Three factor factorial design example pdf. au/yd964/synology-jellyfin-docker.
Three factor factorial design example pdf. 1is an example of a complete factorial design, in which data are collected for all combinations of the independent variable values. This is a FIXED factor. In factorial designs, a factor is a major independent variable. Superpower allows researchers to perform simulation-based power analyses without having extensive pro-gramming knowledge. In this design, a set of experimental units is grouped (blocked) in a way that minimizes the variability among the units within groups (blocks). 2020 (With Results) per liter (nmol/l), with a range of 9 to 33 reported in studies of nondepressed people. . 5AF + ε, where ε is the same as in our 2 3 model (Table 1 Table 7. Sep 1, 2009 · The fundamental concepts, design strategies, and statistical properties of fractional factorial designs are highlighted, including the least cost, shortest time, or most effective use of resources. Factorial treatment designs use several treatment factors, and a treatment applied to an experimental unit is then a combination of one level from each a 2x2 factorial experiment. Example 13. As in Chapter 3, the simplest factorial blocked design is a randomised complete block design, where the blocks are large enough for a complete replicate of the factorial treatments to Apr 17, 2021 · The full factorial experiment design with the three factors A, B, and C consists of 2 3 = 8 factor-level combinations. < one null simple effect and one simple effect. • Des. 9. That is we have 3 factors each of which have two levels and 2 replicates. Calculate the single three-factor interaction (3fi). , one within-subjects factor) in our mixed-effects model. Since each four-level factor will require two columns and each two-level factor will require one column, the base design must have a total of seven columns. Blocking in factorial designs. As the factorial design is primarily used for screening variables, only two levels are enough. It provides the smallest number of runs with which k factors can be studied in a complete factorial design. Notation: Data Matrix Dec 1, 2017 · approach for DOE is explained for two 2 2 and three 2 3 factors as well as general 2 k factorial design, in which k represents number of factors while number 2 r epresents number of levels The design for the previous experiment is an example of a two-stage nested design. Three Factors. iii. , 2016 ) crossed 5 2-level factors, resulting in 32 combinations of factor levels (see Table 1 ). Includes a worked example in R to analyze greenhouse data for two random σ ^ τ β 2 = M S A B − M S E n. CRD under three Factors Factorial Experiment on SPSS-12 Oct 15, 2020 · Abstract and Figures. night) on driving ability. 1 3. 05 level of significance to determine whether there is evidence of an interaction, the decision rule is to reject the null hypothesis of no interaction between brand and temperature if the calculated F value is larger than the critical F value of 4. the remaining 99 df are for interactions of order ≥ 3. Representation of a one-third Fractional Factorial (FF) statistical design with three May 13, 2021 · A 2×2 factorial design allows you to analyze the following effects: Main Effects: These are the effects that just one independent variable has on the dependent variable. Factors Test Multiple Treatment Factors: Factorial Designs 6. Cortisol, a stress hormone, is measured in nanomoles. Repeat for each pulp preparation method. Mar 11, 2023 · In the main "Create Factorial Design" menu, click "OK" once all specifications are complete. (iii) Soil fertility. Other vi Coding Systems for the Factor Levels in the Factorial Design of Experiment. Often, coding the levels as (1) low/high, (2) -/+ or (3) -1/+1 is more convenient and meaningful than the actual level of the factors, especially for the designs and analyses 3 2k-p Fractional Factorial Designs •Motivation: full factorial design can be very expensive —large number of factors ⇒ too many experiments •Pragmatic approach: 2k-p fractional factorial designs —k factors —2k-p experiments •Fractional factorial design implications —2k-1 design ⇒ half of the experiments of a full factorial design Now let’s examine what a three-factor study might look like. Investigating multiple factors in the same design automatically gives us replication for each of the factors. 23. 1: A Two-Factor Design Fertilizer 1 Fertilizer 2 Fertilizer 3 Sprinker Irrigation Drip Irrigation Table7. 