個人數學能力對其未來生涯之研究

Abstract

本研究旨在探討數學能力是否影響未來成就。為了客觀量化數學能力及未來生涯，我們分別以AMC（由美國數學協會主辦的美國數學競賽）分數及個人薪資代表數學能力及未來成就，除了數學能力以外，現有的研究顯示「教育年數」、「工作年資」、「家庭代表薪資」也都為影響個人薪資之因素。經由自行調查收集AMC考試的社會人士之資料，我們利用統計方法，如單邊t檢定、單因子變異數分析、複迴歸分析和路徑分析之統計模型進行分析，得出以下之結論：\n1.AMC人士之平均「個人薪資」顯著高於我國全體受僱人員之平均「個人薪資」。\n2.為了進行單因子變異數分析，我們將連續型自變數「教育年數」分成兩個組別、「工作年資」分成四個組別、「家庭代表薪資」分成四個組別、「AMC分數」分成五個組別。雖然表面上「男性」之平均「個人薪資」顯著地高於「女性」之平均「個人薪資」，但經進一步分析，我們發現職業別為平均「個人薪資」性別差異之干擾變數，因此不同職業別中的「個人薪資」並無顯著地性別差異；另外，「碩士以上」之平均「個人薪資」顯著地高於「大學以下」之平均「個人薪資」；「家庭代表薪資」在最高的組別，其平均「個人薪資」分別顯著地高於「家庭代表薪資」最低兩組的平均「個人薪資」；「AMC分數」最高的組別，其平均「個人薪資」分別顯著地高於「AMC分數」最低兩組的平均「個人薪資」。最後，我們沒有統計的證據顯示「工作年資」對於平均「個人薪資」有影響。\n3.提供複迴歸模型之迴歸參數的95% Bonferroni聯合信賴區間，並顯示若自變數「教育年數」、「工作年資」、「AMC分數」及「家庭代表薪資」增加，則對於95% 信賴區間之「個人薪資」也會同時增加。\n4.提供一些典型AMC人士複迴歸模型之50%與95% 個人薪資預測區間。\n5.我們得到適配良好的路徑分析模型，經由此模型得到，「教育年數」、「工作年資」、「AMC分數」和「家庭代表薪資」對於「個人薪資」皆為直接正向影響。

The main purpose of this research is to study whether the mathematical ability of an individual has an impact on his/her career achievement. To objectively quantify mathematical ability and career achievement, we shall use AMC (American Mathematical Competitions sponsored by the Mathematical Association of America) score and a personal income to represent his/her mathematical ability and career achievement, respectively, in this research. In addition to mathematical ability, the current research shows that “years of education”, “years of working experience”, and “head of household income” are also important possible factors on a person’s income. We use statistical analysis methods, such as t-test, one-way analysis of variance, multiple regression, and path analysis to analyze the data collected through the self-designed sample survey of the persons who have taken the AMC tests or “AMC persons” for short. Our findings are as follows:\n1.The average personal income of AMC persons is significantly higher than that of all employed in Taiwan.\n2.For doing one-way analysis of variance, we classify independent continuous variables “years of education” into “college or below” or “above college” 2 levels, “years of working experience” into 4 levels, “head of household income” into 4 levels, and “AMC score” into 5 levels. Although men’s average personal income is significantly higher than that of women’s, we find that the gender bias is due to occupation, which is the confounding factor. In other words, there is no significance difference on the average personal income of both men and women after considering occupation. In addition, the average personal income of individuals with “college or below” level is significantly lower than the average income of those with “above college” level. The average personal income of those with “head of household income” in the top level is significantly higher than the average income of those of both in the bottom two levels. The average personal income of those with “AMC score” in the top level is significantly higher than the average income of those of both in the bottom two levels. Finally, there is no statistical evidence that “years of working experience” has an effect on average personal income.\n3.The 95% Bonferroni joint confidence intervals of regression parameters in the multiple regression model are provided. These intervals show that there is a 95% confidence level that the personal income will increase if the values of independent variables “years of education”, “years of working experience”, “head of household income” or “AMC score” can be increased, even at the same time.\n4.Some 50% and 95% personal income prediction intervals of typical people having AMC scores are given.\n5.Our path analysis model fits well. Using this model, we find that “years of education”, “years of working experience”, “AMC score”, and “head of household income” all have positive direct influence to “personal income”.