STATISTICS THAT MATTER, Part 1

Testing for Differences Between Two Population Means: The t-test

The t-test is a statistical test applied to evaluate whether the means of two groups are significantly different. The t-statistic, also called t-value, t-stat or simply t, may be generally described as the quotient of the difference between the means of two groups and the variability of the two groups (Harmon, 2011). There are a number of variations for the t-test. For this particular lesson, the independent samples t-test will be discussed.

In this tutorial, actual data will be utilized in demonstrating how an independent samples t-test is performed, first by computation using the formula and a scientific calculator, and then by computerized calculation using the software Statistical Package for the Social Sciences (SPSS) Version 17, and Microsoft Excel (2003). As per experience, integrating theory with a practical application works best in topics concerning numerical ability. Hence, the essentials you need to learn to be able to use independent samples t-test correctly will be elucidated as we solve our tutorial problem.

Moreover, I opted to use socially relevant statistics. If we are to spend time and effort on this tutorial, let us try shooting two birds with one stone. At the end of this tutorial, you would have learned how to properly use independent samples t-test, and you would have achieved a certain degree of awareness on issues of the day that matter. This is one aspect which will set this education site from the rest – let us not just learn statistics and research, let us learn some current events and let us be socially conscious about significant advocacies and developments all around us.

The Problem and the Dataset

For this tutorial, we are interested in solving the following problem:

Is corruption based on the corruption perceptions index in countries with the full presidential system of government higher than countries with the parliamentary system?

Corruption is defined by Detzer (2011) as “the abuse of public power for private benefit (or profit)” (p. 2). Detzer (2011) maintained that this was the same definition adopted by the World Bank and Transparency International. Why are we interested in the aforestated problem? For one, Gerring and Thacker (2004) believe that there is some association with political corruption and the form of government. The duo argued that if polities are minimally democratic to say the least, they are bound to experience lower levels of corruption. The study conducted by Lederman, Loayza and Soares (2005) identified the relationship between a parliamentary system of government and lower level of corruption. This partly explains the interest in the research problem for this tutorial.

One issue should, however, be cleared before we push through with the statistics. How do we measure corruption? Politicians perpetrate corruption in stealth mode. In the Philippines, however, the stewards of corruption commit the act blatantly and aggressively in front of our very faces. Still, measuring corruption per se is more controversial than giving it a definition as articulated by Uslaner (2008). He even cautioned researchers that “any attempt to quantify corruption is thus fraught with danger and will endanger much criticism” (Uslaner, 2008, p. 11). This discussion will, therefore, venture to quantify corruption in terms of corruption perceptions index (CPI) as measured by Transparency International. Uslaner (2008) uses this measure of corruption, which he claims is the most widely use metric for the variable under study. For further reading on how CPI is measured, please visit the URL:
http://www.transparency.org/policy_research/surveys_indices/cpi/2010/in_detail.

To solve the research problem, the following null hypothesis is formulated using a two-tailed or non-directional analysis and a 0.05 level of significance (α = 0.05):

The corruption in countries governed using the full presidential system is equal to the corruption in countries governed using the parliamentary system.

If pres is our variable for the mean CPI for countries/territories with the full presidential system of government, parl is our variable for the mean CPI for countries/territories with the parliamentary system, H0 is our abbreviation for the null hypothesis and H1 is our abbreviation for the alternative hypothesis, then our non-directional hypotheses may be stated as:

H0: pres = parl

and

H1: pres ≠ parl

The dataset for this problem was obtained from two authoritative Websites: CIA World Factbook (2011) and the Transparency International (2010). Here is our dataset:

Solution 1: Computation Using a Scientific Calculator

Since, any scientific calculator can perform descriptive statistical calculations such as computing the mean and the standard deviation, calculation for these values will not anymore be taken be taken up in this tutorial. The variables n1 and n2 are the sample size (in this case, also the population size) of the countries/territories using presidential and parliamentary systems, respectively, whose values are 41 and 43. These values are included below the dataset: xbar1 = 3.3195; s1 = 1.5179; xbar2 = 4.5977; s2 = 1.9731 The approximate normal distribution of the dataset in shown below as Figure 1.

Figure 1. Approximate normal distribution of the dataset (Note: The image was retrieved from Mehta (2011) and superimposed with the values used in this tutorial).

