Introduction
In an environment of growing cost of higher education, there is an intuitive need for students to determine if such their educational investments can be reliably expected to provide them better lifelong earnings. In order to obtain the necessary information on higher education earnings outcomes, a simple literature review of at least three peer-reviewed research articles has been conducted with a focus on the impact of higher education on wage premiums.
Learning about the impact of higher education on wage outcomes is of high importance due to the growing investments today on education, as evidenced by the surging trend in student debt, which in 2012 hit the $1 trillion mark in the United States along. Students have the obligation to know if their higher education is paying off better than otherwise, or at least learning specific programs and levels showing the better or the best lifelong earnings in the contemporary job market. Accordingly, this paper aims to determine whether a higher education is better than otherwise in getting a better paying job today. This common research issue has been analyzed using both descriptive and inferential statistical tests.
Context development
Article 1: Schneider’s Does education pay? (2013)
Focus: Schneider (2013) concentrated its article at discussing the finding of College Measures, an independent group that the American Institutes for Research (AIR) and the Matrix Knowledge Group (MKG) created primarily to collect and analyze wage data in order to generate data for education leaders and upcoming students.
Research question: What is the relative value of higher education credentials in terms of wage premium in five participating American States (i.e., Arkansas, Colorado, Tennessee, Texas, and Virginia)?
Hypothesis: This study appeared to have at least the following hypotheses:
Hypothesis 1: Long-term higher education credentials are worth better than short-term credentials. The long-term credentials referred to both the Bachelor’s and Master’s degrees; while the short-term credentials to the sub-baccalaureate certificates, such as Associate’s degree (2 years), one-year or more certificates (but less than 2 years), and certificates of less than 1 year. Hypothesis 2: Where a student graduates from has an impact on earnings. This hypothesis aimed to classify students according to educational institutions within each State and overall, namely: within state institutions; regional institutions; and private non-profit institutions. Hypothesis 3: Field of study is as important as the place of study. This hypothesis aimed to differentiate two factors – field of study and place of study – in terms of wage premium.
Statistical technique: Although not expressly indicated, the study apparently used the qualitative design using survey as the research method and descriptive statistics, particularly -arithmetic mean, median, and relative frequency distribution (i.e., percentage), as the statistical technique. The arithmetic mean helped in determining the mathematical central tendency of the data (Weiers, 2014); while median identified the most centrally positioned data relative to the other data. The relative frequency distribution groups the data into different equally distributed groups based on a specific range of percentage values.
Article 2: Cole, Paulson, & Shastry’s Smart Money? (2014)
Focus: The study focuses on the effect of education on worker participation financial activities, such as participation in the financial market and management of personal credit, which referred to generically as “financial outcomes” (Cole, Paulson, & Shastry (2014).
Research question: Does education have a causal effect on workers’ financial outcomes (i.e. financial market participation; income from financial instrument investments; and personal credit management).
Hypothesis: The study has the following hypotheses framed as alternative hypotheses:
General hypothesis: Education is positively correlated with financial outcomes.
Specific hypothesis 1: Education is positively correlated with the level of participation in the financial market. The study defines financial participation in terms of equity ownership; that is, of equity such as stocks, bonds, and mutual funds as well as transaction accounts. Specific hypothesis 2: Education is positively correlated with the level of income from investments in financial instruments. This measures the effect of education on nonzero investment income of the study population. Specific hypothesis 3: Education is positively correlated with effective credit management. Credit management is defined using such factors as probability of bankruptcy and foreclosure, slightly higher credit scores, and fewer delinquent card payments.
Statistical technique: The study used a retrospective cohort design using the survey method and simple random selection by random draw as the sampling technique. Descriptive statistics used include measures of central tendency (e.g., arithmetic mean, and median) and of dispersion (e.g. percentile, variance, and standard deviation). To isolate the causal effect of education on the financial outcomes, Cole, Paulson, and Shastry (2014) used the instrument variables technique, identifies instruments (i.e. changes in state compulsory education laws) that causes observable variation in individual educational attainment without affecting confounding factors such as individual ability, parental characteristics, and other potential confounders.
Article 3: Afzal’s Macroeconometric analysis of private returns to education (2011)
Focus: The study focused on the earnings impact of education of the teaching and non-teaching personnel (both gender) in general education institutions in the Lahore District of Pakistan (Afzal, 2011).
Research question: What are relationships between the key determinants of earnings of the employees in institutions of general education in Lahore District, Pakistan?
Hypothesis: This study has three hypotheses, namely:
Hypothesis 1: There is a relationship between earnings and its major determinants (e.g. education, age, experience, occupation, gender, working hours SSC institution sector, family status, family background, computer skills, and spouse education. Hypothesis 2: Female general education employees earn more than their male counterparts. Hypothesis 3: The rate of returns to education increases with the rise in employee educational level.
Statistical technique: This study follows a quantitative design using survey method for data collection and econometric methods for measuring private financial returns to test the three hypotheses. Moreover, the human capital approach was used in analyzing the association between variables in Hypothesis 1. Methodology, however, failed to describe clearly both the econometric and human capital approaches. It did show its use of the multiple regression model to perform multiple correlation analysis.
