Adolescents
4.1 Method
The purpose of Study 2 was to understand self-enhancement for mathematics achievement in Taiwanese and American adolescents using the same method of Study 1. One hypothesis referred that self-enhancers or self-effacers indicated lower academic performance compared to accurate self-assessors. The other hypothesis referred that with a monetary incentive, both self-enhanced and self-effacers who unintentionally or intentionally would show lower mathematics achievement Accurate self-assessors unintentionally or intentionally shows otherwise. The expected results in Taiwanese and American adolescents would be similar.
4.1.1 Participants
The participants for Taiwanese students are the same as Study 1. The participants for America students are 128 students of seventh grade and tenth grades from a public school participated in the study (mean age = 15.09, years, SD = .70), participants include equal numbers of males and females and the probability distribution of the participants is approximately a normal distribution.
4.1.2 Procedure
The procedures in Study 2 are the same as Study 1 in Taiwan and the United States. We normalized the amount offered based on the current exchange rate and the relative per capita GDP in the United States and Taiwan, arriving at a rate of $20.00 NTD to $1.00 USD. Therefore,
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the monetary incentive used in the United States is $20.00 USD. At the end of the semester, all students’ mathematics achievement was collected from school records.
4.1.3Measures 4.1.3.1 Math test
In Taiwan, the math test in Study 2 is the same as Study 1 (see Appendix.1). And, In the United States, the average items gotten right of the math test is 8.79 (SD=5.33) (see Appendix.4).
4.1.3.2 Measuring self-enhancement score(see Appendix.5)
The same as study 1, three kinds of residual discrepancies were used to test the hypothesis respectively in Study 2. These were initial residual discrepancy, adjusted residual discrepancy and residual discrepancy-change.
4.1.3.3 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 in the Spring semester of 2011. The independent variable in study 2 is different from study 1. The reason for choosing mathematics achievement instead of GPA is that different countries included different subjects for GPA. Therefore, it is better to choose the same subject. Since math questions were conducted in the procedure, we decide to use mathematics achievement as independent variable in this cross-cultural comparison.
4.2 Result
In study 2, the curvilinear regression is used to test the hypothesis whether there is a functional relationship between self-perceptions (ie., self-enhancement, self-effacement and accurate self-assessment) and mathematics achievement in Taiwanese and American Adolescents.
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The results of two countries are presented as follows:
4.2.1 Taiwanese Adolescents
4.2.1.1 Initial Residual Discrepancy: The quadratic effect between self-perception and mathematics achievement
The mean number of correct answers in the math test was 11.52 (SD=4.88). Men and women did not differ on their actual performance on the test, t(214) = -0.28, ns. The average perceived performance of the math test was 12.09 (SD=4.63). The polynomial regression equation was fitted to mathematics achievement with the linear and quadratic effects of self-perception as predictors (i.e., Y 63.0331.003X4 0.385X42, where Y = Mathematics achievement, X4 is self-perception as measured by initial residual discrepancies. The maximum value of a quadratic equation is determined when X1 = 1.30. )
Table 4.2a shows results of analysis examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by initial residual discrepancies was used as the predictor (X) in step 2, the linear effect of self-perception was not significant, β = .12, t(210) = 1.73, ns, but the predicted quadratic effect was significant, β = - 0.17, t(210) = -2.47, p< .05, supporting Hypothesis2-1. As shown in Figure 4.2a, the shape of the relationship is consistent with the hypothesis. On the horizontal axis, self-enhancers take parts of the positive values, on the other hand, self-effacers have the negative values. The graph has proved, and as predicted, these two groups of people shows lower mathematics achievement.
Participants, who resulted in scoring closer to zero, shows otherwise.
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Table 4.2a
Summary of the relationship between initial residual discrepancies and mathematics achievement in Study 2 (Taiwanese Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
initial residual discrepancies 1.06 0.12 1.80 0.02 (0.02)
Step 2
initial residual discrepancies
initial residual discrepancies--quadratic effect
1.00 -0.39
0.12 -0.17
1.73 -2.47*
0.04 (0.03)
Note. N = 214. * p < .05.
Figure 4.2a. Curvilinear relationship between initial residual discrepancies and mathematics achievement in Study 2 (Taiwanese Adolescents)
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4.2.1.2 Adjusted Residual Discrepancy: The quadratic effect between self-perception and mathematics achievement (Taiwanese Adolescents)
The average perceived performance (with incentive) of the math test was 12.14 (SD=4.89).
