Week 5 - Assignment: Identify Analysis Tools in Published Research

Journal of Business Research 66 (2013) 1261–1266

Contents lists available at SciVerse ScienceDirect

Journal of Business Research

Is two-tailed testing for directional research hypotheses tests legitimate?☆

Hyun-Chul Cho a,1, Shuzo Abe b,⁎ a Hanyang University, Republic of Korea b Waseda University, Japan

☆ The authors thank Adam Turner at Hanyang Unive the University of Michigan for their helpful comments. ⁎ Corresponding author at: Faculty of Commerce, Wased

Shinjyuku-ku, Tokyo 169-8050, Japan. E-mail addresses: [email protected] (H.-C. Ch

1 Department of Business Administration, Hanyang 1271 Sa-3-dong, Sangrok-gu, Ansan-si, Gyeonggi-do, 42

0148-2963 © 2012 Elsevier Inc. doi:10.1016/j.jbusres.2012.02.023

Open access under CC BY

a b s t r a c t

a r t i c l e i n f o

Article history: Received 1 April 2011 Received in revised form 1 September 2011 Accepted 1 November 2011 Available online 29 February 2012

Keywords: Hypothesis testing One-tailed testing Two-tailed testing Statistical hypothesis Research hypothesis in existential form Research hypothesis in non-existential form

This paper demonstrates that there is currently a widespread misuse of two-tailed testing for directional re- search hypotheses tests. One probable reason for this overuse of two-tailed testing is the seemingly valid be- liefs that two-tailed testing is more conservative and safer than one-tailed testing. However, the authors examine the legitimacy of this notion and find it to be flawed. A second and more fundamental cause of the current problem is the pervasive oversight in making a clear distinction between the research hypothesis and the statistical hypothesis. Based upon the explicated, sound relationship between the research and sta- tistical hypotheses, the authors propose a new scheme of hypothesis classification to facilitate and clarify the proper use of statistical hypothesis testing in empirical research.

© 2012 Elsevier Inc. Open access under CC BY-NC-ND license.

1. Introduction

Standard textbooks on statistics clearly state that non-directional research hypotheses should be tested using two-tailed testing while one-tailed testing is appropriate for testing directional research hy- potheses (e.g., Churchill & Iacobucci, 2002, p. 660; Pfaffenberger & Patterson, 1987, pp. 403–569). However, during the actual conduct of statistical testing, this advice is not often heeded. According to our observation of 492 recent empirical articles that have used struc- tural equation modeling (SEM), regression analysis, and analysis of variance (ANOVA) in five selected marketing research-related jour- nals, the Journal of Marketing, Journal of Marketing Research, Marketing Science, Journal of Consumer Research, and Advances in Consumer Re- search (2001–2005), there were 2703 (N=2703) research hypothe- ses in total. Overall, 90.9% (n=2458) of them are expressed in directional form, but only 9.1% (n=245) of them are described in non-directional form.

However, to test directional research hypotheses, 74.8% (n=368) of the articles used two-tailed testing while only 10.6% (n=52) of the ar- ticles used one-tailed testing, and 14.6% (n=72) of them were non- classifiable. The purposes of this article are (1) to investigate why this practice, which runs counter to standard textbook advice, is happening,

rsity and Richard P. Bagozzi at

a University, 1-6-1 Nishiwaseda,

o), [email protected] (S. Abe). University (ERICA Campus), 5-791, Republic of Korea.

-NC-ND license.

(2) to explicate why it slows down the process of rigorous knowledge building in the fields of marketing and business, and (3) to propose a new scheme of hypothesis classification to eliminate such unnoticed confusion.

There are three probable reasons for this widespread overuse of two-tailed testing for directional research hypotheses tests. One rea- son is technical in nature; quite often, the currently available software programs of standard statistical tools, such as EQS and AMOS in SEM and regression analysis in SPSS, only provide two-tailed p values with regard to the t tests on the free parameters to be tested. When ANOVA is used in experimental research, the significance level on the upper tail in the F-table looks like one-tailed testing, but what it actually provides is “right-sided” two-tailed testing (Kaiser, 1960). It is then understandable that busy researchers who may be unaware of these facts only report the p values provided by their statistical software without considering the difference of p values between one-tailed and two-tailed testing.

The second reason is that some marketing researchers may think that when using two-tailed testing, they can be more rigorous or con- servative in their empirical research. This conception is thought to be influenced by arguments for substituting two-tailed testing for one- tailed testing in other fields of social sciences, mainly in psychology (e.g., Braver, 1975; Howell, 2007, pp. 98–100; Kimmel, 1957).

