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CHAPTER 4

RESULTS

The purpose of the study was to determine the effect of real-world mathematical applications on students' achievement and classroom environments. Specifically, the study examined the effects of group status (experimental or control) and academic status (gifted or nongifted) on the achievement scores and classroom environment scores of intermediate and middle school students. Specific questions to be answered in the study were:

1.Do the variables group status and academic status have an independent and
combined effect on the achievement scores of intermediate and middle school
students?

2.Do the variables group status and academic status have an independent and
combined effect on the classroom environment scores of intermediate and middle
school students?

The sample for the study consisted of 320 intermediate and middle school students who attended schools in a suburban school district. The descriptive profile of participants is provided in the first section of the analysis, while the second section examines the null hypotheses formulated for this investigation. Treatment of the hypotheses was accomplished through the application of the analysis of covariance (ANCOVA) and the Scheffé Post Hoc Test. All of the hypotheses were tested at the .05 level of statistical significance.

Descriptive data gathered for all participants included sex, grade level, ethnicity, group status, and academic status.

Sex

The study sample consisted of 320 intermediate and middle school students. Table 7 reports the sex of study participants.

Table 7 Sex of Study Participants
Sex	Number	Percentage
Male	138	43.1
Female	182	56.9
Total	320	100.0

Ideally, half the study participants would have been male and half would have been female. However, somewhat more than half the study participants (56.9%) were female.

Ethnicity

The participants were from three ethnic groups. Table 8 reports ethnicity of study participants by grade level.

Table 8 Ethnicity of Study Participants by Grade Level
	African American		Hispanic		White		Total
Grade Level	No.	%	No.	%	No.	%	No.	%
Sixth	141	44.1	26	8.1	0	0.0	167	52.2
Seventh	98	30.6	17	5.3	0	0.0	115	35.9
Eighth	26	8.1	11	3.4	1	0.3	38	11.9
Total	265	82.8	54	16.8	1	0.3	320	100.0

In practical terms, the sample was predominantly African American (82.8 %), with one participant indicating a White ethnicity, and the remaining study participants (16.9%) identifying their ethnic background as Hispanic. Slightly more than half of the participants (52.2%) were enrolled in the sixth grade, a little more than a third (35.9%) were enrolled in the seventh grade, and eighth graders constituted only 11.9%.

Group Status

The variable group status referred to whether participants were in the experimental group or in the control group. Table 9 reports the group status of study participants by grade level.

Table 9 Group Status of Study Participants by Grade Level
	Experimental		Control		Total
Grade Level	No.	%	No.	%	No.	%
Sixth	92	28.7	75	23.4	167	52.2
Seventh	30	9.4	85	26.6	115	35.9
Eighth	38	11.9	0	0.0	38	11.9
Total	160	50.0	160	50.0	320	100.0

As dictated by the study's research design, of the total 320 study participants, 50% (160) were in the experimental group and 50% (160) were in the control group. The largest grade-level group in the experimental group was the sixth grade with 92 participants (28.7%), followed by the eighth grade with 38 participants (11.9%) in the experimental group, and the seventh grade with 30 participants (9.4%). The control group was balanced between the sixth grade (75 or 23.4%) and the seventh grade (85 or 26.6%). There were no eighth-grade students in the control group.

Academic Status

The variable academic status was categorized into two attributes for the study, gifted and nongifted. Table 10 reports academic status of study participants by grade level.

Table 10 Academic Status of Study Participants by Grade Level
	Gifted		Nongifted		Total
Grade Level	No.	%	No.	%	No.	%
Sixth	70	21.9	97	30.3	167	52.2
Seventh	65	20.3	50	15.6	115	35.9
Eighth	25	7.8	13	4.1	38	11.9
Total	160	50.0	160	50.0	320	100.0

In accordance with the study's research design, 50% of study participants were drawn from a pool of students identified as gifted by the participating school district and 50% were drawn from a pool identified as nongifted by the participating school district. As shown in Table 10, the number of gifted students in the study was approximately the same for the sixth and seventh grades (70 and 65 or 21.9% and 20.3%), while the eighth grade had only a third as many (25 or 7.8%). Nongifted participants were not as evenly distributed between sixth and seventh grades, with 30.3% in the sixth grade and 15.6% in the seventh grade. With only 4.1% of total participants in the eighth grade and classified as nongifted, it is apparent that the nongifted participants represented a younger group of students than the gifted group.

