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Journal of Education for Business
ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20
Making Knowledge Delivery Failsafe: Adding Step
Zero in Hypothesis Testing
Xia Pan & Qiang Zhou
To cite this article: Xia Pan & Qiang Zhou (2010) Making Knowledge Delivery Failsafe: Adding Step Zero in Hypothesis Testing, Journal of Education for Business, 85:4, 218-222, DOI: 10.1080/08832320903449451
To link to this article: http://dx.doi.org/10.1080/08832320903449451
Published online: 08 Jul 2010.
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DOI: 10.1080/08832320903449451
Making Knowledge Delivery Failsafe: Adding Step
Zero in Hypothesis Testing
Xia Pan
Macau University of Science and Technology, Taipa, Macau, China
Qiang Zhou
Hong Kong Shue Yan University, North Point, Hong Kong, China
Knowledge of statistical analysis is increasingly important for professionals in modern busi-ness. For example, hypothesis testing is one of the critical topics for quality managers and team workers in Six Sigma training programs. Delivering the knowledge of hypothesis testing effec-tively can be an important step for the incapable learners or trainees to improve their learning process. The authors propose a failsafe measure for this knowledge delivery process by adding a direct statement before the conventional procedures of hypothesis testing. The authors tested the effectiveness of this measure statistically. The results showed that the proposed approach could help learners and trainees to select the correct hypotheses and reach the right conclusion in hypothesis testing of applications’ problems.
Keywords: failsafe measure, hypothesis testing, statistical analysis
Knowledge of statistical analysis is increasingly important for professionals in modern business. For example, hypoth-esis testing is one of the most critical topics for quality man-agers and team workers in Six Sigma training programs. De-livering the knowledge of hypothesis testing can be an issue for people who are new to the topic and do not have a strong learning capability. Mistakes and struggling are not uncom-mon for these individuals at the beginning of the training and learning process. Therefore, it is desirable to have a poka-yoke–like failsafe measure to prevent or reduce mistakes. Stevenson (2007) defined poka-yoke as “safeguards built into a process to reduce the possibility of committing an error” (p. 681). Similar explanations or definitions can also be found in other operations management textbooks, such as Heizer and Render (2008), Chase, Jacobs, and Aquilano (2007), and Krajewski, Ritzman, and Malhorta (2007). In the present article, we propose the addition of one more step, Step 0, before the conventional procedures of hypothesis testing. In the present statistics textbooks popularly used in U.S. busi-ness schools and industrial training programs, the ways of addressing and explaining hypothesis testing are commonly
Correspondence should be addressed to Xia Pan, Macau University of Science and Technology, Avenida Wai Long Road, Taipa, Macau, China. E-mail: panpapers@yahoo.com
not effective enough for learners and trainees to quickly and correctly learn the construction of the null and alternative hypotheses. Especially in liberal arts teaching schools, many learners and trainees do not have strong mathematical foun-dations and are often confused in selecting proper forms of null hypothesis,Ho, and alternative hypothesis,Ha. Perhaps
a procedure that can be easily followed without the require-ment of extensive reasoning is necessary. It is remarkable that because Microsoft Excel add-in software is popularly used in these courses and training programs, and although calcu-lation is not a major difficulty for the learners and trainees anymore, setting up correctHoandHabecomes a prominent
issue. When a learner does not achieve the right conclusion in solving an applications problem on hypothesis testing aided by computer software, very often it is because the form of
HoandHais wrongly constructed.
Anderson, Sweeney, and Williams (2003) addressed the correct way to set upHoandHain their best seller,Modern
Business Statistics, as the following:
In general, a hypothesis test about the value of a population meanµtakes one of the following three forms:
Ho:µ≥µ0 Ho:µ≤µ0 Ho:µ=µ0
Ha:µ < µ0 Ha:µ > µ0 Ha:µ=µ0
ADDING STEP ZERO IN HYPOTHESIS TESTING 219
In many situations, the choice ofHoandHais not obvious and
judgment is necessary to select the proper form. However, as the preceding forms show, the equality part of the expression (either≥,≤, or=) always appears in the null hypothesis. In selecting the proper form of Ho and Ha, keep in mind that the alternative hypothesis is what the test is attempting to establish. Hence, asking whether the user is looking for evidence to supportµ < µ0,µ > µ0, orµ=µ0 will help determineHa(p. 338).
The same approach was adopted in Anderson, Sweeney, and Williams (2004) and Anderson, Sweeney, and Williams (2009). However, even if the previous approach is empha-sized, many learners and trainees still make mistakes in se-lecting the right forms of Ho andHa when they work on
applications problems. Other present textbooks address this issue no more than did Anderson et al. (2003) in the previ-ous quote. They mainly depend on examples to explain the selection ofHo andHa. Unlike the text of Anderson et al.