The third reason is that a number of researchers have not paid enough attention to making a clear distinction and a logical linkage be- tween the research hypothesis (RH) (i.e., RH expressed by a verbal statement about some testable relationship between concepts) and its statistical hypothesis (i.e., H0 and H1 expressed by a pair of complemen- tary parameters). They may not be aware of the difference between the two expressive modes or aware of the logical flow in which the research

1262 H.-C. Cho, S. Abe / Journal of Business Research 66 (2013) 1261–1266

hypothesis should be translated into the statistical hypothesis. A convenience-oriented mixing of the research and statistical hypotheses may be a cause of the overuse of two-tailed testing even in situations where the use of two-tailed testing is inappropriate.

The first reason described above is directly accountable for the current overuse of two-tailed testing. However, it rests on assumptions that favor two-tailed testing, which we find problematic. Therefore, it is necessary to examine if the arguments in support of two-tailed testing are valid. The authors believe, however, that the fundamental cause of the current problems lies in the third category: oversight of the proper sequence of hypothesis formation. As long as researchers lack clarity and rigor in defining the logical relationships between the research hy- pothesis and the statistical hypothesis, the current practice will prevail. Based upon careful examination of these points, this paper proposes new definitions of hypothesis to prevent these misconceptions that weaken and mislead scientific methods in empirical research.

2. Examinations of reasons in favor of two-tailed testing

According to the proponents of two-tailed testing, two major reasons support the preference for two-tailed to one-tailed testing (for a more detailed discussion, see Braver, 1975; Harris, 1995, pp. 248–251; Howell, 2007, pp. 98–100; Kimmel, 1957; Pillemer, 1991). First, by substituting two-tailed testing for one-tailed testing at a given level of significance α, researchers subsequently come to use a larger magnitude of the critical value and can conduct a more conser- vative, rigorous test. Second, researchers occasionally find cases where the sign of the parameter to be tested turn out to be significant in the opposite direction from the one anticipated. Using two-tailed testing provides researchers with a “safeguard” against this unexpected result.

2.1. Is two-tailed testing a more rigorous test?

With regard to the first cause mentioned above, two-tailed testing does provide a more conservative, rigid test at a given α level. However, researchers need to recognize that substituting two-tailed testing for one-tailed testing leads to a lack of logical consistency and an inaccurate or mistaken empirical conclusion at a given level of significance α. It is worth noting that statistical testing is just one part of empirical testing for acquiring scientific knowledge. Research hypotheses are usually derived from a “theoretical framework or model” (e.g., Chandran & Morwitz, 2005; Selnes & Sallis, 2003) or from a “conceptual background or model” (e.g., Slotegraaf & Inman, 2004; Smeesters & Mandel, 2006). The directionality or non-directionality of the research hy- pothesis is usually determined by such theoretical grounds. In turn, the directionality/non-directionality of each research hypothesis determines the directionality/non-directionality of its alternative hypothesis.

For example, if a research hypothesis presumes a positive relation- ship between two constructs, then right-tailed testing is appropriate; however, if the relationship is a negative one, then left-tailed testing is undertaken. Because two-tailed testing, by its very nature, does not reflect the directionality of the research hypothesis, it is apparent that it loses the exact logical connection between the directional re- search hypothesis and its statistical hypothesis. Here, it must be em- phasized that the whole process of empirical theory testing must be done logically and consistently as follows: (1) the deduction of the re- search hypothesis from the theory, (2) the exact translation of the re- search hypothesis into its statistical hypothesis, (3) conducting the test of the statistical hypothesis by sample data, (4) supporting (or not supporting) the research hypothesis, and (5) finally, supporting (or not supporting) the theory. Thus, preserving statistical conserva- tiveness at the expense of logical exactness is not a well-conceived approach. In other words, researchers need to use an approach that is both rigorous and logically consistent. If one wants to achieve a more rigorous test result when testing a directional hypothesis,