In the sections that follow, statistical analyses related to each of the study's null hypotheses are reported.

H_o-1: There are no significant differences on achievement scores by group status (experimental or control), academic status (gifted or nongifted), and their interaction (group x status).

There were 320 students who participated in the study. One hundred sixty students were in the experimental group and 160 students were in the control group. The adjusted mean achievement score for the experimental group was 16.15 (SD = 3.06) and for the control, 14.54 (SD = 2.74). In addition, the adjusted mean for the gifted participants was 15.59 (SD = 2.85) and for the nongifted participants, 15.10 (SD = 3.15).

Table 11 reports the ANCOVA results for differences in adjusted mean achievement scores of study participants by group status, academic status, and their interaction. As indicated in Table 11, significant differences were found between the adjusted mean achievement scores of participating students by group status, F = 26.51, df = 1/315, p < .001; however, differences were not found between the two academic status groups at the .05 level, F = .135, df = 1/315, p > .05.

Table 11 ANCOVA Results for Differences in Achievement Scores by Group Status, Academic Status, and Their Interaction
			Achievement Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					.135	.714	.01
	Gifted		15.59	2.85
	Nongifted		15.10	3.15
Group Status					26.51	.000**	.28
	Experimental		16.15	3.06
	Control		14.54	2.74
Academic Status x Group Status					6.97	.009**	.15
	Experimental
		Gifted	15.78	3.01
		Nongifted	16.79	3.04
	Control
		Gifted	15.25	2.53
		Nongifted	14.14	2.78

A two-way interaction effect was found between the participants' group status and academic status, A x B, with regard to their adjusted mean achievement scores, F = 6.973, df = 1/315, p < .01. Further data analysis using the mean results revealed that the experimental group performed significantly better academically than did the control group. Moreover, to measure the strength of association between the significant independent variables and the adjusted mean achievement scores, the Eta squared correlation coefficient was used. The independent variable group status accounted for 28% of the variance in the adjusted mean achievement scores. In addition, the interaction effect between academic status and group status accounted for 15% of the variance in the adjusted mean achievement scores.

The Scheffé test was used as a Post Hoc test. Table 12 reports Scheffé results regarding the adjusted mean achievement scores of study participants by group status and academic status. These results reveal that nongifted participants in the experimental group scored significantly higher than gifted participants in the experimental group.

Table 12 Scheffé Results Regarding Achievement Scores by Group Status and Academic Status
Mean Values
Experimental		Control
Gifted	Nongifted	Gifted	Nongifted	Observed Mean Difference	Scheffé Critical Value
15.78	16.79			-1.01 *	.72
15.78		15.25		.53	.72
15.78			14.14	1.64 *	.59
	16.79	15.25		1.54 *	.83
	16.79		14.14	2.65 *	.72
		15.25	14.14	1.11 *	.72

Figure 2 illustrates the trend analysis of adjusted mean academic achievement scores by academic status and group status. Since the lines in the trend analysis of cell means do not intersect within the plot, an ordinal interaction was depicted between the variables, indicating a degree of superiority changes (Stevens, 1986).

Figure 2. Trend analysis of adjusted mean academic achievement scores by academic status and group status.

H_o-2.0: There are no significant differences on involvement scores by group status, academic status, and their interaction.

Table 13 reports the ANCOVA results for differences in the study participants' perceptions of their classroom learning environments, as measured by the CES's involvement scale, by group status, academic status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on their involvement scores.