Statistical tool discussion
In general, statistics plays a crucial role in sets of data collected in research. Depending on the objectives of research, statistics can help describe the data in an understandable presentation or process data in order to perform estimates, generalize results from one group of people to another a larger group of related people, and forecast probable future behaviors (Weiers, 2014). As such, statistics consists of a range of mathematical techniques known to be capable of achieving the study’s descriptive or inductive objectives. Thus, these techniques came to be referred to as descriptive statistics or inferential statistics, respectively.
Descriptive statistics primarily summarizes and describes data (Weiers, 2014). Description of data can be performed visually or mathematically. Visual descriptions constitute all diagrams, tables, graphs, and distribution by frequency levels. Mathematical descriptions include various mathematical measures of central tendency (e.g. arithmetic mean, median, and mode), of dispersion (e.g. range, quantiles, range, mean absolute deviation, variance, and standard deviation), and of association (e.g. coefficient of correlation, coefficient of determination).
Conversely, inferential statistics makes generalized assumption of a phenomenon observed in a large population of people using only a small sample of such population (Weiers, 2014). Thus, they are used in testing hypotheses. These tests can be categorized into two based on theoretical direction: i.e. one-tail tests and two-tail tests. Based on these categories alone, tests have limits. They can erroneously reject the null hypothesis when it is in fact true (Type I error) or mistakenly not rejecting the null hypothesis when in fact it is wrong (Type II error). Moreover, reducing the probability of a Type I error inevitably increases the probability of a Type II error. To surely avoid rejecting the true hypothesis is to never accept any hypothesis. Thus, oftentimes there is a tradeoff that should be made between the two errors. That is essentially the weakness of probability theory.
Moreover, hypothesis testing also involves analyzing single-sample means or proportions and two-sample means or proportions. The former correlates different variables within a single sample population; while the latter different variables within and between two sample groups. The test statistics for the former includes the z-test and the t-test (one-tail or two-tail); while the latter includes t-test (pooled-variance or unequal-variances), z-test, and F-test. However, there are also tests of variable synergy. These tests include the analysis of variance (ANOVA), F-ratio. Other parametric tests include the Chi-square (probability distribution) (Weiers, 2014).
The limitations of parametric tests include their inability to test hypothesis without establishing many assumptions about the population (e.g. that the population should be normally distributed); they need a large sample size to be useful or at least mathematically acceptable; and they cannot test data that are ordinal and nominal in their measurement scales (Weiers, 2014).
Unlike parametric tests, nonparametric tests do not assume any specific distribution of the population; can be applied even in very small sample size; and can test samples of nominal and ordinal data. These tests include Wilcoxon Signed Ranked test, Kruskal-Wallis test, Friedman test, Sign test, Runs test, Spearman rank correlation, and the regression models, among others. However, they too have their set of limitations, such as less efficient use of data information, lower test power, and relies primarily on statistical tables.
In terms of interpretation, it must be made clear that statistics are only mathematical tools at understanding probabilities. By definition, a probability merely estimates fact and at times not even certainty. Thus, no matter how sophisticated the mathematical model of a statistic, it cannot perfectly predict behavior and other phenomena (Haran, Nicholas, & Keller, 2013). In effect, statistical predictions are at best uncertain (Weiers, 2014). However, despite the clear limitations of statistics, it can reasonably inform on decisions at least with imperfect level of certainty.
Conclusion
A large number of statistics used in the three studies reviewed in this paper are of descriptive types, primarily arithmetic mean and median, both of which were used in all three research articles. In article 1, they were even used to help answer (or loosely “test”) the research hypotheses. Arithmetic mean shares similar elements with more or less all descriptive statistics: sample size, data, variables, assumption of central tendency of the data, and ability to test “qualitative hypotheses”. Technically, however, a hypothesis has no place in a qualitative research as it implies an inductive approach, which is the realm of quantitative research. Qualitative research does not. Thus, according to Creswell (2008), the research question is the appropriate guide in a qualitative inquiry. The use of “qualitative hypotheses” referred to the use of hypothesis in a non-quantitative study anyway, particularly article 1.
References
Afzal, M. (2011). Microeconometric analysis of private returns to education and determinants of
earnings. Pakistan Economic and Social Review, 49(1): 39-68).
Cole, S., Paulson, A., & Shastry, G.K. (2014). Smart money? The effect of education on
financial outcomes. The Review of Financial Studies, 27(7): 2022-2051.
Creswell, J.W. (2008). Research design: Qualitative, quantitative, and mixed methods Approach.
New York: Sage Publication.
Dias, M.A.R. (1998, October 5). The long journey for a utopia becoming reality. The World
Conference on Higher Education: Vision and Action, Paris. Retrieved from: http://www.unesco.org/education/educprog/wche/diaz-e.htm.
Haran, M., Nicholas, R., & Keller, K. (2013). The role of statistics in sustainability research.
Penn State University Math Awareness Month Essays. Retrieved from: http://www.eesi.psu.edu/~ren10/Haran_Nicholas_Keller.The_Role_of_Statistics_in_Sustainability_Research.2013.pdf.
Schneider, Mark. (2013). Does education pay? Issues in Science and Technology, 33-38.
Weiers, R.M. (2014). Introduction to business statistics. (7th Ed.). Singapore: Cengage Learning
Asia.