then it is sufficient to use a more rigid level of significance within one-tailed testing rather than resorting to inaccurate two-tailed test- ing. In this case, one can achieve both objectives simultaneously. In this sense, because one-tailed testing is more liberal than two-tailed testing at a given level of significance, if one wants to maintain the same rigorousness between them in t- or F-testing, then it is enough to halve both the two-tailed p value and the relevant two-tailed α in the “pbα criterion” (e.g., “p=0.09: pb0.10” for inexact two-tailed testing, however, “p=0.045: pb0.05” for exact one-tailed testing). In particular, we need to recall the technical factor that all the calcu- lated p values in F tests are always two-tailed p values (Kaiser, 1960) even though they are located on the upper tales in the F distributions. Therefore, for directional decisions in F tests using planned contrasts, the two-tailed p values should be halved. This technical factor may appear to be a trivial matter; however, when one scrutinizes the true impact it may bring about in the current and future research in marketing and business, its meaning is more than significant. If re- searchers do not pay enough attention to the exactness in making their judgments with regard to their empirical testing results, it would lead to inaccurate or mistaken empirical conclusions in each individual study, and in the long run, it would have cumulative, im- measurable, negative effects on knowledge building.

Here, it is important to note that the authors of the present study are not advocating looser criteria with one-tailed testing; what is needed is to grasp the exact statistics in interpreting statistical testing results. Being inexact under the name of being conservative is not rec- ommendable. In that sense, the authors think that merely reporting testing results such as “It was found to be statistically significant at the 0.05 level of significance (i.e., pb0.05).” is not good enough. Re- searchers need to report the exact p values, confidence intervals (if necessary), and effect sizes, such as correlation coefficients and the mean differences to facilitate knowledge accumulation in their field (Board of Scientific Affairs, 1996). In the field of psychology, a con- tinuing controversy (Harlow, Mulaik, & Steiger, 1997; Nickerson, 2000) has been revolving around the limitations of null hypothesis significance testing.

2.2. Can two-tailed testing be a safeguard against an unexpected result?

Pertaining to the second concern, at first glance there appears to be some value in finding out the significance in the opposite direction with two-tailed testing. For some proponents of two-tailed testing (e.g., Burke, 1953), this seems to be the single most important reason to support two-tailed testing, even if it creates a logically decoupled state between the directional research hypothesis and its statistical hypothesis. In this case, however, the role of statistical testing is sim- ple and clear: it is to provide supportive or non-supportive evidence to the directional research hypothesis (e.g., RH1: … has a positive in- fluence on…) and its underlying theory. The research hypothesis RH1 is supported when the calculated value of the parameter is posi- tive and statistically significant by right-tailed testing. Otherwise, even in the case where the test result is significant in the opposite di- rection, RH1 is not supported (e.g., Piamphongsant & Mandhachitara, 2008; Shukla, 2011; Srite, Galvin, Ahuja, & Karahanna, 2007). This re- sult is because the researchers failed to acquire supporting evidence for the RH1 and its underlying theory. The latter corresponds to cases where the calculated value of the parameter is positive but not significant, or the calculated value is negative regardless of its sig- nificance. Therefore, to empirically negate the directional research hypothesis RH1, it is sufficient to find out whether the calculated value is insignificant in the hypothesized direction. This process can be exemplified in the following action-related example. A firm is con- templating the test of a new product X, which is expected to outsell the existing product Y. If the market test data indicate that the perfor- mance of X is not significantly better than that of Y, then the new product X should not be introduced. Checking if the performance of

1263H.-C. Cho, S. Abe / Journal of Business Research 66 (2013) 1261–1266

X is significantly worse than that of Y is unnecessary and does not bring about any subsequent change in the course of action (Kimmel, 1957, criterion 2).

Two other reasons presented by the proponents of two-tailed testing are that finding such unexpected results may benefit the development of theories in the field (Burke, 1953) and that in social sciences, it is rare to find a well-formulated theory to deduce research hypotheses that accompany stable predictions (Burke, 1953; Pillemer, 1991). The authors cannot completely deny the points in this line of argument, but it also contains weaknesses. Although it is very important to thoroughly investigate the true cause of an unanticipated opposite result, such as possible research-design or theory deficiency, it is worth noting that it should be regarded as a matter to be considered within the discussion section of an empirical research paper. Finding an unexpected result and using it for the development of a newly revised theory belongs to the context of discovery. It should be handled separately from the context of justification, which is theory testing. As far as the statistical test of the directional research hypothesis is con- cerned, it should be conducted in the most logical and systematic way possible. Bringing the exploratory research purpose into the hypothesis testing process and making it a necessary routine procedure should be avoided. In this case, researchers should apply a fundamental principle of contemporary scientific philosophy; that is, researchers should not mix up the context of justification with the context of discovery (Hunt, 1991, pp. 22–26).

