Beyond Fisher
Last Updated: 2017
Microsoft and R. A. Fisher
Due to the dominance of Microsoft Windows and Intel processor in the
computer industry, for most users computing is synonymous to "Wintel."
The same pattern can be found in the field of research methodology.
Today, when most researchers talk about statistical analysis, it is
usually referred to hypothesis testing, which is a fusion of two
schools of thought: Fisher and NeymanPearson (Lehmann, 1993). Between
the two schools, Fisher (1932, 1935) is arguably the dominant one.
The Fisherian legacy is also known as statistical significance testing,
null hypothesis significance testing, hypothesis testing, traditional
inferential statistics, classical procedures, and parametric test.
In the future, Microsoft may announce: "Today I
announce that Microsoft has taken over SAS Institute, IBM SPSS Inc, Stata, SyStat...etc. From now on only hypothesis testing is
available in all statistical software packages. Resistance is futile."


Limitations of the Fisherian approach
Just like that Windows is not suitable for every
application, hypothesis testing has its limitations. There are at least eleven limitations of the Fisherian approach:
 Does not address treatment effectiveness: Statistical
hypothesis testing does not address the issue of treatment
effectiveness. Very often researchers interpret a significant pvalue
as evidence of treatment effectiveness. As a matter of fact, hypothesis
testing does not evaluate how likely the hypothesis is right given the
data P(HD). On the contrary, it assumes that the null hypothesis is
right and examines how likely the data will occur in long run given the
null is true, P(DH) (McClure & Suen, 1994; Cohen, 1994; Loftus,
1996). In order to report the magnitude of the treatment effectiveness, the researcher must report the effect size.
 Easy to reject the null hypothesis:
By definition,
a null hypothesis denotes no difference (zero effect). Loftus (1996)
mocked that "rejecting a typical null hypothesis is like rejecting the
proposition that the moon is made of green cheese. The appropriate
response would be 'Well, yes, okay ... but so what?" Indeed it is very
common for experimentors to compare a control group (do nothing) to a
treatment group. The winner is the treatment group, of course. For more
information, please read the section "maximize variance control" of the
webpage Experimental design as variance control.
 Mismatch of null and alternate hypotheses:
Statistical hypothesis testing is a fusion of two schools: Fisher and
Neyman/Pearson. In the former the null hypothesis is proposed and the
alpha level is associated with the null. In the latter the alternate
hypothesis is proposed; power and beta are associated with the
alternate. very few people notice that when Neyman and Pearson developed their methodology, they left out the p value.
 Problem in reproducibility: The
results yielded from hypothesis testing vary from study to study and
scientists are concerned with the replication problems. A common
misinterpretation of significance is that the p value tells you how
"right" the conclusion is. If the p value is .01, then there is only 1%
chance that the conclusion is wrong. Actually, a p value of .01
corresponds to a Type I error rate (false alarm) of 11%; a p value of
.05 is equivalent to an error rate of 29%. Given the fact that the
result of one particular study could be wrong, it is not surprising to
see that researchers are unable to replicate the original result
(Nuzzo, 2014).
 Provide no information about the population: The
finding resulted from hypothesis testing provides no information about
the form of the underlying pattern of the population. Very often
researchers conduct hypothesis testing either with the assumption of a
particular population distribution (normality) or without asking this
question at all. Indeed, in the parametric test framework the
population, to which inferences are made, is infinite and unknown.
Under this direction, what researchers did is to make inferences from
the population to the sample, but not the sample to the population.
This issue has been discussed in the article regarding misconceived relationships among sample, sampling distributions and population.
 Probability as a relative frequency in long run:
Hypothesis testing is based upon probability, which is defined as a
relative frequency in long run. However, it is problematic to apply
this frequentist view of probability into a single event or a new event
(Carver, 1978). For example, what is the probability that the universe
was formed by a big bang? What is the probability that a newly invented
superJava enabled Webbased instruction is effective in teaching
computer sciences?
 Theoretical distribution: Decisions in hypothesis
testing relies on theoretical sampling distributions, which is not
always empirically verified. This issue has been discussed in the
article
regarding mathematical
reality.
Basically, in hypothesis testing the test statistics is compared
against a “known” distribution. However, this weakly substantiated
assumption (knowing the underlying distribution) results in a false
sense of certainty. In contrast to Fisher, Neyman, and Pearson, the
founder of exploratory data analysis John Tukey (1986) questioned our
reliance on supposedly known distributions; he asserted that progress
of statistics can only be made when we move away from certainty, and we
need to give up the idea that a single body of data can correspond a
unique appropriate analysis
 Point estimate: Unlike confidence interval
(CI) that indicates a possible range of the population parameter,
hypothesis testing yields a point estimate. It is based on the
conviction that in the population there is one and only one fixed
constant that can represent the true parameter. However, this belief is
challenged by Bayesians because in reality the population body is ever
changing and thus there is no such thing as a fixed parameter.