500. With three variables, the most general polynomial model that can be generated from a full 2 level factorial design is. Number of runs required for full factorial grows quickly. The basic split-plot design involves assigning the levels of one factor to main plots. All model terms (the main effects of each factor and all interactions) could be estimated with this design. It helps investigate the effects of Here is an example in three dimensions, with factors A, B and C. An experiment was carried out to evaluate the effects of 3 factors on the total dry matter yield of animal feed. Divide the batch into four sections or samples, and assign one of the temperature levels to each. 1 INTRODUCTION Factorial experiments are the experiments that investigate the effects of two or more factors or input parameters on the output response of a process. First we will analyze the quantitative factors involved, Cycle Time and Temperature and as though they were qualitative - simply nominal factors. In this paper we will describe design of experiment by factorial analysis of variance (ANOVA) method. Jan 1, 2023 · This can make an experiment both more cost efficient and logistically easier to conduct with a smaller number of total conditions. Augmenting an existing factorial or resolution V design with appropriate star points can also produce this design. One of the big advantages of factorial designs is that they allow researchers to look for interactions between independent variables. If equal sample sizes are taken for each of the possible factor combinations then the design is a balanced two-factor factorial design. The experimental factors were: Management. 5 Summary 12. y = β o + β 1x 1 + β 2x 2 + β 3x 3 + β 12x 1x + β. None of the levels were specified as they appear as -1 and 1 for low and high levels, respectively. 5. Factor 2: Treatment. ANOVA Video Tutorial. The table consists of plus and minus signs and includes columns for every main effect, two-factor, three-factor, and a four-factor interaction effect. Experiments of factorial design offer a highly efficient method to evaluate multiple component interventions. So a two-factor study (e. be lost! The 2k design is particularly useful in the early stages of experimental work when many factors are likely to be investigated. Mar 11, 2023 · Thus, factorial design is not a practical choice: a good rule of thumb is 1-3 variables with few states for a manageable factorial analysis. These designs can be used to fit all main effect and 2-factor interaction terms without any confounding between the terms. ClinicalTrials. By simulating data for factorial designs with specific parameters, researchers can gain a better understanding of the factors that determine the statistical power of an ANOVA and learn how to design well-powered experiments. An interaction is a result in Chapter 6 of BHH (2nd ed) discusses fractional factorial designs. Example of a 2x2 factorial An example of an experiment involving two factors is the application of two nitrogen levels, N0 and N1, and two phosphorous levels, P0 and P1 to a crop, with yield (lb/a) as the measured variable. Consequently, these designs are widely used in factor screening experiments. An example of a full factorial design with 3 factors: The following is an example of a full factorial design with 3 factors that also illustrates replication, randomization, and added center points. 15C + 0. Learn more […] Jan 2, 2023 · Figure 5. For example, in our previous scenario we could analyze the following main effects: Main effect of sunlight on plant growth. The analysis begins with a two-level, three-variable experimental design - also written 23 2 3, with n = 2 n = 2 levels for each factor, k = 3 k = 3 different factors. 1 The fractional factorial design expressed in Table 52. 8 Tests to test all combinations. A main effect is the statistical relationship between one independent variable and a dependent variable-averaging across the levels of the other independent variable (s). , AB , AC , and BC ), as well as their three-way interaction ( ABC ). One commonly-used response surface design is a 2k factorial design. Experiments where the effects of more then one one factors are Oct 4, 2022 · We are going to explore the appropriate mixed-effects regression (MER) models for these different situations: When we have a single crossed factor (i. , first-order interaction, as well as the three-factor interaction, i. Suppose that we wish to improve the yield of a polishing operation. A factorial design is often used by scientists wishing to understand the effect of two or more independent variables upon a single dependent variable. The above table contains all the conditions required for a full factorial 4 FACTORIAL DESIGNS 4. Can estimate 127 effects. In this example, time in instruction has two levels and setting has two levels. A level is a subdivision of a factor. But here we’ll include a new factor for dosage that has two levels. Also allows initial study of interactions. < simple effects in same direction, but different sizes. Two-Level Full Factorial Design ¶. 2001). 3. The nested factor in the second stage is head within machine (denoted Head(Machine)). First, we consider an example to understand the utility of factorial experiments. 5 – 0. 1. In the worksheet, Minitab displays the names of the factors and the names of the levels. Mar 5, 2018 · Yates Algorithm. The factor structure in this 2 x 2 x 3 factorial experiment is: Factor 1: Dosage. Main effect is an average effect. 