For the present stage of theory development in the fields of market- ing and business, it is necessary to admit that we have not yet reached the stage of having a core of well-established theories. However, this awareness does not mean that marketing and business researchers should become less theory-oriented. Although the theories we are testing may not be well-established ones, we should deduce research hypotheses as rigidly as possible and follow the most logical steps in testing them. Empirical tests conducted under the light of “theory” (e.g., Anderson, 1983; Hunt, 1991, p. 168), rather than through reasons of convenience, will contribute better to the sound development of scientific knowledge. One cannot overemphasize the vital role of the research hypothesis as well as its underlying theory, however naïve the stage of the theory may be, in conducting statistical testing. It is the underlying “naïve” theory of the research hypothesis that provides the logical reason why construct A positively or negatively influences construct B. The “naïve” theory provides us with the starting point for the future development of better theories. At this point, some researchers (e.g., Burke, 1953) may argue that one-tailed testing should be applied only when the situation accompanies absolute reasons to believe a particular result. However, this notion is also untenable because a research hypothesis is inferential in its very nature. The true purpose of statistical testing is to test the statistical validity of that inference.

The impact of properly using one-tailed testing would be tremen- dous. Researchers could avoid making inaccurate or mistaken empirical conclusions at a given level of significance α (e.g., “p=0.08: p>0.05” for inexact two-tailed testing, however, “p=0.04: pb0.05” for exact one-tailed testing). With a given sample size, the result of one-tailed testing would provide more accurate information whether a directional research hypothesis is supported or not.

3. The confusion between the research and statistical hypotheses

3.1. Prevailing confusion

The previous section has shown that the reasons for supporting two-tailed testing for directional research hypotheses tests are not as legitimate as they first appeared. Additionally, the previous argu- ments have made it clear that, because the directional statistical hy- pothesis should be derived from the directional research hypothesis, using two-tailed testing to test this directional research hypothesis

is not in accord with this basic rule. The authors believe that the cur- rent overuse of two-tailed testing stems from the favorable views on two-tailed testing and from researchers’ blindness because they are unaware that they are breaking this basic rule. Let us now see how this rule, which dictates the flow from the research hypothesis to the statistical hypothesis, is often violated in the fields of marketing, business, and other social sciences.

The following type of hypothesis expression appears frequently in a large amount of the methodology literature.

H1. Males self-disclose more than females.

H0. There is no difference between males and females with respect to self-disclosure (italics added) (Frey, Botan, & Kreps, 2000, p. 326).

It is clear that this example contains definitional confusion be- tween the expressive mode of the research hypothesis (RH expressed by a verbal statement about some testable relationship between con- cepts) and that of the statistical hypothesis (H0 and H1 expressed by a pair of complementary parameters). There is neither a clear distinc- tion nor an exact linkage between the research hypothesis, RH, and its statistical hypothesis, H0 and H1. “RH per se” is identified with the alternative hypothesis H1, and the “opposite of RH” is identified with the null hypothesis H0. In addition, the verbally expressed “H0: …no difference…” and the verbally expressed “H1: …more than…” are not complementary to each other. Under such confusion, (1) sta- tistical testing would be misunderstood as a direct test between “H0: the opposite of RH” and “H1: RH per se,” (2) because the verbally expressed H0 involves only a “no difference (i.e., =) sign,” it is likely to mislead us into believing that two-tailed testing is applicable, and (3) the verbally expressed null hypothesis has been frequently mis- understood as the “object of falsification” (e.g., Ledford, 2001; Miller & Fox, 2001) or as the “object of strong inference” (e.g., Brinberg, Lynch, & Sawyer, 1992; Ruscio, 1999), although the “straw-person” null hypothesis has no basis in theory. One should remember that “falsification (Popper, 1959)” is Popper's alleged basic nature of scien- tific knowledge and that “strong inference (Platt, 1964)” is a process of pitting competing research hypotheses against each other where each is based on a different theory.

However, if one clearly distinguishes the expressive mode of the research hypothesis from that of the statistical hypothesis, then the exact logical linkage between the research hypothesis (i.e., RH) and its statistical hypothesis (i.e., H0 and H1) can be made as follows:

RH. “Males self-disclose more than females.”