 Yield a dichotomous answer based on an arbitrary cutoff:
The conclusion yielded from a significance testing is dichotomous:
either the effect is significant or not. It misleads information
consumers and even researchers to see the world as black or white
(Cumming, 2013). Cumming (2013) suspected that this "fatallyflawed"
approach is widely embraced because the simplified decisionmaking
process has a "seductive appealthe apparent but illusory certainty"
(p.5).
 Arbitrary cutoff: The dichotomous decision
is based on the conventional alpha levels, such as .05. However, there
is nothing "magical" about .05. Actually, using a fixed cut off, as
commonly practiced by many researchers, is going against Fisher's
advice. Fisher (1956) stated, "No scientific worker has a fixed level
of significance from year to year, and in all circumstances, he rejects
hypothesis; he rather gives his mind to each particular case in the
light of his evidence of ideas" (p.41). Rosnow and Rosenthal (1989)
stated his objection against blindly using .05 in a humorous way: "God
loves the .06 nearly as much as .05" (p.1277). Unfortunately, today
hypothesis testing has become mechanical rather than a matter of
judgment.
 Unknown error and circularity: Hypothesis
testing
is said to balance the Type I and Type II error rates, but in reality
it is untrue. The test starts from the premise that the null hypothesis
is true and thus the output is the p value indicating the probability
of observing the statistics given the null is true. If the null is
really true, at most the Type I error rate is 5%. However, the Type II
error rate would be as high as 95%! Schmidt and Hunter (2014)
criticized that there is a fundamental circularity to hypothesis
testing. If the researcher does not know whether the null is true or
not, then he cannot tell whether the error is tied to Type I or Type
II. But if he knows that the null is true, then there is no need to
perform the test. Schmidt and Hunter suggested that there is only one
way to rectify this situation: give up hypothesis testing and report
the confidence interval.
Alternatives
Methodologists have been questioning overdependence on and
misuse of the Fisherian statistical approach for many years. In the summer of 1993, the
Journal of Experimental Education devoted the entire issue to the theme
"Statistical significance testing in contemporary practice: Some
proposed alternatives." Several options such as effect size,
crossvalidation and resampling were proposed (e.g. Thompson, 1993;
Synder & Lawson, 1993). In 1996 a task force formed by the Board of
Scientific Affairs of American Psychological Association (APA) also
suggested that researchers should apply a wide variety of statistical
techniques, such as Exploratory Data Analysis and Bayesian inference.
In response to frequent occurrences of inappropriate use of hypothesis
testing, in 1999 Dr. Leland Wilkinson led the Task Force on Statistical
Inference formed by the same board of APA to address the controversy.
In conclusion, the Task Force did not recommend abandon hypothesis
testing, but suggested using it with caution; also, researchers were
urged to use more options, such as confidence interval and effect size.
After the release of the APA Task Force report, use of effectsize in American SpeechLanguageHearing Association journals
from 19992003 was reviewed (Meline & Wang, 2004). It was found
that reporting of effect size in quantitative studies increased from 5
reports in 1990 to 1994 to 120 reports in 1999 to 2003. However, effect
size was reported less than 30% of the time when inferential statistics
were used, and only half of those reports included an interpretation of
effect size.
Narrowness of graduate programs
Many researchers tend to follow the convention rather than
experimenting with alternate strategies. This conservative behavior may
be owing to the lack of comprehensive training in graduate schools.
Aiken, West, Sechrest, and Reno (1990) published an article surveying
the curriculum of quantitative methods in graduate psychology programs.
It was found that new and important research methodologies such as
structural equation modeling, confirmatory factor analysis, exploratory
data analysis, and metaanalysis were not taught in the majority of
those programs.
Behrens (1996) held a similar view. To rectify the situation that graduate
programs overly stress hypothesis testing, Behrens suggested that graduate
programs should integrate instruction in confirmatory statistics with
alternative data analytic methods such as metaanalysis, Bayesian analysis,
interval estimation approaches, and hybrid combinations.
Schield (1998) also criticized that traditional statistical training
"covers only half the topic needed for statistical literacy. In
addition to descriptive statistics and inferential statistics,
statistical literacy should include Bayesian statistics and most of
allevidential statistics" (p.2).
Aikem, West, and Millsap's (2008) study, which is a replication and extension of
Aiken et al.'s (1990) study, examined whether innovations in quantitative
methodology have diffused into the training of PhDs in psychology. On one hand,
exciting advancements had happened in the domains of statistical analysis (e.g.
multilevel modeling), measurement (e.g. item response theory), and research
design (e.g. propensity scores in observational studies), but on the other hand,
many psychology programs still maintain the traditional curriculum. For example,
slightly fewer than half of all departments responded to the survey offered a
full course on structural equation modeling. Coverage of specialized statistical
methods, such as multilevel modeling, was even sparser. In all Ph.D. programs in
psychology, the measurement requirement occupies a median of only 4.5 weeks.
Even worst is that the research design curriculum has largely stagnated.
