# Assignment-5

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Design of experiments (DOE) is defined as a branch of applied statistics that deals with planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters. DOE is a powerful data collection and analysis tool that can be used in a variety of experimental situations. It allows for multiple input factors to be manipulated, determining their effect on the desired output (response). By manipulating multiple inputs at the same time, DOE can identify important interactions that may be missed when experimenting with one factor at a time. All possible combinations can be investigated (full factorial) or only a portion of the possible combinations (fractional factorial). A strategically planned and executed experiment may provide a great deal of information about the effect on a response variable due to one or more factors. Many experiments involve holding certain factors constant and altering the levels of another variable. This "one factor at a time" (OFAT) approach to processing knowledge is, however, inefficient when compared with changing factor levels simultaneously. Many of the current statistical approaches to designed experiments originate from the work of R. A. Fisher in the early part of the 20th century. Fisher demonstrated how taking the time to seriously consider the design and execution of an experiment before trying it helped avoid frequently encountered problems in analysis. Key concepts in creating a designed experiment include blocking, randomization, and replication. Blocking: When randomizing a factor is impossible or too costly, blocking lets you restrict randomization by carrying out all of the trials with one set of the factor and then all the trials with the other setting. Randomization: Refers to the order in which the trials of an experiment are performed. A randomized sequence helps eliminate the effects of unknown or uncontrolled variables. Replication: Repetition of a complete experimental treatment, including the setup. A well-performed experiment may provide answers to questions such as: What are the key factors in a process? At what settings would the process deliver acceptable performance? What are the key, main, and interaction effects in the process?
What settings would bring about less variation in the output? A repetitive approach to gaining knowledge is encouraged, typically involving these consecutive steps: 1. A screening design that narrows the field of variables under assessment. 2. A "full factorial" design that studies the response of every combination of factors and factor levels, and an attempt to zone in on a region of values where the process is close to optimization. 3. A response surface designed to model the response. ANOVA ANOVA stands for Analysis of Variance. It's a statistical test that was developed by Ronald Fisher in 1918 and has been in use ever since. Put simply, ANOVA tells you if there are any statistical differences between the means of three or more independent groups. One-way ANOVA is the most basic form. Other variations can be used in different situations, including: Two-way ANOVA Factorial ANOVA Welch's F-test ANOVA Ranked ANOVA Games-Howell pairwise test ANOVA helps you find out whether the differences between groups of data are statistically significant. It works by analyzing the levels of variance within the groups through samples taken from each of them. If there are a lot of variances (spread of data away from the mean) within the data groups, then there is more chance that the mean of a sample selected from the data will be different due to chance. As well as looking at variance within the data groups, ANOVA takes into account sample size (the larger the sample, the less chance there will be off picking outliers for the sample by chance) and the differences between sample means (if the
means of the samples are far apart, it's more likely that the means of the whole group will be too). All these elements are combined into an F value, which can then be analyzed to give a probability (p-value) of whether or not differences between your groups are statistically significant. A one-way ANOVA compares the effects of an independent variable (a factor that influences other things) on multiple dependent variables. Two-way ANOVA does the same thing, but with more than one independent variable, while a factorial ANOVA extends the number of independent variables even further.