Adolescents
The purpose of Study 3 is to tracks the prediction of mathematics achievement in Taiwanese and American Adolescents within self-enhancers, accurate self-assessors, and self-effacers across four semesters.
5.1 Method
5.1.1 Participants
The participants in Study 3 are the same as Study 2.
5.1.2 Procedure
The first step is identical to that in Study 2. Then, for two years following the study, all students’ mathematics achievement from school records will be collected each semester.
5.1.3Measures
5.1.3.1 Math test (see Appendix.1 and 2)
The math test in Study 3 is the same as Study 2.
5.1.3.2 Measuring self-enhancement score
In Study 3, initial residual discrepancy was not used to represent self-perception because the scores measured without incentive would be less accurate than those with incentive. Thus, adjusted residual discrepancy and residual discrepancy-change were used to test the hypothesis respectively.
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5.1.3.3 Categorizing self-enhancers, accurate self-assessors, and self-effacers
In Study 3, we categorized self-enhancers, accurate self-assessors, and self-effacers into three distinct groups according to their RESIDUAL scores. Participants who are with residuals within the 95% confidence interval for the mean value of Y at X=x, we label them as accurate self-assessors. Participants who are with residuals higher than the 95% upper confidence limit for the mean value of Y at X=x, we label them as self-enhancers. Participants who are with residuals lower than the 95% upper confidence limit for the mean value of Y at X=x, we label them as self-effacers.
When self-perception is measured by adjusted residual discrepancy, Y is perceived performance value and X is actual performance value. And, when self-perception is measured by residual discrepancy-change, Y is perceived performance with incentive value and X is perceived performance without incentive value.
5.1.3.4 Dependent Variable—mathematics achievement
We recorded data for a variety of mathematics achievement variables from school records.
These variables included teacher assessments of everyday performance (50%) and three exams (50%) of mathematics subject across four semesters since the Spring semester of 2011.
5.2 Result
In Study 3, two kinds of residual discrepancies were used to represent self-perception and test the hypothesis respectively:
5.2.1 Adjusted Residual Discrepancy: accurate self-assessors unintentionally performs best A three-way ANOVA for country, type of self-perception and semester was conducted on the mathematics achievement. The last factor was a within-subject measure. Table 5.2a presents
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relevant means and standard deviations. As shown in Table 5.2b, three-way interaction was not significant, F(6, 891) =1.56, ns. The two-way interaction for Semester × Country was not significant, F(3, 891) = .57, ns., for Semester × Type of Self-Perception was not significant, F(6, 891) =1.25, ns., and for Country × Type of Self-Perception was also not significant, F(2, 297)
=2.27, ns. As shown in Figure 5.2a, subsequent main effects for three types of self-perception on the academic performance indicated that no matter in Taiwan or in the U.S., the mathematics achievement was highest in accurate self-assessors unintentionally (M = .36), then in self-enhancer unintentionally(M = -.08), and lowest in self-effacer unintentionally(M = -.31), F(2, 297) = 13.28, p <.001. The effect sizeη2 is .08. According to Cohen (1988), .059＞η2＞.01 is small effect, .138＞η2＞.059 is medium effect, andη2＞.138 is large effect. Therefore, the effect size here is a medium effect.
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Table 5.2a
Means and Standard Deviations of Dependent Variables According to Countries, Semesters, and Type of Self-Perception (Self-perception measured by adjusted residual discrepancy)
Semester Type of Self-Perception Taiwan America Total
M SD M SD M SD
1 Self-effacer unintentionally -.27 .95 -.28 .89 -.27 .93 Accurate self-assessor unintentionally .09 1.22 .52 1.07 .31 1.15 Self-enhancer unintentionally .01 1.18 -.21 .86 -.06 1.09 2 Self-effacer unintentionally -.29 .94 -.38 .85 -.32 .91
Accurate self-assessor unintentionally .25 1.10 .52 1.0 .38 1.05 Self-enhancer unintentionally -.01 1.15 -.09 .96 -.03 1.09 3 Self-effacer unintentionally -.37 1.02 -.30 .87 -.34 .97
Accurate self-assessor unintentionally .20 1.10 .62 .99 .41 1.06 Self-enhancer unintentionally -.06 1.21 -.28 .88 -.13 1.13 4 Self-effacer unintentionally -.33 .96 -.23 .84 -.30 .92
Accurate self-assessor unintentionally .20 1.10 .46 1.05 .33 1.08 Self-enhancer unintentionally -.04 1.20 -.19 .99 -.09 1.14 Total Self-effacer unintentionally -.31 .97 -.30 .86 -.31 .93
Accurate self-assessor unintentionally .19 1.12 .53 1.02 .36 1.08 Self-enhancer unintentionally -.02 1.18 -.19 .91 -.08 1.11
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Table 5.2b
Three Way ANOVA table for Countries, Semesters, and Type of Self-Perception (Self-perception measured by adjusted residual discrepancy)
SV SS df MS F η2
Within subject
Semester .22 3 .07 .54 .002
Semester*Country .23 3 .08 .57 .002
Semester*Self_Perception 1.03 6 .17 1.25 .008 Semester*Country* Self_Perception 1.29 6 .22 1.56 .010
Error(Semester) 122.46 891 .14 Between subjects
Country 1.14 1 1.14 .34 .001
Self_Perception 89.34 2 44.67 13.28*** .082 Country* Self_Perception 15.29 2 7.64 2.27 .015
Error 999.11 297 3.36
*** p < .001.
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Figure 5.2a. Interaction plots for Country and Type of Self-Perception on the mathematics achievement. (Self-perception measured by adjusted residual discrepancy)
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5.2.2 Residual Discrepancy-Change: self-effacers intentionally perform best, and this is stronger in Taiwan than in the U.S.