Uphill battle
Indeed, the crisis lies on not only the lack of knowledge
of alternate approaches, but also the poverty of conventional research
skills. Inappropriate use of statistics among researchers across
different disciplines were welldocumented (Caever, 1978; Gore et al.,
1977; Gibbons & Freund, 1986; Glass, Peckham, & Sanders,1980;
Maxwell & Delaney, 1990; Morrison & Henkel, 1970; Pedhazur,
& Schmelkin, 1991; Thompson, 1994; Wainer, 1989). The purpose of
alternate methodologies is to compensate the limitations of the
traditional approach. However, when researchers do not understand the
assumptions and limitations of Fisherian school, how could they look
for other proper tools to remediate the problem?
Even if alternate methods were widely adopted, it is likely that the
implementation of alternate methods would be as careless as in the
conventional approach. There is no guarantee that the quality of
research would be improved by introducing new methods alone. If the
attitude toward research methodology does not improve, I am afraid that
papers like "Common methodology mistakes in exploratory data analysis,"
"A critical assessment to misinterpretation of resampling," and "The
case against Bayesian inference" would be as popular as papers against
statistical testing today.
Many people are aware of the narrowness of statistical analysis and
attempt to counter against it. But it is an uphill battle. For
example, at Michigan State University once two professors reformed the
graduate statistics courses by introducing alternate statistics such as
confidence intervals and effect size. The reform, however, was
protested by other faculty members because they worried that graduate
students who received this unorthodox training might not be able to get
their research published (Schmidt, 1996). The norm set by referred
journals is one of many reasons why many researchers, faculty and
graduate students blindly follow statistical testing. Similar
objections are also found in other institutions: "We must continue to
teach hypothesis testing because 90% of the textbooks and journals are
still using it." I heard many
other reasons:
Tool mastering
"Educational and psychological researchers are not mathematics majors.
We don't have to know the detail of statistics." Medical students are
not chemistry and biology majors. Do they need to learn the deep
knowledge of chemistry and biology? Chemistry and biology for
physicians and statistics for social scientists are the means rather
than the end. But without the proper tool, it is impossible for them to
do a good job. The requirement of "tool mastering " is very common in
humanities. For instance, once a Sinologist told me that to study the
history of Yuan dynasty of China, one must achieve a high proficiency
in the Chinese, Mongolian, and Persian languages in order to read first
hand documents. A philosopher specializing in Buddhism also needs to
learn the Chinese, Japanese, Hindu, as well as several other languages
before conducting any meaningful research. Unfortunately, the concept
of "tool mastering" is absent from the mentality of many social
scientists.
Driving a car and building a car: Applications and research
This argument is very similar to the preceding one: "Psychologists and
educators should focus on the subject matter of their own domain rather
than spending time in irrelevant matters. We are concerned with
applications rather than theoretical abstraction." What does it take to
drive a car? Very simple. Just a few days of training is sufficient to
make a qualified driver. But what does it take to build a car? Several
years of training in mechanical and electrical engineering is the
minimum. When an automobile engineer tells consumers that the vehicle
designed by him is safe at all speeds, he is responsible for other
people's lives! By the same token, when psychological researchers
instruct practitioners and policymakers to follow his theory, he is
accountable, too. He must be sure that the application is firmly
founded on a sound theoretical framework. When psychologists claim that
children being raised in nontraditional families do not have a higher
probability to develop maladjusted behaviors; legalizing drugs does not
lead to long term harmful effects to society...etc., I wonder whether
these conclusions are resulted from appropriate implementation of
research methodologies.
By synthesizing the views of Kerlinger and Pedhazur, Daniel (1997)
debunked the myth of insignificance of statistical knowledge in
research:
Because all statistical methods have certain inherent strengths and
limitations and because each method implies certain assumptions about
the data being analyzed, the use of these methods to some degree
influences both the nature and selection of research problems
(Kerlinger, 1969, 1986; Kerlinger & Pedhazur, 1973). Therefore, the
claim that statistical knowledge is unnecessary to good research
practice is unfounded; in fact, Kerlinger noted that "it is almost
impossible to do outstanding research, though one can do acceptable
research, without being something of a methodologist" (p.622).
Kerlinger and Pedhazur (1973) went so far as to say that the researcher
who lacks a basic knowledge of data analytic strategies is a
"scientific cripple" (p.369)
Qualitative researchers may argue that the preceding view
is narrowminded. In my view, statistics is a necessary, but not a
sufficient condition of good research.
What shall we do?
To overcome the flooding of poor research, students in this class are asked to do the following:
 To know the difference between applying research findings and producing research results.
 To develop a sense of accountability to your fellow citizens.
 To understand that proper means are essential to reach the end. There is no shortcut.
 To learn the traditional Fisherian methodology as well as
alternative techniques such as resampling, Bayesian inference, and
exploratory data analysis. In the future, learners should understand
merits and shortcomings of each school and apply the appropriate
technique according to different research problems and data structures.
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