3 used. The fabric is “padded”, and this factor has three levels: 25%, 50%, and 75% . A 2k factorial design is a k-factor design such that (i) Each factor has two levels (coded 1 and +1). described previously, and the next stage is the selection of the environmental design, which involves the form of experimental designs such as: Completely Randomized Design (CRD) Randomized Complete Block Design (RCBD) In two-level factorial designs, can incorporate Boolean variables. A treatment applied to the surface of the fabric. 65F + 0. Quality loss can be used to make decisions based on economic considerations of mean shift versus variability. With 3 factors that each have 3 levels, the design has 27 runs. Example: full 25 factorial would require 32 runs. 4. We will start by looking at just two factors and then generalize to more than two factors. I used the bar notation to specify a complete factorial model and to obtain all cell and marginal means. Surface treatment. This is a full An experimenter is interested in studying the effects of three factors—cutting speed ( Speed ), feed rate ( FeedRate ), and tool angle ( Angle )—on the surface finish of a metallic part and decides to run a complete factorial experiment with two levels for each factor as follows: Factor. 300. a. Main Effects and Interactions. The factors varied were as follows (book has −/+ reversed): Label Definition − + A acid concentration 20 30 B catalyst concentration 1 2 C temperature 100 150 D monomer concentration 25 50 The design was a full factorial in A, B, and C with D Each factor has 2 levels, so the scientist uses Create 2-Level Factorial Design (Default Generators) to create a 5-factor, 16-run experiment, with 4 blocks. to/34YNs3W OR https://amzn. Below is a figure of the factors and levels as well as the table representing this experimental space. Nitrogen flow: N 1, N 2 c. September. Note that, in general, the base design for a 4 m 2n-p design will be a 2 k-p design where k=2 m + n. al. 2 levels (Early first cutting and Late first cutting). In this example three randomly selected operators are Jan 1, 2023 · Abstract. Grass. RANDOMIZED COMPLETE BLOCK DESIGN WITH AND WITHOUT SUBSAMPLES. The results are shown here: Imagine, for example, an experiment on the effect of cell phone use (yes vs. Factorial designs can address more than one question in one study in an elegant manner and significantly reduce the required sample size. From Number of factors, select 5. Factor 3: Setting. shows an example of a 2 4 factorial design. 7. 1: Boxplot for distribution of height by species organized by fertilizer. arranged in a CRD, RCBD, or a Latin-Square and then assigning the levels of a second factor to subplots within each main plot. In a full factorial experiment, factors are completely crossed; that is, the factors and their levels are combined so that the design comprises every possible combination of the factor levels. Each factor has two levels (often labeled + and ) ¡. If factor A has 3 levels and factor B has 5 then it is a 3 x 5 factorial experiment. Fractional factorial designs are among the most important statistical contributions to the efficient exploration of the effects of several controllable factors on a response of interest. The three-level design is written as a 3 k factorial design. 5. Full Factorial Experiment 2 3 1. The columns of the table represent cell phone use, and the rows represent time of day. These are (usually) referred to as low, intermediate and high levels. Traditional research methods generally study the effect of one variable at a time, because it is statistically easier to manipulate. A design which contains a subset of factor level combinations from a full factorial design is called a fractional factorial design. Fractional Factorial Study Design Example 12 of 47. is a service of the National Institutes of Health. Table 5. Microsoft Word - DOE - An example of 2-factor factorial design. The split-plot design results from a specialized randomization scheme for a factorial experiment. Face Centered CCF In this design the star points are at the center of each face of the factorial space, so \( \alpha \) = ± 1. i. High Level. It can be misleading when an interaction is present. Notation for a balanced two-stage nested design with factors Aand B(A). EMS formulas and F-tests for factorial vs nested designs, in two-factor studies. These two approaches are illustrated on the following simple example that deals with Chapter 5 Blocking in factorial designs. In the above-mentioned example, intellectual ability and weekly study habits would both be considered factors. This design also requires 5 levels of each factor. σ ^ 2 = M S E. , 3-factor interactions) may be confounded with the terms in the model. PROC GLM; CLASS Experience Road Time; or to achieve a design target, this action can be tempered by selecting alternate factors and levels to achieve greater robustness in reducing variability. May not have sources (time,money,etc) for full factorial design. Some or all of the higher-order terms (e. 2k Factorial Design. This is shown in the factorial design table