Inferential Statistics Hypothesis Testing

The question that inferential statistics asks and answers, then, can be framed as such Is there compelling evidence of systematic variation in our data More 

3 Between-Group Variation and Within-Group Variation 

Within-group variation represents the variation in SBP responses within each treatment group that is due to chance, i.e., random variation that is not caused by the compound administered to the treatment groups. This variation arises because humans have innate variation (as noted earlier, our biological systems operate such that we do not react identically in identical circumstances occurring at different times) and because all humans are different from each other. Within-group variation is not directly related to the treatment administered, since every subject in each group receives the same treatment. 

4 Comparing Between-Group Variance and Within-Group Variance 

Between-group variance can be called the effect variance, and within-group variance can be called the error variance. The effect variance is directly associated with the treatment administered, while the error variance is due to chance alone. The larger the effect variance when compared with the error variance, the more likely it is that compelling evidence of systematic variation will be revealed by inferential statistical analysis. Conversely, the smaller the effect variance when compared with the error variance, the less likely it is that compelling evidence of systematic variation will be revealed. 

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Up to now we have been discussing descriptive statistics. Inferential statistics uses statistical techniques to make inferences about wider populations from that from which our data are drawn. This involves making estimates and hypothesis testing. 

What are some reasons that inferential statistics (that is, hypothesis testing) are not used very often in early phase studies ... 

After a study has been completed, a statistical analysis provides a means either to reject or to fail to reject the null hypothesis. The statistical conclusion will, in part, be used to justify whether or not further investment is made in the development of a test product. A sound business strategy would dictate that further investment be made only if objective information from the study suggests it. Inferential statistics... 

The aforementioned probability-based considerations may serve as the most important foundations for derivation of statistically assured decisions. In general, in inferential statistics, the first step is the statement of a hypothesis, the significance of which is tested against a given risk a. 

Misconception—Hypothesis testing provides absolute proof that a research hypothesis is correct or incorrect Many novice chemical education researchers don t recognize that results of hypothesis testing using inferential statistics are tentative and based on probabilities, not certainties. This stems from a confusion... 

In the domain of proarrhy thmic cardiac safety, QT prolongation can be regarded as an adverse event of special interest, and therefore an inferential (hypothesis-testing) statistical approach is taken. Three statistical methodologies are applicable here the first two, the intersection-union test and the union-intersection test, are discussed in this section concentration- esponse modeling is then discussed in the following section. 

Munro, B.H., jacobson, B.j., and Braitman, L.E., Introduction to inferential statistics and hypothesis testing, in Statistical Methods for Health Care Research, 2nd ed., Munro, B.H. and Page, E.B. (Eds.), Lippincott, Philadelphia, 1993. 

The need to control the experiment-wise error rate may not apply to exploratory analyses. Statisticians often perform formal statistical tests for exploratory purposes. So, no formal hypotheses are stated and no inferences are made based on them. Even though the act of performing formally an exploratory test involves the same steps as inferential testing, it is conceptually different because of the absence of a null hypothesis. The p-value obtained in such a test should be viewed as a measure of the level of inconsistency of the data with the underlying assumptions of the test rather than error probabilities involved in making causal inferences. 

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