For the normal distribution of the dataset, the limiting values of t for a non-directional or two-tailed analysis for the null hypothesis to be accepted can be found from a t-distribution table which is available as an appendix in most statistics books or online. To find the value of the critical t, we should be aware of the level of confidence specified (α = 0.05) and the degrees of freedom (df). Df may be computed from the formula: 

df = n1 + n2 – 2

df = 41 + 43 – 2

df = 82

The critical t may be obtained from the following t-distribution table. The critical t may be found by using the 0.05 two tail probabilities from column 4 corresponding to the computed df.

Figure 2. Percentage Points of the t-distribution (Knight, n.d.)

It may be observed that there is no exact value for 82 degrees of freedom, but the nearest df where the critical t is available is 80, rather than 100. The critical values of t for a two-tailed or non-directional analysis are, therefore, - 1.990 and + 1.990. These values were marked in Figure 1. The area of the normal curve between – 1.990 and + 1.990 is the acceptance region. If the computed value of t falls within – 1.990 and + 1.990, the null hypothesis will be accepted. As applied to the tutorial problem, when the null hypothesis is accepted, we would have established statistical evidence that, indeed, the corruption in countries governed using the full presidential system equal to (or not statistically different from) the corruption in countries governed using the parliamentary system. The area under the normal curve to the left of - 1.990, as well as the area of the curve to the right of + 1.990 are the rejection regions. If the computed value of t falls beyond – 1.990, meaning less than – 1.990 or beyond + 1.990, meaning greater than +1.990, the null hypothesis will be rejected and the alternative hypothesis will be adopted. This connotes that the corruption in countries governed using the full presidential system is NOT equal to (or is statistically different from) the corruption in countries governed using the parliamentary system. 


To calculate the t-statistic, the formula specified in Weinberg and Abramowitz (2008)  is:

Substituting the values of xbar1, xbar2, s1, s2, n1 and n2 which are rounded off to four digits after the decimal point, the computed value from a scientific calculator of the t-statistic is: t = - 3.297. This point is also marked off in Figure 1 and is found to the left of the -1.990 limit. It may be observed that t = - 3.297 lies in the rejection region on the left. As earlier mentioned, this condition prompts us to reject the null hypothesis and adopt the alternative hypothesis. Therefore, the corruption in countries governed using the full presidential system is statistically different from the corruption in countries governed using the parliamentary system. By looking at their respective means, the independent samples t-test showed us that  the corruption in countries governed using the full presidential system (xbar1 = 3.319) is statistically higher than the corruption in countries governed using the parliamentary system (xbar2 = 4.5977). It should be noted at this point that higher values of the corruption perceptions index  indicate lower levels of corruption.  

The foregoing findings offer support for the advocacy of the Constitutional Reform and Rectification for Economic Competitiveness and Transformation (CoRRECT™) Movement of which I am member of the core group. With a parliamentary system of government, we have better chances of curbing corruption in the country. The CoRRECT™ three point agenda calls for economic liberalization, evolving territorial decentralization, and shift to unicameral parliamentary system. 

The next post will demonstrate the solution to the same problem using Microsoft Excel and SPSS Version 17. Tutorial videos will be provided.

References:

Central Intelligence Agency (2011). World Factbook. Retrieved from https://www.cia.gov/index.html 


Gerring, J. & Thacker, S. C. (2004). Political institutions and corruption: The role of unitarism and parliamentarism, British Journal of Political Science, 34(2), 295-300. 


Harmon, M. (2011). t-Tests in Excel: The complete guide. Incline Village, NV: Excel Master Series. 


Knight, W. (n.d.). Percentage points of the t-distribution. Retrieved from http://www.math.unb.ca/~knight/utility/t-table.htm 


Lederman, D., Loayxa, N. V. & Soares, R. R. (2005). Accountability and corruption: Political institutions matter, Economics & Politics, 17(1), 1-35. 


Mehta, T. (2011). Drawing a normal curve. Retrieved from http://www.tushar-mehta.com/excel/charts/normal_distribution/ 


Transparency International (2010). Corruptions Perceptions Index 2010. Berlin: Transparency International Secretariat. Retrieved from http://www.transparency.org/publications/publications
/annual_reports/ annual_report_2010 


Transparency International (2011). Poll results. Retrieved from http://www.transparency.org/
content/collectedinfo/31738 


Uslaner, E. M. (2008). Corruption, inequality and the rule of law. New York: Cambridge University Press. 


Weinberg, S. L. & Abramowitz, S. K. (2008). Statistics using SPSS (2nd ed.). New York: Cambridge University Press.

The "joys" of plagiarism: Caveats against the copy and paste mentality, Part 2

When the experts are now the violators, how can the academe encourage students to refrain from acts of plagiarism, without provoking an outcry that justice in this land follows a double standard? This spells more headache for professors / instructors of research methods.