(2003), some texts do not have sufficient explanations. Consider such a typical problem in practice as, “a manager wants to make sure the production is as fast as usual in that the average time producing a product is less than 2 minutes.” In Lind, Marchal, and Wathen’s (2003) textbook, the summary on selecting hypotheses is the following:
It is important to remember that no matter how the problem is stated, the null hypothesis will always contain the equal sign. The equal sign (=) will never appear in the alternative hy-pothesis. Why? Because the null hypothesis is the statement being tested (p. 286–287).
In addition, Lind, Marchal, and Wathen (2005, 2006, 2008) stated the same on hypothesis selection. Also in Groeb-ner, Shannon, Fry, and Smith’s (2008) textbook, “the null hypothesis is the statement about the population value that will be tested” (p. 376). In this the pitfall appears when an individual reads the previous problem because the direct statement should beµ <2. Similarly, unclear understanding may also occur, according to Levine, Stephan, Krehbiel, and Berenson’s (2008) summary:
1. The null hypothesis represents the status quo or the current believe in a situation. 2. The alternative hypothesis is the opposite of the null hypothesis and represents a research claim or specific inference you would like to prove (p. 329).
A learner who is inexperienced with hypothesis testing may think of µ <2 as a status quo instead of a research claim, although the latter is actually correct. In their ear-lier edition, Levine, Stephan, Krehbiel, and Berenson (2002) wrote this part as the following: “1. The null hypothesis is the hypothesis that is always tested. 2. The alternative hypothesis is set up as the opposite to the null hypothesis and represents the conclusion supported if the null hypothesis is rejected”
(p. 335). The guideline leaves even more ambiguity in how to selectHoandHa.
Similarly, Bowerman and O’Connell (2003, 2007) and Bowerman, O’Connell, and Murphree (2009) addressed the null hypothesis as the statement being tested that represents the status quo and the alternative hypothesis as the research statement. Ambiguity may occur when an individual has a problem, such as, “we want to confirm the proportion of defective parts is no more than 5%,” in which the research statement is actuallyp >5%. In Weiers (2005), the expla-nation is mainly from the null hypothesis angle: “The null hypothesis tends to be a ‘business as usual, nothing out of the ordinary is happening’ statement that practically invites you to challenge its truthfulness” (p. 364). Then what if the main concern is to verify a usual-status statement that less than 30% of people are absent from a routine event? Obviously it is not possible to putp<30% in the null statement, and it is necessary to interpret the usual status as at least 30% of people attend the event. This difficulty also happened in Moore and McCabe’s (2006) study, in which “the null hypothesis is a statement of ‘no effect’ or ‘no difference’” (p. 403). Therefore, all in all, there should be room to improve the effectiveness of delivering this part of knowledge.
A FAILSAFE-MAKING IMPROVEMENT MEASURE
Although trainees eventually learn how to select the proper hypothesis after they do sufficient exercises following the above guidelines, it seems necessary to provide them with a strict, simple rule on the construction of Ho and Ha. In
present textbooks, setting upHo andHais the first step in
the procedures of hypothesis testing. We suggest adding one more step, Step 0, before constructingHo andHa,that is,
addressing the direct statement of the application problem. Specifically, following the rule that “equal sign always ap-pears inHoand it will never appear inHa, and the three signs
<,=, and>must be all included in the pair ofHoandHa,”
we have the following: Step 0: Address the direct statement. Step 1: If the direct statement contains an equal sign, put it asHo; otherwise, put it asHa. The other steps are the same
as in convention.
For example, in the problem, “a manager wants to make sure the production is as fast as usual: the average time pro-ducing a product is less than 2 minutes,” the direct statement is simply µ <2 for the keywords less than. Hence, Ho is
µ≥2 andHais µ <2. And in the problem, “we want to
confirm the proportion of defective parts is no more than 10%,” the direct statement isp≤10%, for the keywordsno more than. Hence,Hoisp≤10%, andHais p>10%.
The direct statement is picked up from the applications problem directly. It is easier for learners to find out the direct statement than to select hypotheses without it. Although it does not look much different from that of the conventional
approach (because in principle they are the same), Step 0 helps to avoid possible mistakes and reduces confusion in setting up Ho andHa. The tip or secret is to look for the
keywords, such as no more than,less than,increased, and
changes, from the applications problems. It is much easier to directly pick up this type of keyword than to think and reason the relations between the quantities in the problems, sometimes in the depth of inferential principles. This releases the burden of learners who are neither strong in nor good at reasoning.