Table 13 ANCOVA Results for Differences in Involvement Scores by Group Status, Academic Status, and Their Interaction
			Involvement Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					12.35	.001***	.19
	Gifted		2.49	.49
	Nongifted		2.28	.54
Group Status					1.03	.310	.06
	Experimental		2.43	.49
	Control		2.35	.56
Academic Status x Group Status					.03	.863	.01
	Experimental
		Gifted	2.53	.48
		Nongifted	2.32	.49
	Control
		Gifted	2.44	.50
		Nongifted	2.25	.59

As shown in Table 13, significant differences were found between the two academic groups, F = 12.35, df = 1/315, p < .001. The adjusted mean on the involvement component for gifted participants was 2.49 (SD = .49) and for the nongifted, 2.28 (SD = .54). Moreover, the involvement adjusted mean score for the experimental group was 2.43 (SD = .49) and 2.35 (SD = .56) for the control group. However, no difference was found between the experimental and control groups with respect to their adjusted mean involvement scores, F = 1.07, df = 1/315, p > .05.

Additionally, statistically significant interaction effects were not found between participants' group status and academic status, A x B, regarding their adjusted mean involvement scores, F = .03, df = 1/315, p < .05. Further data analysis employing the adjusted mean results revealed that students in the gifted group had significantly higher involvement scores than those in the nongifted group. Moreover, the measure of the strength of association between the independent variable academic status and the adjusted mean involvement scores was computed using the 2 coefficient. It was concluded that academic status accounted for 2% of the variance in the adjusted mean involvement scores.

H_o-2.1: There are no significant differences on affiliation scores by group status, academic status, and their interaction.

Table 14 reports ANCOVA results for differences in adjusted mean affiliation scores by group status, academic status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on their classroom environment's affiliation component scores.

Table 14 ANCOVA Results for Differences in Affiliation Scores by Group Status, Academic Status, and Their Interaction
			Affiliation Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					.10	.750	.01
	Gifted		2.50	.50
	Nongifted		2.48	.53
Group Status					.88	.349	.05
	Experimental		2.50	.49
	Control		2.47	.54
Academic Status x Group Status					.10	.751	.01
	Experimental
		Gifted	2.51	.49
		Nongifted	2.51	.50
	Control
		Gifted	2.49	.50
		Nongifted	2.46	.58

As shown in Table 14, the adjusted mean affiliation scores for gifted and nongifted participants were 2.50 and 1.48, with standard deviations of .50 and .53, respectively. Additionally, the adjusted mean affiliation score for the experimental group was 2.50 (SD = .49) and 2.47 (SD = .54) for the control group. A statistically significant difference was not found between the experimental and control groups, F = .88, df = 1/315, p > .05, or between the gifted and nongifted participants at the .05 level, F = .101, df = 1/315, p > .05.

H_o-2.2: There are no significant differences on rule clarity scores by group status, academic status, and their interaction.

Table 15 reports ANCOVA results for differences on adjusted mean rule clarity scores by academic status, group status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on their classroom environment's rule clarity component scores.

Table 15 ANCOVA Results for Differences in Rule Clarity Scores by Group Status, Academic Status, and Their Interaction
			Rule Clarity Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					3.72	.055	.11
	Gifted		2.68	.42
	Nongifted		2.60	.43
Group Status					1.66	.199	.07
	Experimental		2.65	.42
	Control		2.63	.45
Academic Status x Group Status					7.17	.008**	.15
	Experimental
		Gifted	2.76	.41
		Nongifted	2.54	.40
	Control
		Gifted	2.61	.44
		Nongifted	2.66	.46

As indicated in Table 15, the adjusted mean rule clarity scores for gifted and nongifted participants were 2.68 and 2.60 with standard deviations of .42 and .43, respectively. Furthermore, the adjusted mean for the experimental group was 2.65 (SD = .42) and 2.63 (SD = .45) for the control group. The analysis of the independent and combined effect of the study participants' group status and academic status with regard to their perceptions toward the rule clarity scale revealed no significant differences between students in the experimental group and students in the control group, F = 1.66, df = 1/315, p > .05. Neither were there differences between the gifted and nongifted groups, F = 3.72, df = 1/315, p > .05. However, statistically significant interaction effects were found between the study participants' group status and academic status with regard to their perceptions toward rule clarity, F = 7.17, df = 1/315, p > .01. Moreover, to assess the strength of association between the combined effect of academic status and group status on the adjusted mean rule clarity scores of students, the 2 was used. It was concluded that 15% of the variance in the adjusted mean rule clarity scores was associated with the combination effect of academic status and group status.