 Hicks (2011)* [Clip art licensed from the Clip Art Gallery on DiscoverySchool.com].

It was by choice that the writing of this article was deferred so as not to taint it with political color. This is definitely not a political article, but rather an open letter to the academe and the judiciary. Hence, instead of “striking while the iron is hot”, the most opportune time to publish is now ... when the smoke is going down.

Scenario 1 vs. Scenario 2

Imagine a scenario where a research consultant was requested to review a master’s thesis prior to conferment of a graduate degree. The consultant was shocked to have found that about half of the first three chapters were plagiarized. When the student was asked to explain his side, he claimed it was not done on purpose since it was simply copy pasted from an online article. Hence, there was absence of malicious intent. He further claimed that he was not aware that copying lines and lines of text in toto constitutes plagiarism because the source was cited. The consultant explained that no quotation marks were seen in the plagiarized portions of the thesis. The committee tasked to resolve the problem at hand decided to be a little lenient with the student, asking him to rework the plagiarized parts of the thesis by paraphrasing. However, since graduation is just a few days away, the student’s graduation was withheld until the end of the following semester.

For the second scenario, an associate justice of the Supreme Court (SC) wrote a decision exonerating the defendant of a high profile case. The counsel of the plaintiff later discovered that the decision contained plagiarized portions, at times even complete paragraphs, from foreign works. The associate justice was brought to court on charges of plagiarism. The accused pleaded not guilty of the charge, on the excuse that his research assistant accidentally deleted the footnotes containing the citations for the plagiarized parts of the decision. The associate justice was cleared in the matter of charges of plagiarism by his peers from the SC, who allegedly did not find malicious intent, and thus, the charges lacked merit.

Rhetorical questions

If the general policy regarding plagiarism for students declare that “the student’s intention is irrelevant – the action of copying text alone indicates plagiarism” (Smith, 2009, p.70). Why should an associate justice be treated more leniently? An associate justice is supposed to be an expert in jurisprudence. Besides, we were thought in school and at home that we should be responsible for our own actions, why can’t the expert judge be more responsible than a student?

Can we handle the truth?

It may be a very unfortunate fact and a very inconvenient truth that a former US Attorney and Appellate Judge, who is now in private practice has this to say about plagiarism in the judicial context:“... a judicial writer cannot commit legal plagiarism because the purpose of his writing is not to create a literary work but to dispose of a dispute between parties”(George. 2007, p. 726). This may be considered as one of the joys of plagiarism – dipping one’s fingers in boiling oil sans the agony of chafing.

Even then, George (2007) also cautioned in the context of ethical practice that judges should properly cite their sources, including law review articles, legal periodicals, judicial decisions, etc. As a personal rule, George (2007) maintained that “...while the judge may unwittingly use the language of a source without attribution, it is not proper even though he may be relieved of the stigma of plagiarism” (p. 726).

George’s (2007) position regarding the immunity of judges from plagiarism was supported by only a quarter of Filipino lawyers consulted for this article [although, this may be developed into a full-blown research if God permits]. The remaining three quarters adhere to the age-old tenet that no one is above the law and that no one is also below it.

Common Knowledge

One possible reason offered by George (2007) for the judges’ rather loose sense of practicing attribution of resources used in their judicial rulings is that their educational preparation and experience, as well as the requisites of their position warrant that only reliable, but time-tested legal theories and concepts are used with the exact wording. This brings to the fore another usually misinterpreted concept related to plagiarism –common knowledge.

As defined in Stepchyshyn and Nelson (2007), a statement regarded as common knowledge “does not need to be attributed to a source” (p. 53). Bothma, Cosijn, Fourie, and Penzhorn (2008 ) ruled that “facts that are likely to be known by many people and can be found in many places” are considered as common knowledge. It is common knowledge that sampaguita is our national flower. But that sampaguita is of Castilian origin and has the scientific name jasminium sambac are facts and their source must be cited [in this case Corriente, 2008 )]. Stepchyshyn and Nelson (2007) maintained that basic facts or common knowledge do not require citation, but interpretation of such facts should always be properly referenced. The common rule of thumb is that if a statement or fact is not common knowledge or if there are doubts whether or not something is common knowledge, the best course of action is to cite the source. This discussion refers to common knowledge for the general public.

There is also common knowledge for specialized audience, like for practitioners of the law. In which case, landmark cases which set standards and/or precedents and hold true with the passage of time may be reasonably considered common knowledge. An example would be Cayetano v. Monsod (1991), which has frequently been cited regarding the legal definition of the practice of law. In reference to Scenario 2, the case rulings were from foreign authors which other justices and lawyers may not really be familiar with. Hence, those may not be considered as common knowledge.