in Figure 3. Example: An experiment is carried out to evaluate the effects of three factors on the amount of wear sustained by fabrics in a standard abrasion test. 1 5. Example: Suppose the yield from different plots in an agricultural experiment depends upon 1. The data set contains eight measurements from a two-level, full factorial design with three factors. Feed (excluding I) is termed the design resolution” For this example, Design Resolution = III. For example, a recent factorial experiment ( Schlam et al. The factor in the rst stage is Machine. Mar 4, 2022 · Representation of a Complete Factorial (FC) statistical design with three levels and three factors (33). These levels are numerically expressed as 0, 1, and 2. Because 1⁄4=(1⁄2)2=2-2, this is referred to as a 25-2 design. , second-order interaction. When we have multiple crossed factors (i. 4 Importance of Interaction. 6 levels (KBG, MB, OG, PRB, PRM, and TF). 2. Cutting speed. Very useful design for preliminary analysis 2. We can find the mean plant growth of all plants Jan 1, 2010 · Huang et al. 1 Introduction The treatment design in our drug example contains a single treatment factor, and one of four drugs is administered to each mouse. x = -1 if no catalyst. 1 - Factorial Designs with Two Treatment Factors. The original analysis was performed primarily by Lisa Gill of the Statistical Engineering Division. Often, coding the levels as (1) low/high, (2) -/+, (3) -1/+1, or (4) 0/1 is more convenient and meaningful than the actual level of the factors, especially for the designs and analyses of the factorial experiments. These studies are often called gauge capability studies or gauge repeatability and reproducibility (R&R) studies. 4 Statistical Analysis of 23 Factorial Experiments 12. = III: Main effects are confounded with two factor interactions (1 with 2) and 3=1+2. In this example we have two factors: time in instruction and setting. It is possible 12. 1 Full Factorial Design For this experiment we are conducting a full factorial design. You can interchange C and S and still get the same result. An experiment with only 8 runs is a 1/4th (quarter) fraction. The Three patterns that have an interaction: = vs. To run the two-factor factorial model with interaction in SAS proc mixed, we can use: /*Runs the two-factor factorial model with interaction*/. When interaction is present we should examine the effect of any factor of interest at each level of the interacting factor before making interpretation (Minimum et. However, selecting 3 for the number of levels and consulting the array selector, we see that an L18 array will suffice for a Taguchi analysis. It looks almost the same as the randomized block design model only now we are including an interaction term: Y i j k = μ + α i + β j + ( α β) i j + e i j k. 5A + 0. 5) 2 or more factors Not the same as doing two one-way ANOVAs Tests for the effects of each independent variable plus their interaction. A. a= number of levels of factor A b= number of levels of factor Mar 29, 1999 · Table 3. The four cells of the table represent the four possible Introduction. The factors are: Proportion of filler. proc mixed data=greenhouse_2way method=type3; class fert species; Microsoft PowerPoint - Lecture5_factorial. 18 is a much more feasible number of experiments than 108. An Experimental Design for a 2 7-3 design, where E=ABC, F=BCD, and G=ACD. The analysis of variance (ANOVA) will be used as one of the primary tools for statistical For example, in the first run of the experiment, Factor A is at level 1. + High - Low Factor B High + Low - Low High Factor C Factor A + - a ab abc bc c (1) b ac (a) Geometric Figure 6-4 The \(2^3\) factorial design Factorial Design Matrix Table 3. = IV: Main effects ar e confounded with three factor interactions (1 with 3) and 4=1+3. 2. We start by encoding each fo the three variables to something generic: (x1,x2,x3) ( x 1, x 2, x 3). Temperature: T 1, T 2 b. Select the 1/2 fraction design. The design of an experiment plays a major role in the eventual solution of the problem. Can \weed out" unimportant factors. Nov 29, 2016 · That means for a three factor factorial experiment we shall have two-factor interaction, i. Thus, the design is a 3 × 2 factorial design where Lecture Type is a betweensubjects factor and - Time (pre/post) is a within-subjects factor. to/3x6ufcEThis lecture explains Two-Factor Factorial Design Experiments. Design of Experiments - Montgomery Chapter 6. Fractional As the factorial design is primarily used for screening variables, only two levels are enough. It is popular in psychological research to investigate the effects of two factors on behavior or outcome. Calculate in the same way as above. Factors B and C are at level 3. Factorial designs are the basis for another important principle besides blocking - examining several factors simultaneously. The randomized complete block design (RCBD) is perhaps the most commonly encountered design that can be analyzed as a two-way AOV. 0 license and was authored, remixed, and/or curated