## small effect sizes seem “biased” toward the null hypothesis

### Business and Investing: The bias of the null hypothesis

Recall that a ** p-value** is the probability that the test statistic would "lean" as much (or more) toward the alternative hypothesis as it does if the real truth is the null hypothesis.

### BIAS AGAINST THE NULL HYPOTHESIS: THE REPRODUCTIVE HAZARDS OF ..

In hypothesis testing, a null hypothesis and an alternative hypothesis are formed. Typically, the null hypothesis reflects the lack of an effect and the alternative hypothesis reflects the presence of an effect (supporting the research hypothesis). The investigator needs to have sufficient evidence, based on data collected in a study, to reject the null hypothesis in favor of the alternative hypothesis.

When you perform hypothesis testing, you only set the size of Type I error and guard against it. Thus, we can only present the strength of evidence against the null hypothesis. One can sidestep the concern about Type II error if the conclusion never mentions that the null hypothesis is accepted. When the null hypothesis cannot be rejected, there are two possible cases: 1) one can accept the null hypothesis, 2) the sample size is not large enough to either accept or reject the null hypothesis. To make the distinction, one has to check . If at a likely value of the parameter is small, then one accepts the null hypothesis. If the is large, then one cannot accept the null hypothesis.

## The Null Hypothesis: Determining Bias.

3) A decision is made whether or not to reject the null hypothesis and accept the alternative hypothesis instead. If the probability that the observed differences resulted from sampling variability is very low (typically less than or equal to 5%), then one concludes that the differences were "statistically significant" and this supports the conclusion that there is an association (although one needs to consider bias and confounding before concluding that there is a valid association).

## Null Hypothesis Example P Value

The chi-square uses a procedure that assumes a fairly large sample size. With small sample sizes the chi-square test generates falsely low p-values that exaggerate the significance of findings. Specifically, when the * expected* number of observations under the null hypothesis in any cell of the 2x2 table is less than 5, the chi-square test exaggerates significance. When this occurs,

**Fisher's Exact Test is preferred**.

## Average bias - Analyse-it®

The null hypothesis, H_{0} is a commonly accepted hypothesis; it is the opposite of the . Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to . If that sounds a little convoluted, an example might help. Back in the day (way back!) scientists thought that the Earth was at the center of the Universe. That mean everything else — the sun, the planets, the whole shebang, all of those celestial bodies revolved around the Earth.

## Journal of Articles in Support of the Null Hypothesis;

Each *t* value has associated probabilities. In this case, we want to know the probability of observing a *t* value as extreme or more extreme than the *t* value actually observed, if the null hypothesis is true. This is the *p*-value. At the completion of the study, a statistical test is performed and its corresponding *p*-value calculated. If the *p*-value _{0} is rejected in favor of H_{1}.