Table 16 reports Scheffé results regarding adjusted mean rule clarity scores by group status and academic status. As reported in Table 16, gifted students in the experimental group had a more favorable perception toward rule clarity than did the nongifted students in the experimental group and the gifted students in the control group.

Table 16 Scheffé Results Regarding Rule Clarity Scores by Group Status and Academic Status
Mean Values
Experimental		Control
Gifted	Nongifted	Gifted	Nongifted	Observed Mean Difference	Scheffé Critical Value
2.76	2.54			.22 *	.13
2.76		2.61		.15 *	.13
2.76			2.66	.10	.13
	2.54	2.61		-.07 *	.13
	2.54		2.66	-.12	.13
		2.61	2.66	-.05	.13

Figure 3 illustrates the trend analysis regarding the classroom environment's adjusted mean rule clarity scores by academic status and group status. Inasmuch as the lines in the trend analysis of cell means do intersect within the plot, a disordinal interaction was depicted, indicating a degree of superiority reversion.

Figure 3. Trend analysis regarding adjusted mean rule clarity scores by academic status and group status.

Ho-2.3: There are no significant differences on task orientation scores by group status, academic status, and their interaction.

Table 17 reports ANCOVA results for differences on adjusted mean task orientation scores by group status, academic status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on their classroom environment's task orientation component scores.

Table 17 ANCOVA Results for Differences on Task Orientation Scores by Group Status, Academic Status, and Their Interaction
			Task Orientation Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					8.33	.004**	.15
	Gifted		2.70	.55
	Nongifted		2.45	.58
Group Status					.09	.770	.05
	Experimental		2.58	.58
	Control		2.58	.55
Academic Status x Group Status					28.58	.000***	.28
	Experimental
		Gifted	2.76	.40
		Nongifted	2.39	.67
	Control
		Gifted	2.42	.63
		Nongifted	2.74	.39
** p <.01 *** p <.001

As indicated in Table 17, the adjusted mean task orientation score for the gifted participants was 2.70 (SD = .55) and 2.45 (SD = .58) for the nongifted participants. The adjusted mean task orientation score for the experimental group was 2.58 (SD = .58) and 2.58 (SD = .55) for the control group. The ANCOVA results indicated there was no statistically significant difference between experimental and control groups, F = .09, df = 1/315, p > .05. However, a significant difference was found between the gifted and nongifted students, F = 8.33, df = 1/315, p < .01.

In addition, results of the ANCOVA also revealed a first-order interaction effect between the participants' group status and academic status (A x B) with regard to their perceptions toward the task orientation, F = 28.58, df = 1/315, p < .001. The adjusted mean results revealed that gifted participants had more favorable perceptions toward the task orientation component than those in the nongifted group. Furthermore, the Eta squared strength of association test was used to test the significant main effect of academic status, as well as the combination effect of academic status and group status, on the adjusted mean task orientation scores of students. It was concluded that 15% of the variance in the adjusted mean task orientation scores was associated with academic status. Also, it was concluded that 28% of the variance in adjusted mean task orientation scores was associated with academic status and group status combined.

Table 18 reports Scheffé results regarding adjusted mean task orientation scores by group status and academic status. As indicated in Table 18, experimental group gifted students expressed more favorable perceptions than experimental group nongifted students and control group gifted students. Moreover, control group nongifted students had significantly more favorable perceptions than experimental group nongifted students and control group nongifted students with respect to the task orientation component of the classroom environment.