by Penn State's Department of Statistics. Two patterns that have no interaction: 4. An experiment with 3 levels of Factor A, 4 levels of Factor B, and 2 levels of Factor C will be referred to as a 3x4x2 factorial experiment. The Split-Plot Design. What does Design Resolution mean? • Des. In the "Effect" column, we list the main effects and The modeling designs for 2 to 5 factors are all full-factorial or resolution V designs. This variety requires 3 levels of each factor. , two within-subjects factors) in our mixed-effects model. Factorial experiment design or simply factorial design is a systematic method for Each combination of a single level selected from every factor is present once. In general, an n-factor study decreases the required sample size by a factor of n. Consider 2k design. One could have considered the digits -1, 0, and +1, but this may be confusing with respect to the 2 Jan 5, 2024 · Some common types of it include: 2×2 factorial design: It involves two independent variables, each with two levels. Only 7 df for main effects, 21 for 2-factor interactions. 1 Two Factor Factorial Designs A two-factor factorial design is an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest. The three inputs (factors) that are considered important to the operation are An experimental design consists of a careful description of how a particular hypothesis can be experimentally tested. 1 Coding (High(+1), Low(-1)) 3-way Factorial Designs The simplest factorial design is a 2x2, which can be expanded in two ways: 1) Adding conditions to one, the other, or both IVs 2) Add a 3rd IV (making a 3-way factorial design) Learning Psyc Methods Learning Psyc Content Ugrads Grads Ugrads Grads Computer Instruction Lecture Instruction Identify the three IVs in this What’s Design of Experiments – Full Factorial in Minitab? DOE, or Design of Experiments is an active method of manipulating a process as opposed to passively observing a process. 1. Example: 2 3: Polysilicon Growth i. , 2 × 2, 3 × 3, or 4 × 4) requires half the number of patients that running two separate 2-4 factors: Full or fractional factorial design 5 or more factors: fractional factorial or Plackett-Burman 4 Types of Experimental Designs Fractional Factorial Design: Use a fraction of the full factorial design. Defect density. 494, the upper-tail Jan 3, 2022 · An L9 with three-factor partial factorial design can be converted to a full factorial L27 with the addition of 18 experiments for factor C levels 2 and 3. DOE enables operators to evaluate the changes occurring in the output (Y Response,) of a process while changing one or more inputs (X Factors). In factorial designs, there are two kinds of results that are of interest: main effects and interactions. 2 in the textbook discusses a two-factor factorial with random effects on a measurement system capability study. Sep 9, 2021 · A 2×3 factorial design is a type of experimental design that allows researchers to understand the effects of two independent variables on a single dependent variable. This experiment is an example of a 2 2 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels #factors, producing 2 2 =4 factorial points. Legume. no) and time of day (day vs. 3×3 factorial design: It involves three independent variables, each with three levels. Low Level. In an incomplete, or frational factorial design, certain treatment combinations are deliberately Jan 2, 2023 · This page titled 6. This factor is not in the control of Let's take a look two examples using this same dataset using Minitab v19. For this Feb 27, 2019 · We illustrate this by simulating a 2 6 full factorial design (64 runs) with the model y = 1. For now we will just consider two treatment factors of interest. Dec 6, 2016 · the 2-factor factorial design with levels a for factor A, levels b for factor B and n replicates, or general full factorial designs with k -factors including 2 or more than 2 levels and n repli cates. Using excels built in spread sheet, graph and cell calculation abilities we can both design and analyze a full factorial experiment. The output shows that all three main effects are significant, as is the interaction between experience and time. Res. For example, suppose a botanist wants to understand the Chapter 6 of BHH (2nd ed) discusses fractional factorial designs. A dataframe with input variable values is Jan 16, 2011 · A 2x2x3 factorial experiment means a factorial experiment consisting of 3 factors with levels for each factor of 2, 2, and 3. Both the factors are in the control of the experimenter. (1998) give an extensive list of minimum aberration fractional factorial split-plot designs. Chapter 5. > simple effects in opposite directions. g. The following table is obtained for a 2-level, 4 factor, full factorial design. At the 0. Therefore, as we go on increasing the number of factors in any factorial experiment, then the type of interaction increases. It means that k factors are considered, each at 3 levels. < vs. What is to be optimized? a. Completely Randomized Factorial Designs (Ch. 4 can be used as a guide for which three-level array mode is best suited for the DoE goals, balancing the project effort versus results expected, within the constraint of time and An experiment is a test or series of tests. gov. Advantages of a Factorial Design. Conduct replicates 2 and 3 similarly. Common applications of 2k factorial designs (and the fractional factorial designs in Section 5 2. In general, 2k-p design is a (1⁄2)p fraction of a 2k design using 2k-p runs. To examine the main and interaction impact of these two factors, a researcher Consider an alternate experimental design: In replicate 1, select a pulp preparation method, prepare a batch. 