- STAT 425 - Statistical Design and Analysis of Experiments - Winter 2018
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- Design of Experiments (DOE) Tutorial
- Statistical Design and Analysis of Industrial Experiments

The following table summarize the matching of statistical methods with the types of data. However, this does not imply that the suggested statistical methods are the ONLY ones for the data. In fact, data analysis is a dynamic and exploratory process. Thus, the alternative statistical methods may be used sometimes. Analysis of covariance??? Which statistical software should be used? With the leap in desktop computing power over the past few years, many statistical softwares that traditionally target the mainframe computers have now had their user-friendly PC versions available.

This enables individual researchers to carry out statistical analysis with little help from computer specialists. However, apart from a real danger of i misapplication of statistical methods by the researchers with limited statistical backgrounds and ii invalid interpretation of outputs from the analysis, there is also a difficulty to choose which statistical softwares should be used in analyzing the research data.

General Statistical Resources has compiled the most commonly used statistical softwares that are currently used by researchers in different disciplines. A brief description of each software is also given to facilitate your choice. It should be noted that SAS has dominated the statistical computing market for the last 20 years and it is no surprise that most AAFRD researchers have chosen SAS as their workhorse for the statistical analysis. This document is maintained by Stacey Tames.

This information published to the web on February 11, Let us briefly describe these three types of research data. In designed experiments, some form of treatment is applied to experimental units and responses are observed.

For example, in a food processing experiment, portions of fruit, such as slices of apples, are treated with different preservatives and the shelf lives of the portions of fruit are determined. Most experiments in agri-food research are designed experiments because the researchers often want to determine effects of different treatments.

Independent variable Dependent variable y. Agri-News This Week. Types of experimental data Data analysis is the application of one or more statistical techniques to a set of data as collected from one of the following three types of research projects: 1 designed experiments, 2 sample surveys and 3 observational studies. Independent variable. Dependent variable y. For more information about the content of this document, contact Rong-Cai Yang.

## STAT 425 - Statistical Design and Analysis of Experiments - Winter 2018

In this case, it can be an issue if a carryover effect from a treatment given in a previous period influences the response in the following treatment. It should be noted that crossover designs should be avoided when significant carryover effects are expected [ 16 ]. Even if a significant carryover effect is not expected, the potential for a carryover effect should not be ignored in crossover designs. A sufficient rest or wash-out period between two treatment periods is one of the practical ways to minimize carryover effects.

More importantly, the order of treatments for each animal should be balanced to avoid confounding of treatment and period effects and to minimize the influence of carryover effects. In a balanced crossover design, each treatment follows each of the other treatments an equal number of times, and each treatment is assigned once for each animal and the same number of times in each period.

When a carryover effect is suspected, its significance also needs to be tested by statistical analysis. The AJAS editorial board recommends authors describe the procedure used to minimize possible carryover effects and show that carryover effects are not significant in their study when using a crossover design. Randomization is an essential procedure to ensure the reliability of the experiment and the validity of the statistical analysis.

The purpose of an experiment is to make inferences about the population mean and variance, and the statistical analysis assumes the observations are from a random sample from a normally distributed population. This assumption can be valid only through randomization. In animal nutritional studies, two randomization processes are required: random sampling of experimental units and random allocation of treatments to experimental animals.

Theoretically, experimental animals represent the animal population of interest; thus, they need to be randomly selected from the population. However, this is usually not feasible, if not impossible, in the real world and whether experimental animals can be considered a random sample is questionable.

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Nevertheless, whenever possible, randomization must be practiced in selecting experimental animals to eliminate biases and to obtain valid estimates of experimental error variance. For example, when a deep analysis is performed on selected animals e. Random allocation of treatments to experimental units is the most important and critical step to justify and establish the validity of statistical inferences for the parameters of the population and tests of hypothesis. The experimental errors are assumed to be independently and normally distributed.

Estimation of parameters and statistical inferences can be possible if and only if this assumption is valid. Random assignment of treatments to experimental animals is the only method that guarantees the independence of observations and permits us to proceed with the analysis as if the observations are independent and normally distributed. The authors are required to describe the randomization procedure used for their animal trials.

## Design of Experiments (DOE) Tutorial

Statistical analysis is conducted to test the hypotheses and significance of tests in a study. There are many methods for conducting statistical analysis and various methods yield different results and conclusions. Proper statistical methods should be applied when conducting an experiment, and details of statistical methods should be provided in the statistical methods section of a manuscript to allow reviewers and readers to assess the quality of statistical methods used in the study. When submitting a manuscript for publication in AJAS, authors should clearly define their statistical models used for the statistical analysis.

Statistical models are usually expressed as linear models with the overall mean of the response variable, fixed or random variables that are known to influence the response variable, and unexplained experimental random error. The statistical model should be consistent with the experimental design and be appropriate to analyze the observations from the experiment. A clear description of the statistical model as an equation, as well as in words, is useful to understand the analytical procedure and the meaning of statistical implications and to evaluate the correctness and relevance of the statistical methods used in the study.

Thus, the statistical model is often used as a criterion for the recommendation of manuscript rejection by reviewers and editors [ 11 ]. Various statistical methods are available, and the choice of method depends on the data type of observations, research questions to answer, and the statistical model. If observations of the response variables are binary i. Sometimes research questions are not about means but seek to understand the quantitative relationship between response variables or between the response variable and treatment e.

The linear or non-linear regression analysis is the method to be used in this case. When the response variable of interest is a continuous variable and the research question is about means or an interval of the value, either parametric or non-parametric statistical methods can be applied.

A t-test is used for comparing two samples or treatments, whereas the ANOVA is used when there are more than two treatments. For example, if two samples are paired e.

## Statistical Design and Analysis of Industrial Experiments

Additionally, because different levels of complexity can exist in statistical models e. Parametric methods assume that the observations are independent and normally distributed around their mean. This assumption is generally true in animal nutritional studies as long as randomization is practiced. However, it is always a good practice to test this assumption, especially if variables are expected not to follow it.

For example, particle size normally has a log-normal distribution [ 17 ], and thus statistical tests need to be performed on transformed values. If the observations are not normally distributed or the sample size is not large enough, non-parametric analyses e. Non-parametric methods do not assume a normal distribution of experimental errors and more powerful to detect differences among treatments than parametric methods e. Because non-parametric methods have more statistical power, they can exaggerate the significance of the difference between treatments. A parametric method is thus preferred when it is applicable.

When an ANOVA reveals that the probability that treatment means are all equal is sufficiently small enough to conclude that at least one of the treatment means is different from the others, we may ask further questions, such as which ones are different from each other? Before conducting further analyses, two things are to be considered.

First, we need to determine how small is sufficiently small. When the p-value obtained using an ANOVA test is less than the level of significance, the results may be meaningful and need to be discussed; thus, comparing the means becomes interesting.