When testing a research hypothesis, which the researcher has good reason to believe is true, it is customary to use a null hypothesis. Null hypothesis is typically a hypothesis of no difference or of no association between variables. If the research hypothesis is that men have a higher rate of suicide than do women, the null hypothesis would be that there is no difference in suicide rates between men and women. Researcher then try to disprove the null hypothesis and if they fail to reject it, they accept the research hypothesis.
Theoretical and empirical evidence examples show how null hypothesis rejection can occur when only a small proportion of individuals differ from all others, demonstrating that these tests are incapable of supporting inferences to general group differences.
Large-Scale Simultaneous
Hypothesis Testing: The Choice of a Null Hypothesis - Efron, Bradley.
Abstract: Current scientific techniques in genomics and image processing routinely produce
hypothesis testing problems with hundreds or thousands of cases to consider
simultaneously. This poses new difficulties for the statistician, but also opens new
opportunities. In particular, it allows empirical estimation of an appropriate null
hypothesis.
The empirical null hypothesis may be considerably more dispersed than the usual theoretical null distribution that would be used for any one case considered separately. An empirical Bayes analysis plan for this situation is developed, using a local version of the false discovery rate to examine the inference issues. Two genomics problems are used as examples to show the importance of correctly choosing the null hypothesis.
Statistical Power and the
Testing of Null Hypotheses: A Review of Contemporary Management Research and
Recommendations for Future Studies -
Luke H. Cashen, Scott W. Geiger.
The purpose of this study is to determine how well contemporary management research fares
on the issue of statistical power with regard to studies specifically predicting null
relationships between phenomena of interest. This power assessment differs from
traditional power studies because it focuses solely on studies that offered and tested
null hypotheses. On average, the power assessment revealed that for those studies that
found nonsignificance of results and consequently affirmed their null hypotheses, the
actual Type II error rate was nearly 15 times greater than what is advocated in the
literature when failing to reject a false null hypothesis. Recommendations for researchers
proposing and testing formal null hypotheses are also discussed.
Sex and Gender
Comparisons: Does Null Hypothesis Testing Create a False Dichotomy?
Olga Eizner Favreau, Departement de psychologie, University de Montreal.
In an ongoing debate about the value of doing tests for sex differences, those
in favour claim that if sex differences exist, it is important to know about
them. However, the null hypothesis tests that are used for inferring group
differences can detect only mean differences and provide no information about
how the differences are distributed across groups.
When is it Acceptable to Accept a Null Hypothesis: No Way, Jose? - Jose M. Cortina, Robert G. Folger. Previous research has suggested that there exists a bias in the social sciences against no-effect hypotheses. This is regrettable given the importance of establishing not only when an effect does occur but also the boundary conditions of that effect. The purposes of this article are two-fold The first purpose is to review relevant portions of the history of hypothesis testing in an attempt to identify the sources of bias against hypotheses of no effect.
Random walks in the
history of life - James L. Cornette,
and Bruce S. Lieberman.
The simplest null hypothesis for evolutionary time series is that the observed data follow
a random walk. Throughout most of the Phanerozoic, the random-walk null hypothesis is not rejected for
marine diversity, accumulated origination or accumulated extinction, suggesting that
either these variables were correlated with environmental variables that follow a random
walk or so many mechanisms were affecting these variables, in different ways, that the
resultant trends appear random. The only deviation from this pattern involves rejection of
the null hypothesis for roughly the last 75 million years for the diversity and
accumulated origination time series.
Rushton's Defenders and Their Hasty Rejection of the Null Hypothesis -
Zack Z. Cernovsky,
University of Western Ontario.
Rosenthal and Rubin (1985) pointed out that in research on extreme situations (e.g., new
treatments for terninally ill patients) any noticeable statistical trend in the desirable
direction is valuable. Hasty and eager acceptance of weak, biased, and unrepresentative data
as scientific evidence of genetically based and relatively immutable racial differences in
human potential amounts to psychological warfare on oppressed racial groups. Similar
defamation of vulnerable minorities by Nazi pseudoscientists led to the loss of millions
of human lives in the past. Statistical theory classifies similar endeavors as a Type I
error (a misleading rejection of the null hypothesis).
Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root
Alternative - Zhijie Xiao.
We propose a new test for the null hypothesis that a time series is stationary around a
deterministic trend. The test is valid under general conditions on stationarity.
Asymptotic distributions of the test statistic are derived under both the null hypothesis
and the alternative hypothesis of a unit root. It is shown that the limiting distribution
has the classical Kolmogoroff– Smirnoff form. Critical values for the null
distribution are calculated. Consistency of the tests is proved.
Null Hypothesis Significance Testing: Effect Size Matters - Gliner J. A.; Vaske J. J.; Morgan G. A.
Abstract: A statistically significant outcome only indicates that it is likely that there
is a relationship between variables. It does not describe the extent (strength) of that
relationship. In this article, emphasis is placed on the importance of assessing the
strength of the relationship between the independent and dependent variables using effect
size indices.
A Note on the Bandwidth Choice When the Null Hypothesis is Semiparametric - JORGE BARRIENTOS-MARIN. Abstract: This work presents a tool for the additivity test. The additive model is widely used for parametric and semiparametric modeling of economic data. The additivity hypothesis is of interest because it is easy to interpret and produces reasonably fast convergence rates for non-parametric estimators. Another advantage of additive models is that they allow attacking the problem of the curse of dimensionality that arises in non- parametric estimation. Hypothesis testing is based in the well-known bootstrap residual process. In nonparametric testing literature, the dominant idea is that bandwidth utilized to produce bootstrap sample should be bigger that bandwidth for estimating model under null hypothesis.
Reconsidering the null hypothesis: Is maternal rank associated with birth sex ratios in primate groups? - Gillian R. Brown, and Joan B. Silk. Trivers and Willard hypothesized that vertebrates adaptively vary the sex ratio of their offspring in response to the mother's physical condition. This hypothesis has produced considerable debate within evolutionary biology. Here we use meta-analysis techniques to evaluate claims that nonhuman primate females facultatively adjust the sex ratio of their progeny in relation to their own dominance rank in a uniform way.
The Proposal for a Null
Hypothesis Test and Search for New Physics in the Top Dilepton Sample -
Andrew Ivanov.
We propose a null hypothesis test to search for new physics in top dilepton decays. We
used data collected by the CDF Run 2 experiment in proton-antiproton collisions at a
center-of-mass energy of 1.96 TeV at the Fermilab Tevatron. The test is based on a
comparison of several kinematic variables; the Kolmogorov-Smirnov statistic is used to
quantify the consistency of the variables' distributions in the data with those expected
from the production of t\bart and SM background. In this way we determine an overall
confidence level on the hypothesis that the Run 2 data can be explained by purely SM
physics.