Table 18 Scheffé Results Regarding Task Orientation Scores by Group Status and Academic Status
Mean Values
Experimental		Control
Gifted	Nongifted	Gifted	Nongifted	Observed Mean Difference	Scheffé Critical Value
2.76	2.39			.37 *	.16
2.76		2.42		.34 *	.16
2.76			2.74	.02	.16
	2.39	2.42		-.03	.16
	2.39		2.74	-.35 *	.16
		2.42	2.74	-.32	.16

Figure 4 illustrates the trend analysis regarding the adjusted mean task orientation scores by academic status and group status. Inasmuch as the lines in the trend analysis of cell means do intersect within the plot, a disordinal intersection was depicted, indicating a degree of superiority reversion.

Figure 4. Trend analysis regarding adjusted mean task orientation scores by academic status and group status.

Ho-2.4: There are no significant differences on satisfaction scores by group status, academic status, and their interaction.

Table 19 reports ANCOVA results for differences on adjusted mean satisfaction scores by group status, academic status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on their classroom learning environment's satisfaction component scores.

Table 19 ANCOVA Results for Differences on Satisfaction Scores by Group Status, Academic Status, and Their Interaction
			Satisfaction Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					14.85	.000***	.21
	Gifted		2.59	.48
	Nongifted		2.36	.60
Group Status					2.07	.151	.08
	Experimental		2.53	.54
	Control		2.42	.57
Academic Status x Group Status					11.10	.001***	.18
	Experimental
		Gifted	2.75	.40
		Nongifted	2.32	.58
	Control
		Gifted	2.43	.50
		Nongifted	2.40	.63
*** p <.001

As shown in Table 19, the adjusted mean score on the satisfaction scale for gifted participants was 2.59 (SD = .48) and for nongifted participants was 2.36 (SD = .60). The adjusted mean satisfaction scores for the experimental and control groups were 2.53 and 2.42, with standard deviations of .54 and .57, respectively.

The differences found in the adjusted mean satisfaction scores of the experimental and control groups were not statistically significant, F = 2.07, df = 1/315, p > .05. However, differences were found between the perceptions of gifted and nongifted participants regarding satisfaction.

Moreover, group status and academic status did significantly interact on the perceptions of study participants toward the satisfaction component, F = 11.10, df = 1/315, p < .001. Additionally further data analysis, using the adjusted mean results, revealed that the gifted participants had more favorable perceptions than their nongifted counterparts regarding the satisfaction component. In addition, the Eta squared coefficients reported that 21% of the variance in the adjusted mean satisfaction scores was associated with academic status. Also, academic status and group status together were associated with 18% of the variance in adjusted mean satisfaction scores.

Table 20 reports Scheffé results regarding study participants' adjusted mean satisfaction scores by group status and academic status. As indicated in Table 20, the Scheffé Post Hoc test revealed that experimental group gifted participants exhibited a significantly more favorable perception toward the satisfaction component than did the nongifted participants in both the experimental group and the control group and the gifted participants in the control group.

Table 20 Scheffé Results Regarding Satisfaction Scores by Group Status and Academic Status
Mean Values
Experimental		Control
Gifted	Nongifted	Gifted	Nongifted	Observed Mean Difference	Scheffé Critical Value
2.75	2.32			.43 *	.17
2.75		2.43		.32 *	.17
2.75			2.40	.35 *	.17
	2.32	2.43		-.11	.17
	2.32		2.40	-.08	.17
		2.43	2.40	.03	.17

Figure 5 illustrates the trend analysis regarding adjusted mean satisfaction scores by academic status and group status. Inasmuch as the lines in the trend analysis of cell means do intersect within the plot, a disordinal intersection was depicted, indicating a degree of superiority reversion.

Figure 5. Trend analysis regarding adjusted mean satisfaction scores by academic status and group status.

H₀-2.5: There are no significant differences on innovation scores by group status, academic status, and their interaction.