H0. μMale≤μFemale [the negation of the assertion]

H1. μMale>μFemale [the assertion]

Evidently, because the null hypothesis, “H0: μMale ≤μFemale,” includes the “≤” sign, there is no way to apply two-tailed testing to it. It is worth noting that statistical testing is the test between “H0: μMale ≤μFemale” and “H1: μMale >μFemale”, and this test result should be used as indirect evidence for supporting or not-supporting RH; that is, “rejecting/not-rejecting the ‘straw-person’ H0” leads to “accepting/not-accepting the ‘substantive’ H1” and this result, in turn, leads to “supporting/not-supporting RH,” respectively (e.g., Kerlinger & Lee, 2000, p. 279).

Clarifying the difference between the research and statistical hy- potheses is important; it prevents us from classificatory confusion caused by the oversight of the coexistence of two different types of research hypotheses. Almost all the research hypotheses derived from theories can be classified into two types: the research hypothe- sis in existential form (RHEF) and the research hypothesis in non- existential form (RHNF). The former RHEF, which is most common, involves verbal assertions about the existence of some testable

1264 H.-C. Cho, S. Abe / Journal of Business Research 66 (2013) 1261–1266

relationships between concepts, such as “has a negative influence on” (e.g., Bagozzi, 1980), “is positively related to” (e.g., Loken & Ward, 1990), or “is greater than” (e.g., Biehal & Sheinin, 2007). However, the latter RHNF is occasionally set up as a research hypothesis. It usu- ally includes verbal assertions about the nonexistence of some testable relationship between concepts, such as “has no influence on” (e.g., Bagozzi, 1980), “is unrelated to” (e.g., Loken & Ward, 1990), or “there is no difference” (e.g., Biehal & Sheinin, 2007). Unfortunately, RHEF has been frequently misunderstood as the alternative hypothe- sis and RHNF as the null hypothesis (e.g., Balachander & Ghose, 2003).

In translating RHEF or RHNF into its own statistical hypothesis, it is important to note the fundamental difference, as in the following example:

RH1. “Regret has no influence on complaint intentions, whereas satisfaction has a negative influence on complaint intentions” (Tsiros & Mittal, 2000, H6; this is a good example involving both RHEF and RHNF).

RH1a. “Regret has no influence on complaint intentions” (italics added). [RHNF]

H0. γ11=0 (the assertion)

H1. γ11≠0 (the negation of the assertion)

RH1b. “Satisfaction has a negative influence on complaint intentions” (italics added). [RHEF]

H0. γ21≥0 (the negation of the assertion)

H1. γ21b0 (the assertion)

When translating each of the two types of the research hypothesis into its statistical hypothesis, as statisticians commonly note, the null hypothesis H0 and the alternative hypothesis H1 should be mutually exclusive and collectively exhaustive (e.g., Casella & Berger, 1990, p. 345); an equality sign (i.e., =, ≤, or ≥) should always appear in the null hypothesis, H0 (e.g., Harnett & Soni, 1991, p. 331). The above ex- ample clearly shows a distinction and a logical linkage between the expressive mode of the research hypothesis (i.e., RHEF and RHNF) and that of the statistical hypothesis (i.e., each pair of H0 and H1). Note that in the case of translating RHEF, such as RH1b, into its statis- tical hypothesis, researchers should place the assertion in the alterna- tive hypothesis H1; however, when translating RHNF, such as RH1a, into its statistical hypothesis, the assertion should be put in the null hypothesis H0, rather than in the alternative hypothesis H1. Note that this logic of proof to accept H0 in RHNF is weak. As Wonnacott and Wonnacott (1984, p. 277) note, “Statistical testing does not pro- vide a formal criterion to accept the null hypothesis.” If the test result that the null hypothesis H0 of RHNF is accepted, it does not guarantee that H0 is true. All one can do is adopt a smaller confidence interval so that it includes the value assumed by H0 (frequently 0, but not always 0), then one can have stronger evidence for the null hypothesis (Frick, 1995; Nickerson, 2000). Researchers need to prepare a larger sample size to achieve a small confidence interval.

The above examinations of the current definitional and classificatory confusion with regard to the research and statistical hypotheses have shown that without a clear distinction between the research hypothesis and the statistical hypothesis, the basic rule of empirical testing where the two expressive modes of the research hypothesis (i.e., RHEF and RHNF) determine the form of the statistical hypothesis is easily violated. As a result, a less rigorous form of statistical testing, such as adopting two-tailed testing for a directional research hypothesis test, has become a common practice. The current confusion involves other forms of mis- understanding as well, such as starting from the use of logic of disproof (i.e., proof by contradiction) as the basis for setting up the null and alter- native hypotheses (e.g., Anderson, Sweeney, & Williams, 1999, p. 330)

and then moving back to specifying the research hypothesis and, as a consequence, overlooking a certain category of the research hypothesis (i.e., RHNF), which should be handled with additional carefulness. Un- less researchers make a clear distinction between the research and sta- tistical hypotheses and observe the correct relationships between them, less rigorous use of statistical testing is hard to eliminate. Thus, while it is less convenient and looks somewhat redundant, it is important to fol- low the orderly sequence of the empirical testing procedure even when researchers use statistical null hypothesis testing methods.

