Statistical description hypothesis

Statistical thermodynamic reasoning is also based on a second hypothesis called the average value hypothesis, which states  

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The following description and corresponding MathCad Worksheet allows the user to test if two correlation coefficients are significantly different based on the number of sample pairs (N) used to compute each correlation. For the Worksheet, the user enters the confidence level for the test (e.g., 0.95), two comparative correlation coefficients, r, and r2, and the respective number of paired (X, Y) samples as N and N2. The desired confidence level is entered and the corresponding z statistic and hypothesis test is performed. A Test result of 0 indicates a significant difference between the correlation coefficients a Test result of 1 indicates no significant difference in the correlation coefficients at the selected confidence level. 

All those visualization tools which allow the exploration of uni- and oligo-variate data can be considered as instruments of descriptive statistics. Descriptive statistics is usually defined as a way to summarize/extract information out of one or a few variables compared to inferential statistics, whose aim is to assess the validity of a hypothesis made on measured data, descriptive statistics is merely explorative. In particular, some salient facts can be extracted about a variable ... 

To explain the difference between the experimental results and theory, Doherty et al. (4J have given an empirical and a theoretical hypothesis. The theoretical hypothesis concerns the question of the meaning to be attached to the concept of the "equivalent random link" in the statistical theory of the randomly-jointed chain. According to Doherty et al., the assumption that the optical properties of the chain are describable by a randomly jointed model, using the same value of n, as for the description of stress has no strictly logical foundation. 

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. 

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. 

In tables where the dispersion of each data set is shown by an appropriate statistical parameter, you must state whether this is the (sample) standard deviation, the standard error (of the mean) or the 95% confidence limits and you must give the value of n (the number of repUcates). Other descriptive statistics should be quoted with similar detail, and hypothesis-testing statistics should be quoted along with the value of P (the probabiUty). Details of any test used should be given in the legend, or in a footnote. 

In this section the aims of a statistical analysis will be considered. Three rather dilferent functions must be distinguished, namely, description, estimation and hypothesis testing. The beginning is to set up a database (on paper or in a computer file) that contains a complete list of the raw data. This (on paper) might have a structure as shown in Table 7.1. 

Formal hypothesis testing is less likely to occur for secondary endpoints. Descriptive statistics are more likely to be presented. It is also possible that findings of particular interest may lead to a primary objective in a subsequent trial. That is, these data are more suited to hypothesis formation than hypothesis testing. It is important to emphasize here that data leading to the formation of a hypothesis cannot be used to test that hypothesis As just noted, a new dataset must be generated. 

Descriptive Statistics (e.g., mean, median, variance, standard deviation) Hypothesis Testing (e.g., paired and un-paired t-tests chi-squared test) Principles of Statics (e.g., forces moments couples torques free-body diagrams)... 

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