It should be noted that in the previous approach, we require that the three signs<,=, and>must be all included in the pair ofHoandHa. This is what most business statistics
text-books presently require. However, in the history of statistics, there was no such requirement, and not all present textbooks require this, either (e.g., Keller & Warrack, 2003). For exam-ple, a pair of hypotheses can be in the form ofHo:µ=µ0
andHa :µ < µ0. Although the inferential principles are the
same, the approach needs to have “the three signs <,=, and > all included in the pair of Ho and Ha.” This
re-quirement helps to keep inexperienced learners from making mistakes.
EVIDENCE FOR THE EFFECTIVENESS
To test the effectiveness of the addition of Step 0, we con-ducted an empirical study on business statistics courses. The data were collected from classes of a non-Association to Ad-vance Collegiate Schools of Business (AACSB)-accredited U.S. school’s undergraduate course and graduate course in different semesters. The majority of the learners were part-time, nontraditional students. The undergraduate students were between the ages of 25 and 35, with about 65% being women and 70% having daytime jobs. Most of the gradu-ate students were between the ages of 30 and 40, with 45% being women. All the graduate students study in part-time and about 30% of them took some management roles in their jobs. The graduate-level and some undergraduate-level learn-ers were more likely to have chances to someday be involved in an environment of quality implementation in which train-ing on this topic is required. In other words, we think the pool of learners reflects to some extent the general situa-tions in industries, in the learning capability of the trainees in groups like Six Sigma green belts. The textbook for the undergraduate-level courses was kept the same, so the home-work problems were often the same for different classes. The textbook for the graduate-level course was different.
We randomly selected the learners’ homework and exams to collect their scores on applications problems about hy-pothesis testing. We tested the effectiveness of adding Step 0 in two aspects. First was the effectiveness of setting up the correct forms of the hypothesis, and the second was on concluding in the hypothesis testing. Because our focus was not on the other procedures of hypothesis testing, such as
calculation, we reviewed the scoring so that only the parts of performance on hypothesis construction and conclusion were filtered and rescored, and the performance on the intermedi-ate procedure was not scored. The performance on hypothesis construction was rescored using a 5-item Likert-type scale ranging from 1 (totally wrong) to 5 (perfectly correct), and the scores of 2, 3, and 4 were assigned approximately on the basis of the degree of correctness. The performance on con-clusion was rescored on a 3-item Likert-type scale ranging from 0 (wrong conclusions) to 2 (correct conclusions).
In the first part of the study, we compared the perfor-mance of hypothesis construction. The comparisons were made between graduate- and undergraduate-level learners, between higher and lower performance learners, and among a combination of graduate- and undergraduate-level learn-ers. The sample sizes ranged from 8 to 11 participants for each group. Based on the instructor’s subjective judgment on the learners’ general learning capability and performance in the course, samples for higher and lower performance learn-ers were selected. That is, the sampling was random among the higher performance learners and among the lower per-formance groups. The observations for higher perper-formance learners and lower performance learners were not necessarily selected in the samples for graduate- and undergraduate-level learners in the first two tests because of the random sampling. To test the effectiveness of Step 0, we formed the following hypothesis: The performance without Step 0 would be lower than that with Step 0. We took random samples instead of using the complete data records from the small classes be-cause records were not collected on site but handed in after the classes. Hence, because of students’ occasional absence from class, the complete records on take-home exercises can-not guarantee the reflection of in-class learning outcome (i.e., some hand-ins may be the result of self-learning), and we do not have the record showing the correspondence of at-tendance and the hand-ins. On the other hand, because the absence was only a small percentage of the whole, we be-lieve that random sampling would possibly have reduced the effect of this noise.
A goodness-of-fit test for normality showed that the data were not normally distributed. The nonnormality was par-tially due to the way of scoring and the scale. In this, attest was not available because of the nonnormality, and the ordi-naryztest was not available either because the sample sizes were not large enough. We alternatively used the Wilcoxon rank sum test to compare the medians of the two groups in our context. This test was used to replace a two-tailedt
test when the populations being compared are not normal. It consists of combining the two samples, sorting the results, assigning ranks to the sorted values (giving the average rank to any tied observation), and then letting the statistic be the sum of the ranks for the observations in the first sample. If the two populations have the same median, then the sum of the ranks of the first sample and those in the second sample should be close to the same value. Therefore, the hypotheses
ADDING STEP ZERO IN HYPOTHESIS TESTING 221
are lower tailed tests on the medians, like Ho:md=md0
andHa :md < md0.