Plagiarism and the Academe

How can the academe discourage plagiarism among students and faculty when everyone knows that is it so easy to commit plagiarism and get away with it? “The decision [i.e. dismissal of plagiarism case against an SC associate justice] has created unimaginable problems for Philippine academia, which will from now on have to find a disciplinary response to plagiarism committed by students and researchers on the justification of the majority decision” (Carpio-Morales, as cited in Rodis, 2010, para. 11).

Law practitioners who were consulted on the matter have varied opinions. One lawyer believes that “the academe can only try to discourage plagiarism but we can’t do anything with it, since plagiarism is the highest form of flattery to the one who authored the work”(R. De Las Alas, personal communication, January 29, 2011*). Another lawyer opined that: “Academic institutions should just implement the policy against plagiarism as an independent mandate. Students should not use the incident as a justification not to follow the school policy against plagiarism” (C. Cordero, personal communication, February 1, 2011*. In a limited context, one lawyer proposed “teaching law students the proper way of annotating or citing their sources from jurisprudence” (S. Salazar, personal communication, February 6, 2011*).

To date, experts from the academe invited to enlighten readers on the matter have yet to send their responses. However, this author, who used to be with the academe and has extensive exposure with undergraduate and graduate student research shares the rather pessimistic views of Carpio-Morales (2010). Prior to the actual events similar to Scenario 2, too many students have not taken plagiarism matters seriously. The problem lies not, however, in the absence of attributions to the source, but perhaps from their assumption that merely citing the reference is enough. Writing researches, theses or dissertations involves ethical responsibility and this starts with the practice of giving credit to other researchers who earlier contributed to the reservoir of knowledge, not by copying text word for word, but by paraphrasing.

Faculty members teaching methods of research are the first line of defense against flagrant plagiarism in the tertiary level. But the faculty members handling other subjects also have important roles to play. Familiarization with the in-text and reference citations in whatever style requires practice. Hence, application of these styles of documentation should be required not only in the course methods of research, but in all other courses in the curriculum.

The copy paste mentality among researchers (and even among judges and justices) should be replaced with ethical responsibility. Let us show to the world that we are “educated” in the strongest essence of the word. There is no semblance of being educated in researches and related material devoid of scholarly practice. One can not be proud of a masterpiece completed by slashing parts of Rembrandt, Monet, Picasso, Van Gogh, De Goya and Matisse. Plagiarism is a plague and ethical responsibility is the only cure. The university is the best training ground for ethical responsibility – let us rally towards a truly informed society not by stealing lines and lines of text from the Internet. Let us craft our own masterpiece with our unique strokes, notes and texts.

* Emails and other electronic forms of communication are given parenthetical citations but are not included in the reference list in the APA style of documentation.

References

Bothma, T., Cosijn, E., Fourie, I. & Penzhorn, C. (2008 ). Navigating information literacy: your information society survival toolkit. Capetown: Princeton Education.

Cayetano v. Monsod, 100113 PHL 1 (1991). Retrieved from <http://www.chanrobles.com/scdecisions/ jurisprudence1991/sep1991/gr_100113>_1991.php>

Corriente, F. (2008 ). Dictionary of Arabic and allied loanwords: Spanish, Portuguese, Catalan, Gallician and kindred dialects. Leiden, NDL: Brill.

George, J. J. (2007). Judicial opinion writing handbook (5th ed.). New York: Willian S. Hein & Co.

*Hicks, M. A. (2011). [Clip art licensed from the Clip Art Gallery on DiscoverySchool.com]. Retrieved from http: //school.discoveryeducation.com/clipart/clip/judge.html

Rodis, R. (2010). License to plagiarize. Retrieved from <http://globalnation.inquirer.net/columns/columns/ view/20101021-298952/License-to-plagiarize>

Smith, W. S. (2009). Plagiarism, the Internet and student learning: improving academic integrity. New York: Routledge.

Stepchyshyn, V. & Nelson, R. S. (2007). Library plagiarism policies. Chicago, IL: American Library Association.

How to cite this article in APA format:

Marquez, E. Z. S. (2011). The "joys" of plagiarism: Caveats against the "copy and paste" mentality - Part 2. Retrieved from <http: //essem.webs.com/apps/blog/show/5970895-the-joys-of-plagiarism-caveats-against-the-copy-and-paste-mentality-part-2>

All articles posted in this Website are my original works. References used (when applicable) are properly acknowledged using the APA style of documentation.