### 统计代写|工程统计作业代写Engineering Statistics代考|Uses of Statistics

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Uses of Statistics

You will use statistics in five ways. One is in the design of experiments or surveys. In this instance, you need the answers to some questions about an event or a process. An effective experiment is one that has been designed so that the answers to your questions will be obtained more often than not. An efficient experiment is one that is unbiased (predicts

the correct value of the parameter) and that also has the smallest variance (scatter about the true value of the population parameter in question). Efficiency also means that the answers will have been obtained with the minimum expenditure of time (yours, an operator’s, a technician’s, etc.) and other resources.

The second way you will use statistical techniques is with descriptive statistics. This method involves using sample data to make an inference about the population. The population is the entire or complete set of possible values, attributes, etc. that are common to, describe, or are characteristic of a given experiment or event. A sample is a subset of that data. Descriptive statistics are used for describing and summarizing experimental, production, reliability, and other types of data.

The description can take many forms. The average, median, and mode are all measures of centrality. Variance, standard deviation, and probable range are all measures variation. The descriptor may be a probability, which refers to the chance an event might happen (such as getting three or more successes in five-coin flips) or the chance that a value might exceed some threshold (the probability of seeing someone taller than $6 \mathrm{ft} 8$ in on your next shopping trip).

It is essential that your samples are random samples if you are to have any reasonable expectation of obtaining reliable answers to your questions. To obtain a random sample, you must first define, not just describe, the population under consideration. Then you can use the principles of random selection of population values or experimental conditions to obtain the random sample that is essential to statistical inference.

A third statistical use is estimating the uncertainty of a value, estimating the possible range of values it might have. The value might be an average from a sample and the question is what range of population means could have generated that sample average. The value might be a predicted outcome from a model when all model coefficient values and influences are not known with certainty.

A fourth use of statistics is in the testing of hypotheses. A hypothesis about any event, process, or variable relationship is a statement of anticipated behavior under specified conditions. Hypotheses are tested by determining whether the hypothesized results reasonably agree with the observed data. If they do, the hypothesis is likely to be valid. Otherwise, the hypothesis is likely to be false. Hypotheses could be relatively complex, such as the model matching the data, the design being reliable, or the process being at steady-state.

The fifth use of methods in this book is to obtain quantitative relationships between variables by use of sample data. This aspect of statistics is loosely called “curve fitting” but is more properly termed regression analysis. We will use the method of least squares for regression because that technique provides a conventional way to estimate the “best fit” of the data to the hypothetical relationship.

## 统计代写|工程统计作业代写Engineering Statistics代考|Stationarity

In statistics, a stationary process does not change in mean (average) or variance (variability). It is steady, but any measurement is subject to random variation. The value of the data perturbation changes from sample to sample, but the distribution of the perturbations does not change.

This is in contrast to classic deterministic analysis of transient and steady-state processes. A steady process flatlines in time. The measurement achieves a particular value

and remains at that value. When the process is in a transient state the average or mean changes in time.

In statistics the term stationary means that the steady-state process will not deterministically flatline. Instead, the data will be continually fluctuating about a fixed value (mean) with the same variance. In statistics, a stationary process is not in a transient state.

Level of confidence is a measure of how probable your statistical conclusion is. As an example, after testing raw materials A and B for their influence on product purity, you might be $95 \%$ confident that A leads to higher purity. But you cannot extend this result to report that you are $95 \%$ sure that using raw material A is the better business decision. You have only tested product purity. You have not evaluated product variability, other product characteristics, manufacturing costs, process safety implications, etc. You can only be $95 \%$ confident in your evaluation of purity. Be careful that you do not project statistical confidence about one aspect onto your interpretation of the appropriate business action.

## 统计代写|工程统计作业代写Engineering Statistics代考|Correlation is Not Causation

Statistics does not prove that some event or value caused some other response. Causation refers to a cause-and-effect mechanism. Correlation means that there is a strong relationship between two variables, or observations.

As an example, there is a strong correlation to people awakening and the sun rising, but one cannot claim that people awakening causes the sun to rise. The cause-and-effect mechanism for this observed correlation is more akin to the opposite. As another example,

there is a strong correlation between gray hair and wrinkles, but that does not mean that gray hair causes wrinkles. The mechanism is that another variable, age, causes both observations.

So, more so than just tempering claims about confidence in taking action from testing a single aspect, be careful not to let indications of correlation dupe you into claiming causation. If you have an opinion as to the cause-and-effect mechanism, and you have correlation that supports it, before you claim it is the truth, perform experiments and seek data that could reject your hypothesized mechanism. State exactly, mechanistically how the treatment leads to the outcome expectations. State what else you expect should be observed, and what should not be observed. State when and where these should be observed. Do the experiments to see if your hypothesized theory is true.

Traditionally, statistics deals with the probable outcomes from a distribution. This book is grounded in that mathematical science, and many examples reveal how to describe the likelihood of some extreme value.

But more than this, the basis (the “givens”) in any particular application have uncertainty, which is unlike the basis of givens in a schoolbook example. In the real world, to make decisions based on the statistical analysis, the impact of uncertainty needs to be considered. Further, concerns over possible negative choices might not just be about monetary shortfalls. They may be related to disparate issues such as reputation.

This book includes a chapter on propagation of uncertainty, another on stochastic simulation, and frequent discussions on Equal-Concern approaches for combining disparate metrics.

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