Table 21 reports ANCOVA results for differences on adjusted mean innovation scores by group status, academic status, and their interaction. These values seek to measure the separate and combined effects of participants' group status and academic status on innovation scores.

Table 21 ANCOVA Results for Differences on Innovation Scores by Group Status, Academic Status, and Their Interaction
			Innovation Scores
Variable			Adjusted M	SD	F	p	Eta2
Academic Status					.052	.471	.01
	Gifted		2.71	.35
	Nongifted		2.70	.32
Group Status					2.11	.147	.08
	Experimental		2.71	.35
	Control		2.70	.32
Academic Status x Group Status					27.99	.000***	.28
	Experimental
		Gifted	2.81	.30
		Nongifted	2.60	.31
	Control
		Gifted	2.61	.37
		Nongifted	2.79	.31

As reflected in Table 21, the ANCOVA results for the study participants' perceptions with respect to adjusted mean innovation scores by group status and academic status revealed no main effect difference for the two status groups, F = 2.11, df = 1/135, p > .000, as well as for the two academic groups, F = .52, df = 1/315, p > .05). The adjusted mean innovation score for the gifted participants was 2.71 (SD = .35) and 2.70 (SD = .32) for nongifted participants. Additionally, the adjusted mean score for the experimental group was 2.71 (SD = .35) and 2.70 (SD = .32) for the control group.

The ANCOVA results for the study participants' perceptions with respect to the innovation component by group status and academic status revealed no main effect difference for the two status groups, F = 2.11, df = 1/315, p >.000, as well as for the two academic groups, F = .52, df = 1/315, p > .05. The interaction effects between the participants' group status and academic status were found to be significant regarding their perceptions toward the innovation component, F = .27.99, df = 1/315, p < .001. Additionally, the Eta squared strength of association test was used to assess the significant interaction effect of academic status and group status on the adjusted mean innovation scores. It was concluded that 7% of the variance in the adjusted mean innovation scores was associated with academic status and group status combined.

Table 22 reports the Scheffé results regarding the adjusted mean innovation scores by group status and academic status. As shown in Table 22, the Scheffé test results revealed that experimental group gifted participants had significantly higher perception scores than experimental group nongifted participants and control group gifted participants with respect to innovation. Control group nongifted participants had more favorable perceptions than experimental group nongifted participants and control group gifted participants toward the innovation component.

Table 22 Scheffé Results Regarding Innovation Scores by Group Status and Academic Status
Mean Values
Experimental		Control
Gifted	Nongifted	Gifted	Nongifted	Observed Mean Difference	Scheffé Critical Value
2.81	2.60			.21 *	.10
2.81		2.61		.20 *	.10
2.81			2.79	.02 *	.10
	2.60	2.61		-.11	.10
	2.60		2.79	-.19	.10
		2.61	2.79	.18 *	.10

Figure 6 illustrates the trend analysis regarding adjusted mean innovation scores by academic status and group status. Inasmuch as the lines in the trend analysis of cell means do intersect within the plot, a disordinal intersection was depicted, indicating a degree of superiority reversion.

Figure 6. Trend analysis regarding adjusted mean innovation scores by academic status and group status.

Table 23 summarizes the ANCOVA results for the CES component adjusted mean scores.

Table 23 Summary of ANCOVA Results for CES Component Adjusted Mean Scores
	Academic Status					Group Status
	Gifted		Nongifted			Experimental		Control
CES Component	M	SD	M	SD	F	M	SD	M	SD	F
Involvement	2.49	.49	2.28	.54	12.35***	2.43	.49	2.35	.54	1.03
Affiliation	2.50	.50	2.48	.53	.10	2.50	.49	2.47	.54	.88
Rule Clarity	2.68	.42	2.60	.43	3.72	2.65	.42	2.63	.45	1.66
Task Orientation	2.70	.55	2.45	.58	8.33*	2.58	.58	2.58	.55	.09
Satisfaction	2.59	.48	2.36	.60	14.85***	2.53	.54	2.42	.57	2.07
Innovation	2.71	.35	2.20	.32	.52	2.71	.35	2.70	.32	2.11

Eight major null hypotheses were formulated and tested in the study. All of the null hypotheses were tested for difference with regard to the variables group status and academic status. Sections of seven of the null hypotheses were found to be significant. Table 24 summarizes these.