A three-way ANOVA for country, type of self-perception and semester was conducted on the
mathematics achievement. The last factor was a within-subject measure. Table 5.2c presents relevant means and standard deviations. As shown in Table 5.2d, three-way interaction was significant, F(6, 867) = 3.0, p < .01. As shown in Table 5.2e, simple main effects analyses of the results for Country × Self-Perception found significant interaction on each semester F(2, 289)
>5.75, p < .01, and the effect sizeη2 is .04~.07, which is small to medium effect. Simple main effects for Country × Semester found significant only on self-effacer intentionally, F(2, 289)
=3.29, p < .05, and the effect sizeη2 is .02, which is small effect. Simple main effects for Self-Perception × Semester found significant only in the U.S., F(6, 867) =2.46, p < .05, and the effect sizeη2 is .03, which is small effect.
Subsequent results included: As shown in Table 5.2f, Table 5.2g, Table 5.2h and Table 5.2i and Figure5.2b, Figure5.2c, Figure5.2d and Figure5.2e , four of the simple simple main effects comparing each semester found significant for self-perception at Taiwan, country at self-effacer intentionally, and country at self-enhancer intentionally. That is, for Taiwanese, the mathematics achievement was highest in self-effacer intentionally (M = .61~ .68), then in accurate self-assessors intentionally (M = -.28~ -.37), and lowest in self-enhancer intentionally (M = -.80~
-.89). For American, the mathematics achievement was higher in self-effacer intentionally (M
= .15~ .30) than self-enhancer intentionally (M = -.21~ -.49). For self-enhancer intentionally, the mathematics achievement was higher in the U.S (M = -.21 and -.35) than in Taiwan (M = -.80 and -.89) in semester1 and semester3. In addition, as shown in Table 5.2j, simple simple main effects comparing countries found significant for country at semester. That is, for self-effacer intentionally, the mathematics achievement was higher in Taiwan (M = .61~ .68) than in the U.S
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(M = .15~ .30) each semester. Furthermore, as shown in Table 5.2k, simple simple main effects comparing Self-Perception found significant for self-perception at four semesters. That is, in the U.S., the mathematics achievement was higher in self-effacer intentionally (M = .15~ .30) than self-enhancer intentionally (M = -.21~ -.49).
Table 5.2c
Means and Standard Deviations of Dependent Variables According to Countries, Semesters, and Type of Self-Perception (Self-perception measured by residual discrepancy-change)
Semester Type of Self-Perception Taiwan America Total
M SD M SD M SD Accurate self-assessor intentionally -.33 1.03 .004 .87 -.23 1.00 Self-enhancer intentionally -.83 .85 -.36 .77 -.66 .85
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Table 5.2d
Three Way ANOVA table for Countries, Semesters, and Type of Self-Perception (Self-perception measured by residual discrepancy-change)
SV SS df MS F η2
Within subject
Semester .43 3 .15 1.04 .004
Semester*Country .21 3 .07 .49 .002
Semester*Self_Perception 2.08 6 .35 2.49* .017 Semester*Country* Self_Perception 2.50 6 .42 3.00** .020
Error(Semester) 120.60 867 .14 Between subject
Country 1.48 1 1.48 .59 .002
Self_Perception 227.98 2 113.99 45.08*** .238 Country* Self_Perception 36.93 2 18.47 7.30*** .048
Error 730.81 289 2.53
* p < .05. ** p < .01. *** p < .001.
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Table 5.2e
Two Way interaction simple main effect table for Countries, Semesters, and Type of Self-Perception (Self-perception measured by residual discrepancy-change)
SV SS df MS F η2
Country* Self_Perception
Semester1 19.22 2 9.61 12.76*** .073 Semester2 11.23 2 5.62 7.82*** .047
Semester3 8.78 2 4.39 5.75** .035
Semester4 13.54 2 6.77 9.04*** .055 Country*Semester
Self-efface intentionally 1.131 3 .377 3.291* .027 Accurate self-assess intentionally .599 3 .200 1.354 .015 Self-enhance intentionally 1.088 3 .363 2.170 .027 Self_Perception *Semester
In Taiwan .74 6 .12 1.12 .011
In the U.S. 2.98 6 .50 2.46* .052
* p < .05. ** p < .01. *** p < .001.