The results of the first part of the study are the following: For undergraduate-level learners, Step 0 was significantly effective atp<.1. For graduate-level learners, the effect of Step 0 was almost significant atp≤.1. The mixed samples of graduate- and undergraduate-level learners showed sig-nificant effect atp<.05. For higher performance learners, there was no significant difference between the condition when Step 0 was applied and the condition when it was not applied, whereas for lower performance learners the effect was significant. This finding indicated that the addition of Step 0 helped the learners who were not good at reasoning or did not have strong learning ability to perform better in the selection of correct hypotheses. This finding was rea-sonable because the higher performance learners could un-derstand and grasp the conventional way (without Step 0) quickly so that they could select the right hypotheses for ap-plications problems, and whether they used Step 0 did not matter. However, for those who were not good at reasoning, following an inflexible and mechanical way that did not re-quire deliberate thinking might have let them reach the right answer more easily. The mixed samples of graduate- and undergraduate-level learners showed that, in general, Step 0 had a strongly significant effect due to the larger sample sizes.
The second part of our study was the investigation into whether adding Step 0 helped the learners to obtain the final conclusions of the hypothesis-testing problems. In fact, the more important issue in hypothesis testing was to get the right conclusions on the research issues of the applications problems, besides the effectiveness for selecting correct hy-potheses forms. We randomly selected several cases from the with-Step-0 group and the without-Step-0 group and tested whether the group with Step 0 performed better in getting the right conclusions. Instead of using a 5-item Likert-type scale ranging from 1 (totally wrong) to 5 (perfectly correct), we used a 3-item Likert-type scale ranging from 0 (wrong con-clusions) to 2 (correct conclusions). This is because whether a conclusion is correct can be and is preferred to be clearly judged. A score of 1 was assigned only when we inferred that the incorrect conclusion was due to the students’ acci-dental or unexplainable thinking errors. The sample was a combination of graduate- and undergraduate-level learners (N =16). Again, the t test was not available because of the nonnormality, and the Wilcoxon rank sum test was used instead.
The results of the second part of the study indicated that atp≤.1, adding Step 0 yielded a higher median score than did not adding Step 0, although the effect was insignificant at p <.05. In other words, adding the direct statement or argument may have helped the learners and trainees to reach the correct final conclusion to the hypothesis-testing prob-lems. This was reasonable because when the learners picked up the direct statement or argument, they were more aware
of giving answers on the statement or argument later when they finished the problem.
SUMMARY AND DISCUSSION
The previous tests showed the effectiveness of the addition of a direct statement in the procedure of construction hypothe-ses for application problems. The samples were collected from a non-AACSB teaching school at which most learners were nontraditional. Because the test among selected higher performance learners suggests the effect of this addition was insignificant, the proposed Step 0 may be just as effective for the learners whose learning capability is not strong enough. Whether this approach is effective in better schools and pro-grams is a question to be tested. Nevertheless, in some situ-ations, the proposed approach can be helpful and likely can help the learners to solve problems better. Hence, introduc-tion of this approach to others may be worthwhile.
This proposed approach of adding a Step 0 can be also justified by the concept of poka-yoke, which is a well recog-nized principle in production and operation management (see Bandyopadhyay, 1993; Chase et al., 2007; Stewart & Mel-nyk, 2000). Shingo (1985) originated the concept of poka-yoke as part of the Toyota Production System. It is an idea to set up failsafe devices to block inadvertent mistakes, or a method of preventing errors by putting limits on how an operation can be performed to force the correct completion of the operation. This concept has proved to be very effective in improving human performance. The original term of this measure,baka-yoke, which means making the incapable peo-ple become capable, is perhaps more suitable for the issue in the present article. In learning hypothesis testing, one of the areas in which trainees easily make mistakes is the area of setting up the null and alternative hypotheses. Adding Step 0 is a poka-yoke–like device that helps the learners to re-duce the chance of making mistakes. Hence, the proposed approach can be justified by behavioral science.
We should note that there were limitations in the present study. First, the data of grading was based on the instructor’s subjective observation and judgment. Although this is often reasonable and reliable (indeed, according to what is mathe-matically wrong or correct), it is not objective. Whether the proposed approach of direct statement was really useful may depend on further strict and more objective examination and practical applications.
In addition, the approach of adding a direct statement in the procedure focused on the goal of selecting a correct hy-pothesis. However, this focus looks more mechanical and depends less on understanding the inferential principle of hypothesis testing than does the conventional way. Whether this approach has a side effect for understanding the prin-ciple is an important issue and needs to be tested further. Thus, a trade-off of values may exist. For applications pur-pose (which is the goal of most business statistics courses
and the core business courses, e.g., operations management), perhaps it is more important to obtain the correct solution to the problems. For pure education and training purposes, un-derstanding principles may be even more important. Where to draw the line in the trade-off may depend on the types of education and training programs and learners.
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