 (see appendix B, Table 40). The difference in mean scores produced a statistically significant result in the level of confidence exhibited by blacks versus whites but both groups had means scores above the neutral score of four indicating they both felt some degree of uncertainty. Also the eta squared was only 4 percent (see Table 24).
 
 

Table 24: ANOVA table for level of confidence in estimation
Source	df	III SS	MS	F	p value	R2
Race	1	6.822	6.882	3.945	.050 *	.042
error	90	155.645	1.729
Total Corrected	91	162.467

* statistically significant difference (p .05)

Table of Contents

Chpt. 1

Chpt. 2

Chpt. 3

Chpt. 4

Chpt. 5

Chpt. 6

Chpt. 7