It may be thought that making a clear distinction between the re- search hypothesis and the statistical hypothesis is simple enough. Al- though it may look simple at a glance, it is not that easy, because the problem lies between two different levels of methodology. Generally speaking, there are three levels of methodology. The uppermost level is that of scientific philosophy, in which the basic questions addressed are “How can we draw a demarcation line between scientific knowl- edge and all the other types of knowledge?” or “How can we assure that scientific knowledge is making an advance?” The second level of methodology is concerned with the development and test of a spe- cific theory. It is related to logical and empirical validity of a theory. Finally, the third level of methodology is more technical in nature. Generally, it is related to how to conduct statistical testing. All three levels are important, but no less important are the interrelationships between and among the three levels. This article mainly discusses the relationships between the second and third levels of methodology and asserts that the second level of methodological decision dictates the lower level consideration. Some researchers who pay attention to the third level may miss the hierarchical relationships between and among the three levels of the methodology.

3.2. Two legitimate situations for two-tailed testing

This paper does not propose the elimination of two-tailed testing in the context of theory testing because there are two different types of situations where two-tailed testing is appropriate. First, when researchers do not have sufficient level of knowledge that pro- vides for the directionality of the research hypotheses, the research hypotheses may take the form of non-directional ones and the subse- quent use of two-tailed testing is appropriate (e.g., Gravetter & Wallnau, 2007, p. 253). Second, two-tailed testing should be used when researchers set up non-directional research hypotheses (i.e., RHNF) pertaining to the nonexistence of some testable relationship between concepts, such as “has no influence on” (e.g., Bagozzi, 1980), “has no relation to” (e.g., Loken & Ward, 1990), or “is no differ- ence” (e.g., Biehal & Sheinin, 2007).

3.3. Four new definitions regarding research and statistical hypotheses

Now, based upon a clear distinction and upon an exact connection between the expressive mode of the research hypothesis (i.e., RHEF and RHNF) and that of the statistical hypothesis (i.e., H0 and H1), the authors propose the following four new definitions with regard to the research hypothesis and the statistical hypothesis. These four definitions are meant to remove the prevailing confusion in defini- tional and classificatory hypothesis use associated with the process of empirical hypothesis testing in marketing and business research. They provide marketing and business researchers not only with a new scheme of hypothesis classification but also with clear guidelines for the orderly setting up of the statistical hypothesis, H0 and H1.

Definition 1. The research hypothesis derived from theory and/or extended observation is a verbal statement about the assertion of some testable relationship between two or more concepts.

Definition 2. The statistical hypothesis is the assertion and its negation that are expressed by a pair of mutually exclusive and collectively

1265H.-C. Cho, S. Abe / Journal of Business Research 66 (2013) 1261–1266

exhaustive parameters or statistical terms about some characteristic of a population distribution. Between the assertion and its negation described by a pair of complementary parameters or statistical terms, the part involving an equality sign (i.e., =, ≤, or ≥) always appears in the null hypothesis H0, and the other part not involving an equality sign always appears in the alternative hypothesis H1.

Definition 3. The expressive mode of the research hypothesis con- sists of the research hypothesis in existential form (i.e., RHEF) and the research hypothesis in non-existential form (i.e., RHNF). RHEF is a research hypothesis that involves the assertion about the existence of some testable relationship between concepts, such as “has a posi- tive effect on,” “has a negative relation to,” or “there is a difference.” On the other hand, RHNF is a research hypothesis that includes the assertion about the nonexistence of some testable relationship be- tween concepts, such as “has no effect on,” “has no relation to,” or “there is no difference.” In rare cases, if the assertion has two forms together, such as “has no influence or negative influence on,” then it is classified as RHNF.

