Hypotheses testing

In statistical analysis, often a central objective is to evaluate a claim made about a specific population. A statistical hypothesis consists of two mutually exclusive, dichotomous statements of which one will be accepted and the other rejected (Lapin, 1977 Salsburg, 1992). 

The graphic and regression methods are a means of estimating the concentration-response curve. Hypothesis testing is an alternative to the analysis of the concentration-response data. 

Analysis of variance (ANOVA) is the standard means of evaluating toxicity data to determine the concentrations that are significantly different in effects from the control or not-dosed treatment. The usual procedure is (Gelber et al. 1985)  

Testing for equivalence of the control or not-dosed treatment with the carrier control 

In chronic studies, the data often are expressed as a percentage of control, although this is certainly not necessary. Hatchability, percentage weight gain, 

The concept of statistical significance therefore allows the initial version of the research question, Does the new drug alter SBP more than placebo to be reframed as follows Does the new drug alter SBP statistically significantly more than placebo It therefore facilitates the reframing of the research hypothesis and the null hypothesis in the same manner. The research hypothesis associated with the modified (improved) research question is framed as follows  

The null hypothesis associated with the improved research question is framed as follows  

Once the research hypothesis and the null hypothesis have been created, the process of hypothesis testing can take place. 

5 Conducting a Statistical TfcsT and Obtaining a ItesT Statistic 

Statistical analyses result in a test statistic being calculated. For example, two common tests that will be introduced in this chapter are the f-test and a test called analysis of variance (ANOVA). The /-tests result in a test statistic called /, and ANOVA results in a test statistic called F. When you read the Results sections of regulatory submissions and clinical communications, you will become very familiar with these test statistics. The test statistic obtained determines whether the result of the statistical test attains statistical significance or not. 

In Section 5.5 a question was raised concerning the adequacy of models when fit to experimental data (see also Section 2.4). It was suggested that any test of the adequacy of a given model must involve an estimate of the purely experimental uncertainty. In Section 5.6 it was indicated that replication provides the information necessary for calculating the estimate of (. We now consider in more detail how this information can be used to test the adequacy of linear models [Davies (1956)]. 

In our clinical trials we generally have some very simple questions  

In order to evaluate the truth or otherwise of these statements we begin by formulating the questions of interest in terms of hypotheses. The simplest (and most common) situation is the comparison of two treatments, for example in a placebo controlled trial, where we are trying to detect differences and demonstrate that the drug works. 

Assume that we are dealing with a continuous endpoint, for example, fall in diastolic blood pressure, and we are comparing means. If and p.2 denote the mean reductions in groups 1 and 2 respectively then our basic question is as follows  

We formulate this question in terms of two competing hypotheses  

We base our conclusion regarding which of these two statements (hypotheses) we prefer on data and the method that we use to make this choice is the p-value. 

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There will be incidences when the foregoing assumptions for a two-tailed test will not be true. Perhaps some physical situation prevents p from ever being less than the hypothesized value it can only be equal or greater. No results would ever fall below the low end of the confidence interval only the upper end of the distribution is operative. Now random samples will exceed the upper bound only 2.5% of the time, not the 5% specified in two-tail testing. Thus, where the possible values are restricted, what was supposed to be a hypothesis test at the 95% confidence level is actually being performed at a 97.5% confidence level. Stated in another way, 95% of the population data lie within the interval below p + 1.65cr and 5% lie above. Of course, the opposite situation might also occur and only the lower end of the distribution is operative. 

How Many Samples. A first step in deciding how many samples to collect is to divide what constitutes an overexposure by how much or how often an exposure can go over the exposure criteria limit before it is considered important. Given this quantification of importance it is then possible to calculate, using an assumed variabihty, how many samples are required to demonstrate just the significance of an important difference if one exists (5). This is the minimum number of samples required for each hypothesis test, but more samples are usually collected. In the usual tolerance limit type of testing where the criteria is not more than some fraction of predicted exceedances at some confidence level, increasing the number of samples does not increase confidence as much as in tests of means. Thus it works out that the incremental benefit above about seven samples is small. 

Jui y trials represent a form of decision making. In statistics, an analogous procedure for making decisions falls into an area of statistical inference called hypothesis testing. 

Solving an indoor air quality problem is a cyclical process of data collection and hypothesis testing. Deeper and more detailed investigation is needed to suggest new hypotheses after any unsuccessful or partially-successful control attempt. Even the best planned investigations and mitigation actions may not produce a resolution to the problem. You may have made a careful investigation, found one or more apparent causes for the problem, and implemented a control system. Nonetheless,... 

It is worth considering hypothesis testing in general from the standpoint of the choice of models one has available to fit data. On the surface, it is clear that the more complex a model is (more fitting parameters) the greater the verisimilitude of the data to the calculated line (i.e., the smaller will be the differences between the real and predicted values). Therefore, the more complex the model the more likely it will accurately fit the data. However, there are other factors that must be considered. One is the physiological relevance... 

Hypothesis Testing Examples with Dose-response Curves... 

There are statistical procedures available to choose models (hypothesis testing), assess outliers (or weight them), and deal with partial curves. 

Human embryonic kidney cells, 21 Human genome, 2 Hydrogen bonding, 10 Hypothesis testing definition of, 239 description of, 227, 233 dose-response curves for, 239-243 F-test, 242t... 

In passing we remark that there are well-known statistical methods of hypothesis testing and parameter estimation used in decisionmaking. Sequential analysis is a method of sampling used to decide whether to accept or reject a lot with defective items, or whether to continue sampling. Also, there are various statistical methods used in quality control of a manufacturing process, to decide on how much the quality should be improved to be acceptable. 

Producing burn-out correlations would appear to be almost a pastime Milioti (Ml2), for example, was able to compile a total of 59 different burnout correlations, and the number still grows. Most of these correlations are based on very restricted ranges of system parameters, however, and although they work well within the restrictions, they usually deviate markedly on extrapolation. Some of the earlier correlations are also readily seen to be inconsistent with now well-established experimental facts, even simple though important facts such as the linear or nearly linear relationship between and Ah. As mentioned earlier, the hypothesis-testing technique exploited by Barnett is a very effective tool for showing up defects, and the method has... 

When there are many samples and many attributes the comparison of profiles becomes cumbersome, whether graphically or by means of analysis of variance on all the attributes. In that case, PCA in combination with a biplot (see Sections 17.4 and 31.2) can be a most effective tool for the exploration of the data. However, it does not allow for hypothesis testing. Figure 38.8 shows a biplot of the panel-average QDA results of 16 olive oils and 7 appearance attributes. The biplot of the... 

Since Og is known exactly (i.e., there is no uncertainty in its value, it is a given number) the above hypothesis test is done through a y2-test. Namely,... 

Koch, K.R., Parameter Estimation and Hypothesis Testing in Linear Models, Springer-Verlag, New York, NY, 1987. 

The next hypothesis tested was whether combining monoclonal antibody therapy with chemotherapy could increase... 

CHEMLAB can provide information such as energetic feasibility, hydrogen bonding potential, etc. These can be used to explain observed behavior or to predict the properties of proposed compounds. Hypothesis testing is the greatest utility of molecular modeling. 

This extension in the laboratory can be seen as the fantastic hypothesis testing application of molecular modeling. It is rare to find a chemical problem where there are not at least a few theories of the molecular mechanism involved. How many times has each of us heard steric affect or hydrogen bonding invoked as the explanation of a variety of experimental observations made at the bench level How useful would it be to be able to actually build accurate, quantitative models to investigate such ideas ... 

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