The polynomial regression equation was fitted to mathematics achievement with the linear and quadratic effects of self-perception as predictors (i.e., Y 62.5690.87X5 0.393X52, where Y
= Mathematics achievement, X5 is self-perception as measured by Adjusted residual discrepancies. The maximum value of a quadratic equation is determined when X5 = 1.11. )
Table 4.2b shows results of analyses examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by adjusted residual discrepancies was used as the predictor (X) in step 2, the linear effect of self-perception was not significant, β = .09, t(210) = 1.30, ns, but the predicted quadratic effect was significant, β = - 0.15, t(210) = -2.20, p< .05, supporting Hypothesis2-2. As shown in Figure 4.2b, the shape of the relationship is consistent with the hypothesis. This quadratic effect shows similar results to the outcomes in Figure 4.2a, but less significant.
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Table 4.2b
Summary of the relationship between adjusted residual discrepancies and mathematics achievement in Study 2 (Taiwanese Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
adjusted residual discrepancies 0.79 0.08 1.17 0.01 (0.01)
Step 2
adjusted residual discrepancies
adjusted residual discrepancies--quadratic effect
0.87 -0.39
0.09 -0.15
1.30 -2.20*
0.03(0.02)
Note. N = 214. * p < .05.
Figure 4.2b Curvilinear relationship between adjusted residual discrepancies and mathematics achievement in Study 2 (Taiwanese Adolescents)
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4.2.1.3 Residual Discrepancy-Change: The linear effect between self-perception and mathematics achievement
Different from initial residual discrepancies and adjusted residual discrepancies, the polynomial regression equation was only fitted to mathematics achievement with the linear effects of self-perception as predictors. (i.e., Y 60.0533.170X , where Y = Mathematics achievement, X6 is self-perception as measured by residual discrepancy-change).
Table 4.2c shows results of analyses examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by residual discrepancy-change was used as the predictor (X) in step 1, the linear effect of self-perception was significant, β = .24, t(210) = 3.52, p< .001. However, when residual discrepancy-change was used as the predictor (X) in step 2, the linear effect of self-perception was still significant, β
= .23, t(210) = 3.36, p< .001, but the predicted quadratic effect was not significant, β = - 0.09, t(210) = -1.29, ns. Hypothesis2-3 was not supported. As shown in Figure 4.2c, The linear effect showed that self-effacers intentionally was related to higher academic performance, whereas self-enhancers intentionally associated with lower academic performance.
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Table 4.2c
Summary of the relationship between residual discrepancy-change and mathematics achievement in Study 2 (Taiwanese Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
residual discrepancy-change 3.17 0.24 3.52*** 0.06 (0.06)
Step 2
residual discrepancy-change
residual discrepancy-change --quadratic effect
3.04 -0.35
0.23 -0.09
3.36***
-1.29
0.06 (0.01)
Note. N = 214. ** p < .01.
Figure 4.2c. Curvilinear relationship between residual discrepancy-change and mathematics achievement in Study 2 (Taiwanese Adolescents)
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4.2.2 American Adolescents
4.2.2.1 Initial Residual Discrepancy: The quadratic effect between self-perception and mathematics achievement
The mean number of correct answers in the math test was 8.79 (SD=5.33). The average perceived performance of the math test was 12.12 (SD=5.29). The polynomial regression equation was fitted to mathematics achievement with the linear and quadratic effects of self-perception as predictors (i.e., Y 0.510.005X7 0.002X72, where Y = mathematics achievement, X7 is self-perception as measured by initial residual discrepancies. The maximum value of a quadratic equation is determined when X1 = 1.25. )
Table 4.2d shows results of analysis examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by initial residual discrepancies was used as the predictor (X) in step 2, the linear effect of self-perception was not significant, β = .00, t(128) =-1.14, ns, but the predicted quadratic effect was significant, β = .00, t(128) = -2.84, p< .05, supporting Hypothesis2-1. As shown in Figure 4.2d, the shape of the relationship is consistent with the hypothesis. On the horizontal axis, self-enhancers take parts of the positive values, on the other hand, self-effacers have the negative values. The graph has proved, and as predicted, these two groups of people shows lower academic performance.
Participants, who resulted in scoring closer to zero, shows otherwise.