Definition 4. The research hypothesis should be translated into the statistical hypothesis. In the case of translating RHEF into its statistical hypothesis H0 and H1, researchers should put the negation of the as- sertion expressed by the parameter(s) or statistical terms in the null hypothesis H0, and the assertion described by the parameter(s) or statistical terms in the alternative hypothesis H1. However, when translating RHNF into its statistical hypothesis H0 and H1, researchers should put the assertion expressed by the parameter(s) or statistical terms in the null hypothesis H0 and the negation of the assertion de- scribed by the parameter(s) or statistical terms in the alternative hy- pothesis H1.

4. Conclusions

According to the authors’ observation of 2703 research hypotheses in JM, JMR, MS, JCR, and ACR (2001–2005), 90.9% (n=2458) are judged to be directional research hypotheses. Of the 492 articles that contain the directional research hypotheses, 368 articles (74.8%) use two- tailed testing, 52 articles (10.6%) use one-tailed testing, and the remaining 72 articles (14.6%) were non-classifiable. The authors have identified three categories of reasons that caused this over- whelming use of two-tailed testing for directional research hypothe- ses. One category of reasons is researchers’ oversight of the currently available p values in t- or F tests usually being those for two-tailed testing. For correct directional decisions, we have noted that the two-tailed p values should be halved. Otherwise, researchers are likely to draw inaccurate or mistaken empirical conclusions at a given level of significance α (e.g., “p=0.08: p>0.05” for inexact two-tailed test- ing, however, “p=0.04: pb0.05” for exact one-tailed testing).

The second category of reasons is the notion that two-tailed test- ing is scientifically more conservative and safer. This paper's conclu- sion is that the arguments made by the proponents for two-tailed testing are not legitimate. Although two-tailed testing is more conser- vative in theory, it decouples the link between the directional re- search hypothesis and its statistical hypothesis, possibly leading to doubly inflated p values. The authors have also shown that the argu- ment for finding the significant result in the opposite direction has meaning only in the context of discovery rather than in the context of justification. In the case of testing the research hypothesis and its underlying theory, researchers should not simultaneously address the context of discovery and that of justification. The authors have also shown that no matter how naïve the present stage theories might be, theory-oriented appraisal of the collected data remains important.

The third and most fundamental category of reasons is that there is frequently no clear distinction and no exact linkage between the

research hypothesis and the statistical hypothesis. To prevent such confusion, the authors have proposed to make a clearer distinction and an exact connection between the expressive mode of the re- search hypothesis (i.e., RHEF or RHNF expressed by a verbal state- ment about some testable relationship between concepts) and that of the statistical hypothesis (i.e., H0 and H1 expressed by a pair of complementary parameters). Additionally, this article has shown the two legitimate situations where two-tailed testing is to be used: for every non-directional RHEF, such as “RH2: …has an effect on…”, and for all non-directional RHNF, such as “RH3: … has no relation to….”

Finally, based upon the foregoing arguments, the authors have proposed a new scheme of hypothesis classification called “four new definitions of the research and statistical hypotheses” to more ef- fectively contribute to scientific knowledge development in the fields of marketing and business.

References

Anderson, P. F. (1983, fall). Marketing, scientific progress, and scientific method. Journal of Marketing, 47, 18–31.

Anderson, D. R., Sweeney, D. J., & Williams, T. A. (1999). Statistics for business and economics (7th ed.). Cincinnati, OH: South-Western.

Bagozzi, R. P. (1980, spring). Performance and satisfaction in an industrial sales force: An examination of their antecedents and simultaneity. Journal of Marketing, 44, 65–77.

Balachander, S., & Ghose, S. (2003, Jan.). Reciprocal spillover effects: A strategic benefit of brand extensions. Journal of Marketing, 67, 4–13.

Biehal, G. J., & Sheinin, D. A. (2007, April). The influence of corporate messages on the product portfolio. Journal of Marketing, 71, 12–25.

Board of Scientific Affairs (1996). Task force on statistical inference initial report. American Psychological Association http://www.apa.org/science/leadership/bsa/statistical/ tfsi-initial-report.pdf

Braver, S. L. (1975). On splitting the tails unequally: A new perspective on one- versus two-tailed tests. Educational and Psychological Measurement, 35(2), 283–301.

Brinberg, D., Lynch, J. G., Jr., & Sawyer, A. G. (1992, Sep.). Hypothesized and confounded explanations in theory tests: A Bayesian analysis. Journal of Consumer Research, 19, 139–154.

Burke, C. J. (1953). A brief note on one-tailed tests. Psychological Bulletin, 50(5), 384–387.

Casella, G., & Berger, R. L. (1990). Statistical inference. Pacific Grove, CA: Wadsworth & Brooks/Cole.