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Table 5.2f
Simple simple main effect table for Type of Self-Perception and Countries in Semester1 (Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Self_Perception at Taiwan 81.77 2 40.89 65.84*** Self-effacer >
Accurate >
Self-enhancer Self_Perception at the U.S. 2.72 2 1.36 1.39
Country at self-efface intentionally 12.56 1 12.56 16.33*** Taiwan>
U.S.
Country at accurate self-assess intentionally
.60 1 .60 .74
Country at Self-enhance intentionally 6.33 1 6.33 9.69** U.S.>
Taiwan
** p < .01. *** p < .001.
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Table 5.2g
Simple simple main effect table for Type of Self-Perception and Countries in Semester2 (Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Self_Perception at Taiwan 84.65 2 42.32 69.97*** Self-effacer >
Accurate >
Self-enhancer Self_Perception at the U.S. 12.01 2 6.01 6.49** Self-effacer >
Self-enhancer Country at self-efface intentionally 8.27 1 8.27 11.04*** Taiwan>
U.S.
Country at accurate self-assess intentionally
1.47 1 1.47 1.94
Country at Self-enhance intentionally 1.75 1 1.75 2.79
** p < .01. *** p < .001.
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Table 5.2h
Simple simple main effect table for Type of Self-Perception and Countries in Semester3 (Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Self_Perception at Taiwan 74.40 2 37.20 57.37*** Self-effacer >
Accurate >
Self-enhancer Self_Perception at the U.S. 9.04 2 4.52 4.69* Self-effacer >
Self-enhancer Country at self-efface intentionally 5.03 1 5.03 5.94* Taiwan>
U.S.
Country at accurate self-assess intentionally
.00 1 .00 .00
Country at Self-enhance intentionally 3.89 1 3.89 5.96* U.S.>Taiwan
* p < .05. *** p < .001.
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Table 5.2i
Simple simple main effect table for Type of Self-Perception and Countries in Semester4 (Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Self_Perception at Taiwan 74.99 2 37.50 59.09*** Self-effacer >
Accurate >
Self-enhancer Self_Perception at the U.S. 6.87 2 3.43 3.59* Self-effacer >
Self-enhancer Country at self-efface intentionally 10.05 1 10.05 12.28*** Taiwan>
U.S.
Country at accurate self-assess intentionally
1.73 1 1.73 2.16
Country at Self-enhance intentionally 2.12 1 2.12 3.64
* p < .05. *** p < .001.
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Table 5.2j
Simple simple main effect table for Type of Countries and Semester in self-effacer intentionally (Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Coutry at Semester1 12.56 1 12.56 16.33*** Taiwan>U.S.
Coutry at Semester2 8.27 1 8.27 11.04*** Taiwan>U.S Coutry at Semester3 5.03 1 5.03 5.94* Taiwan>U.S.
Coutry at Semester4 10.05 1 10.05 12.28*** Taiwan>U.S Semester at Taiwan .27 3 .089 1.237
Semester at the U.S .93 3 .309 1.646
* p < .05. *** p < .001.
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Table 5.2k
Simple simple main effect table for Type of Self-perception and Semester in the U.S.
(Self-perception measured by residual discrepancy-change)
SV SS df MS F Post hoc
Self-perception at Semester1 2.72 2 1.362 1.39
Self-perception at Semester2 12.01 2 6.01 6.49** Self-effacer >
Self-enhancer Self-perception at Semester3 9.04 2 4.52 4.69* Self-effacer >
Self-enhancer Self-perception at Semester4 6.87 2 3.43 3.59* Self-effacer >
Self-enhancer Semester at self-efface
intentionally
.93 3 .31 1.65
Semester at accurate self-assess intentionally
.86 3 .29 1.24
Semester at self-enhance intentionally
1.70 3 .57 2.79* Semester1 >
Semester2
* p < .05. ** p < .01.
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Figure 5.2b. Interaction plots for Country and Type of Self-Perception on the mathematics achievement in Semester 1. (Self-perception measured by residual discrepancy-change)
Figure 5.2c. Interaction plots for Country and Type of Self-Perception on the mathematics achievement in Semester 2. (Self-perception measured by residual discrepancy-change)
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Figure 5.2d. Interaction plots for Country and Type of Self-Perception on the mathematics achievement in Semester 3. (Self-perception measured by residual discrepancy-change)
Figure 5.2e. Interaction plots for Country and Type of Self-Perception on the mathematics achievement in Semester 4. (Self-perception measured by residual discrepancy-change)
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To conclude, when self-perception measured by adjusted residual discrepancy, no matter in Taiwan or in the U.S., people who unintentionally self-assess accurately performs best and those who unintentionally self-efface performs worst.
When self-perception measured by residual discrepancy-change, the three-way interaction was significant. First, for Taiwanese, the mathematics achievement was highest in self-effacer intentionally, then in accurate self-assessors intentionally, and lowest in self-enhancer intentionally in four semesters. For Americans, the mathematics achievement was higher in self-effacer intentionally than self-enhancer intentionally in three semesters. Second, for self-enhancer intentionally, Americans outperformed Taiwanese in two semesters. For self-effacer intentionally, Taiwanese outperformed Americans in four semesters.
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