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Table 4.2d
Summary of the relationship between initial residual discrepancies and mathematics achievement in Study 2 (American Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
initial residual discrepancies -0.01 -0.10 -1.64 0.02 (0.02)
Step 2
initial residual discrepancies
initial residual discrepancies--quadratic effect
-0.01 -0.00
0.00 0.00
-1.14 -2.84*
0.08 (0.06)
Note. N = 214. * p < .05.
Figure 4.2d Curvilinear relationship between initial residual discrepancies and mathematics achievement in Study 2 (American Adolescents)
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4.2.2.2 Adjusted Residual Discrepancy: The quadratic effect between self-perception and mathematics achievement
With monetary incentive, only 36.8% of the participants didn’t change their answer. Then, t test was conducted to understand if participants’ answer became more accurate with incentive. In order to know the positive and negative difference between self-perception score and zero, we need to take the absolute value of initial and adjust discrepancy. The results showed a significant difference (t=3.59, p< .001), and the absolute value of adjust discrepancy is smaller (M = 3.25) than initial discrepancy (M = 4.30). That is, participants would self-assess more accurately with monetary incentive.
The average perceived performance (with incentive) of the math test was 12.12 (SD=5.29).
Similar to Phase 1, the polynomial regression equations was fitted to mathematics achievement with the linear and quadratic effects of self-perception as predictors. (i.e.,
Table 4.2e shows results of analyses examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by adjusted residual discrepancies was used as the predictor (X) in step 2, the linear effect of self-perception was not significant, β = .01, t(128) = .74, ns, but the predicted quadratic effect was significant, β = 0.00, t(128) = -3.51, p< .001, supporting Hypothesis2-2. As shown in Figure 4.2e, the shape of the relationship is consistent with the hypothesis. This quadratic effect shows similar results to the outcomes in 4.2e, but less significant.
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Table 4.2e
Summary of the relationship between adjusted residual discrepancies and mathematics achievement in Study 2 (American Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
adjusted residual discrepancies -0.01 -0.10 -1.12 0.01 (0.01)
Step 2
adjusted residual discrepancies
adjusted residual discrepancies--quadratic effect
0.00 -0.00
0.01 0.00
0.74 -3.51***
0.09 (0.09)
Note. N = 214. *** p < .001.
Figure 4.2e Curvilinear relationship between adjusted residual discrepancies and mathematics achievement in Study 2 (American Adolescents)
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4.2.2.3 Residual Discrepancy-Change: The quadratic effect between self-perception and mathematics achievement
The polynomial regression equation was fitted to mathematics achievement with the linear and quadratic effects of self-perception as predictors. (i.e., Y 0.5040.003X0.002X2, where Y = mathematics achievement, X1 is self-perception as measured by residual discrepancy-change. The maximum value of a quadratic equation is determined when X2 = 1.50. )
Table 4.2f shows results of analyses examining the relationship between self-perception and mathematics achievement. As can be seen, when self-perception measured by residual discrepancy-change was used as the predictor (X) in step 2, the linear effect of self-perception was not significant, β = .07, t(128) = .73, ns, but the predicted quadratic effect was significant, β
= 0.22, t(211) = -2.45, p< .05, supporting Hypothesis2-3. As shown in Figure 4.2f, the shape of the relationship is consistent with the hypothesis. The graph has proved, and as predicted, self-effacers intentionally and self-enhancers intentionally shows lower mathematics achievement.
Participants, who resulted in scoring closer to zero both the times, shows otherwise.
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Table 4.2f
Summary of the relationship between residual discrepancy-change and mathematics achievement in Study 2 (American Adolescents)
Predictor B β t R2 (ΔR2)
Step 1
residual discrepancy-change 0.01 0.11 1.20 0.01 (0.01)
Step 2
residual discrepancy-change
residual discrepancy-change --quadratic effect
0.00 -0.00
0.07 0.22
0.73 -2.45*
0.06(0.05)
Note. N = 214. * p < .05.
Figure 4.2f. Curvilinear relationship between residual discrepancy-change and mathematics achievement in Study 2 (American Adolescents)
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In short, these results showed that for Taiwanese adolescents, the results are similar to Study 1. That is, accurate self-assessors, accurate self-assessors unintentionally, and self-effacers intentionally are related to the short term higher academic performance. However, for American adolescents, all the results reveal that accurate self-assessors, accurate self-assessors unintentionally, and accurate self-assessors intentionally outperformed their peers in school.
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