Table 24 Summary of Null Hypotheses Tests
Null Hypothesis	Variable	M	SD	df	F	Conclusion
Ho-1	Experimental	16.15	3.06
	(Group)			1/315	26.511***	Rejected
	Control	4.54	2.74
	Gifted	15.59	2.85
	(Academic)			1/315	.135	Failed to Reject
	Nongifted	15.10	3.15
	Group x Academic	15.49	2.84	1/315	6.973*	Rejected
Ho-2.0	Experimental	2.43	.49
	(Group)			1/315	1.03	Failed to Reject
	Control	2.35	.56
	Gifted	2.49	.49
	(Academic)			1/315	12.35***	Rejected
	Nongifted	15.10	3.15
	Group x Academic	15.49	2.84	1/315	6.973*	Rejected
Ho-2.1	Experimental	2.50	.49
	(Group)			1/315	.88	Failed to Reject
	Control	2.47	.54
	Gifted	2.50	.50
	(Academic)			1/315	.10	Failed to Reject
	Nongifted	2.48	.53
	Group x Academic	2.49	.52	1/315	.10	Failed to Reject
Ho-2.2	Experimental	2.65	.42
	(Group)			1/315	1.66	Failed to Reject
	Control	2.63	.45
	Gifted	2.68	.42
	(Academic)			1/315	3.72*	Rejected
	Nongifted	2.60	.43
	Group x Academic	2.64	.43	1/315	7.17***	Rejected
Ho-2.3	Experimental	2.58	.58
	(Group)			1/315	.09	Failed to Reject
	Control	2.58	.55
	Gifted	2.70	.55
	(Academic)			1/315	38.33*	Rejected
	Nongifted	2.45	.58
	Group x Academic	2.58	.56	1/315	25.58***	Rejected
Ho-2.4	Experimental	2.53	.54
	(Group)			1/315	2.07	Failed to Reject
	Control	2.42	.57
	Gifted	2.59	.48
	(Academic)			1/315	14.85***	Rejected
	Nongifted	2.36	.60
	Group x Academic	2.48	.56	1/315	11.01***	Rejected
Ho-2.5	Experimental	2.71	.35
	(Group)			1/315	.52	Failed to Reject
	Control	2.70	.32
	Gifted	2.71	.35
	(Academic)			1/315	2.11	Failed to Reject
	Nongifted	2.70	.32
	Group x Academic	2.70	.34	1/315	27.99***	Rejected

Regarding null hypothesis 1, group status was found to have an independent effect, and group status and academic status were found to have a combination effect on the achievement scores of participants. In addition, academic status had a separate effect on the perceptions of participants regarding the involvement component. Furthermore, regarding hypothesis 2.2, statistically significant effects were found between the group status and academic status of the participants' perceptions toward the rule clarity learning environment component.

In addition, analyses of data with regard to hypotheses 2.3 and 2.4 revealed that academic status had an independent effect on the task orientation and satisfaction classroom environment components. Also, group status and academic status had a combined effect on the perceptions of participants toward the task orientation and satisfaction components. Finally, analysis of data pertaining to hypothesis 2.5 revealed that group status and academic status had a combination effect on the perceptions of participants toward the innovation learning environment component.

Table 25 summarizes the ANCOVA interaction results for each of the CES component scales.

Table 25 Summary of ANCOVA Interaction Results for Classroom Environment Scale Components
Environment	Academic Status x Group Status
Scale
Component	M	SD	F
Involvement	2.39	.53	.03
Affiliation	2.49	.52	.10
Rule Clarity	2.64	.43	7.17**
Task Orientation	2.58	.56	28.58***
Satisfaction	2.48	.56	11.10***
Innovation	2.70	.34	27.99***