Data Analysis Hypothesis testing

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... 

The F test in Equation 4-12 told us that the standard deviations of Rayleigh s two experiments are different. Therefore, we can select the other t test found in the TOOLS menu in the DATA ANALYSIS choices. Select t-Test Two-Sample Assuming Unequal Variances and fill in the blanks exactly as before. Results based on Equations 4-8a and 4-9a are displayed in cells E15 to G26 of Figure 4-8. Just as we found in Section 4-3, the degrees of freedom are df =7 (cell F21) and Calculated = 21.7 (cell F22). Because Calculated s greater than the critical value of t (2.36 in cell F26), we reject the null hypothesis and conclude that the two means are significantly different. 

PLS can be applied to data obtained from experiments designed to test some hypothesis. The BHT example is a part of a study investigating behavioural and neurochemical effects of dopamine agonists. The hypothesis tested was whether BHT has behavioural effects (that is, the null-hypothesis that the behaviour of BHT-treated animals does not differ from the behaviour of vehicle treated control animals is used). The analysis of the BHT data would in traditional statistics have been analysed by MR or by ten independent simple... 

The use of statistical tests to analyze and quantify the significance of sample data is widespread in the study of biological systems where precise physical models are not readily available. Statistical tests are used in conjunction with measured data as an aid to understanding the significance of a result. Their aid in data analysis fills a need to answer the question of whether or not the inferences drawn from the data set are probable and statistically relevant. The statistical tests go further than a mere qualitative description of relevance. They are designed to provide a quantitative number for the probability that the stated hypothesis about the data is either true or false. In addition, they allow for the assessment of whether there are enough data to make a reasonable assumption about the system. 

The data must be tested in order to establish the nature of error variation to enable decision on whether the transformation of the data, the utilization of distribution-free statistical analysis procedures, or the test against simulated zero-hypothesis data is necessary. 

Hypothesis tests may compare the collected data to an action level or compare two sets of data to each other. A statistician will select a statistical analysis test that is appropriate for the intended use of the data and the type of the collected data distribution and will identify assumptions underlying the test. The probabilities for false rejection decision... 

This chapter introduces basic concepts in statistical analysis that are of relevance to describing and analyzing the data that are collected in clinical trials, the hallmark of new drug development. (Statistical analysis in nonclinical studies was addressed earlier in Chapter 4.) This chapter therefore sets the scene for more detailed discussion of the determination of statistical significance via the process of hypothesis testing in Chapter 7, evaluation of clinical significance via the calculation of confidence intervals in Chapter 8, and discussions of adaptive designs and of noninferiority/equivalence trials in Chapter 11. 

DAnTE Pacific Northwest National Laboratory Allows users to perform various downstream data analysis, normalization, data reduction, and hypothesis testing steps (http // omics.pnl.gov/software/DAnTE.php)... 

Analysis will then probably progress to hypothesis testing — looking to see whether the answer provided to one question influences the pattern of answers to another question. As so many questionnaire data are nominal scale, contingency chi-tests tend to dominate. 

A data matrix produced by compositional analysis commonly contains 10 or more metric variables (elemental concentrations) determined for an even greater number of observations. The bridge between this multidimensional data matrix and the desired archaeological interpretation is multivariate analysis. The purposes of multivariate analysis are data exploration, hypothesis generation, hypothesis testing, and data reduction. Application of multivariate techniques to data for these purposes entails an assumption that some form of structure exists within the data matrix. The notion of structure is therefore fundamental to compositional investigations. 

Statistical methods frequently employed in effluent toxicity evaluations include point estimation technique such as probit analysis, and hypothesis testing like Dunnett s analysis of variance (anova). Point estimation technique enables the investigator to derive a quantitative dose-response relationship. This method has been generally applied to statistical analyses of acute effluent monitoring data. 

The most important parameter is a clear identification of the specific question that the toxicity test is supposed to answer. The determination of the LC50 within a tight confidence interval will often require many fewer organisms than the determination of an effect at the low end of the dose-response curve. In multispecies toxicity tests and field studies, the inherent variability or noise of these systems requires massive data collection and reduction efforts. It is also important to determine ahead of time whether a hypothesis testing or regression approach to data analysis should be attempted. 

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. 

---