Chandran, S., & Morwitz, V. G. (2005, Sep.). Effects of participative pricing on consumers’ cognitions and actions: A goal theoretic perspective. Journal of Consumer Research, 32, 249–259.

Churchill, G. A., Jr., & Iacobucci, D. (2002). Marketing research: Methodological foundations (8th ed.). Fort Worth, TX: Harcourt College Publishers.

Frey, L. R., Botan, C. H., & Kreps, G. L. (2000). Investigating communication: An introduction to research methods (2nd ed.). Needham, Heights, MA: Allyn & Bacon.

Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138. Gravetter, F. J., & Wallnau, L. B. (2007). Statistics for the behavioral sciences (7th ed.).

Belmont, CA: Thomson Wadsworth. Harlow, L. L., Mulaik, S. A., & Steiger, J. H. (1997). What if there were no significance tests?

Mahwah, NJ: Lawrence Erlbaum Associates, Publishing. Harnett, D. L., & Soni, A. K. (1991). Statistical methods for business and economics. Reading,

MA: Addison-Wesley. Harris, M. B. (1995). Basic statistics for behavioral science research. Needham Heights,

MA: Allyn & Bacon. Howell, D. C. (2007). Statistical methods for psychology (6th ed.). Belmont, CA: Thomson

Wadsworth. Hunt, S. D. (1991). Modern marketing theory: Critical issues in the philosophy of marketing

science. Cincinnati, OH: South-Western Publishing Co. Kaiser, H. F. (1960, May). Directional statistical decisions. Psychological Review, 67,

160–167. Kerlinger, F. N., & Lee, H. B. (2000). Foundations of behavioral research (4th ed.). Fort

Worth, TX: Harcourt College Publishers. Kimmel, H. D. (1957). Three criteria for the use of one-tailed tests. Psychological Bulletin,

54(4), 351–353. Ledford, S. K. (2001). The implications of Kumho tire: Applying Daubert analysis to

warning-label testimony in products liability cases. Indiana Law, 76, 465–483. Loken, B., & Ward, J. (1990, Sep.). Alternative approaches to understanding the

determinants of typicality. Journal of Consumer Research, 17, 111–126. Miller, H. T., & Fox, C. J. (2001). The epistemic community. Administration & Society,

32(6), 668–685. Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and

continuing controversy. Psychological Methods, 5(2), 241–301. Pfaffenberger, R. C., & Patterson, J. P. (1987). Statistical methods: For business and

economics (3rd ed.). Homewood, IL: Irwin. Piamphongsant, T., & Mandhachitara, R. (2008). Psychological antecedents of career

women's fashion clothing conformity. Journal of Fashion Marketing and Management, 12(4), 438–455.

1266 H.-C. Cho, S. Abe / Journal of Business Research 66 (2013) 1261–1266

Pillemer, D. B. (1991). One- versus two-tailed hypothesis tests in contemporary educational research. Educational Researcher, 20(9), 13–17.

Platt, J. R. (1964). Strong inference. Science, 146(3642), 347–353. Popper, K. R. (1959). The logic of scientific discovery. New York: Harper and Row

(Original work published 1934 in German). Ruscio, J. (1999). Statistical models and strong inference in social judgment research.

Psycoloquy, 10(27) social bias 17. Selnes, F., & Sallis, J. (2003, July). Promoting relationship learning. Journal of Marketing,

67, 80–95. Shukla, P. (2011). Impact of interpersonal influences, brand origin and brand image

on luxury purchase intentions: Measuring interfunctional interactions and a cross-national comparison. Journal of World Business, 46(2), 242–252.

Slotegraaf, R. J., & Inman, J. J. (2004, Aug.). Longitudinal shifts in the drivers of satisfaction with product quality: The role of attribute resolvability. Journal of Marketing Research, 41, 269–280.

Smeesters, D., & Mandel, N. (2006, March). Positive and negative media image effects on the self. Journal of Consumer Research, 32, 576–582.

Srite, M., Galvin, J. E., Ahuja, M. K., & Karahanna, E. (2007). Effects of individuals’ psychological states on their satisfaction with the GSS process. Information Management, 44, 535–546.

Tsiros, M., & Mittal, V. (2000, March). Regret: A model of its antecedents and consequences in consumer decision. Journal of Consumer Research, 26, 401–417.

Wonnacott, T. H., & Wonnacott, R. J. (1984). Introductory statistics for business and economics (3rd ed.). New York: John Wiley & Sons.