2 would be annotated as 2 3−1, noting that each factor has two levels, that there are three factors, and that only half of the complete factorial is selected Jan 24, 2017 · So, for example, a 4×3 factorial design would involve two independent variables with four levels for one IV and three levels for the other IV. B. Choose Stat > DOE > Factorial > Create Factorial Design. In the completely randomized design, a random sample is included in each cell (nest) of the design Each subject appears I specified Type I – this would not be appropriate if the design were nonorthogonal. A fractional factorial design is often used as a screening experiment involving many factors factors in eight runs on the stability R of a product, with a desired level of 25 on the scale used. 2AB – 0. Click Designs. Silane Flow: S 1, S 2 ii. For the ST interaction, there are two estimates of S T: ( − 1 + 0) / 2 = − 0. However, in many cases, two factors may be interdependent, and This statement is now explained by an example: Consider a design with five factors at 2, 2, 3, 3, 6 levels. Because the manager created a full factorial design, the manager can estimate all of the 5. This requires: (a) an explicit specification of the treatment factors to be tested; (b) the specific range of values over which these treatment factors will be tested; (c) the manner in which observations will be generated, recorded, and reported; and (d) the criteria that will Feb 1, 2023 · The average CS interaction is therefore ( − 13 − 14) / 2 = − 13. The Yates algorithm is demonstrated for the eddy current data set. In a factorial experimental design, experimental trials (or runs) are performed at all combinations of the factor levels. where i = 1, …, a, j = 1, …, b, and k = 1, …, n. Example of a 2x2 factorial Below is an example of a CRD involving two factors: nitrogen levels (N0 and N1) and phosphorous levels (P0 and P1) applied to a crop. e. The video demonstrations are based on Minitab v19. (ii) The 2 kexperimental runs are based on the 2 combinations of the 1 factor levels. All possible combinations of the variables are used in the various runs. (i) variety of crop and (ii) type of fertilizer. The predicted DoE outcome can be determined when design factors are set to Within this approach, the term factorial refers to a design which has two or more independent variables, also known as factors (Kerlinger & Lee, 2000 ). of main e ects and low-order interactions from only a fraction of the full factorial design. We’ll use the same factors as above for the first two factors. The main effect of multiple components can be measured with the same number of participants as a classic two-arm randomized controlled trial (RCT) while maintaining adequate statistical power. These factor-level combinations are used to calculate the main effects of factors A , B , and C , their two-way interaction (i. 6 Solutions / Answers 12. to illustrate the design and notation. If k = 7 → 128 runs required. 3: Random Effects in Factorial and Nested Designs is shared under a CC BY-NC 4. Sometimes we depict a factorial design with a numbering notation. n=3*2=6 Some interactions among factors may The factor memory size was eliminated. Mar 23, 2022 · For books, we may refer to these: https://amzn. In the following table, I represent the betweensubjects factor, Lecture Type, as Factor - A, and the within-subjects factor, Time, as Factor . < simple effects of the same size in the same direction. We now consider splitting the treatments in a factorial design into blocks. = +1 if catalyst used. 6. It can also be two Full factorial example. This data set was taken from an experiment that was performed a few years ago at NIST by Said Jahanmir of the Ceramics Division in the Material Science and Engineering Laboratory. In this type of design, one independent variable has two levels and the other independent variable has three levels. Oct 20, 2019 · The video explains with an example and an exercise that you can perform how to design and analyze a 3 factor, two level, designed experiment. The purpose of the experiment is to identify factors that have the most effect on eddy current measurements. The 6-level factor can be thought of as consisting of two pseudo-factors, a 2-level and a 3-level pseudo-factor, according to the factorization of the number 6 into the two primes 2 and 3. vs rp sz ww wb ob et nj jw zj