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A Brief Introduction to Factorial Design

  • Pragya Soni
  • Apr 27, 2022
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Research and innovation are the important aspects of life sciences. Research is further classified into several types. From the experimental research to final research. All these categories of research ensure quality product and techniques development. In this blog we will study about Factorial Design, which is basically the subset of experimental design.



What is Experimental Research?


Before analyzing the term Factorial Design. Let us understand a brief description of the main subject, Experimental Research. Experimental research is the most popular form of research design. It is a form of quantitative research method. It is widely employed in the physical sciences, life sciences, social sciences, physiology, education as well as another field.


Remember our high school experiments and practicality, when in class 8th and 9th we used to prepare sodium chloride by mixing sodium hydroxide and hydrochloric acid in a beaker? 


Or, consider a simple biology experiment, where we study the effect of sunlight on a plant’s growth. Those experiments are more or less similar to experimental research. Experimental research mainly consists of classical science experiments.




In scientific terms, Experimental Research is defined as a scientific approach to research. In an experimental research one or more independent variables are manipulated and their casualty with dependent variables is applied. In shorter words, the relation between one independent variable and another dependent variable is studied.


Usually, the effect of the independent variables on dependent variables is recorded and measured. In research, variables are defined as any characteristics or attributes, physical or chemical that can take different values throughout the research. Researchers often manipulate the values of variables to derive a universal conclusion.


Also Read | Different Types of Research Methods



Types of Experimental Research Design


There are broadly three types of experimental research designs that are employed according to the needs and desires of the researchers as well as experiments. The three types of experimental research design are as follows:

Types of experimental research design:1. Pre-experimental research design2. Quasi-experimental research design3. True experimental research design

Types of Experimental Research Design


  1. Pre-experimental Research Design


Pre-experimental research design is the simplest form of research design. It is evaluated with no control group. Under this process, a group of dependent variables are observed under the effect of an independent variable that is suspected to bring change in the other. 


Pre-experimental research design is further classified into three categories:


  • One-shot case study research design (here only one dependent variable is considered)
  • One-group pretest-posttest research design (consider both pretest and posttest studies)
  • Static group comparison (multiple dependent variables are placed under the observation)



  1. Quasi-experimental Research Design


As the term itself suggests, quasi means half or partially. Quasi-experimental research design is the intermediate between pre and true experimental research. It is quite similar to the true experimental research design but yet not the same as the latter. 


Under this process variables are not selected randomly; they are selected by some proper procedures. The common examples of quasi-experimental design include the variables from the education field. 


In educational research, administrators are unwilling to allow random selection of the variables or students to serve research purposes. Other examples include, the time series testing and the counterbalanced design.



  1. True Experimental Research Design


As the name suggests true experimental research design is the final research designing. It is responsible for the approval or dismissal of a hypothesis. It is the most accurate and hence toughest experimental design of all. Usually, it is conducted on at least 2 randomly assigned dependent variables.


The components of a true experimental research design are a control group, a variable, and random distribution. This experimental design is further classified as posttest control group design, pretest-posttest control design and Solomon four group design.


Also Read | Hypothesis Testing



What is Factorial Design?


Now let us come to the term factorial design. Factorial design is an aspect of experimental design. As explained in the above part of the blog, many experiments require two or more variables for the research conduct. 


In practical form, it becomes hard for the researchers to find all the possible combinations of the levels of the variables and factors for the investigation process.


Thus, researchers employ a technique named Factorial Design. Factorial design helps to complete the trial and replication of an experiment. It also investigates all possible combinations of the variables and functions. Thus, factorial design makes the tasks of researchers easier and reliable.



How does Factorial Design Work?


A factorial design simply works by replicating the levels of factors or variables. Let us consider a simple example to understand this process more clearly. For a particular experiment, there are two variables used A and B. Variable A has a levels, while the other variable B has b levels.


The factorial design will form a replicate that contains all possible ab combinations. In literal terms, factorial design will investigate the influence of all the experimental variables, factors and integration effects on the response. If the variable or factor consists of k factors. 


The total of 2k experiments will be performed. Or, if the 2 variables are involved in the research a total of 4 experiments would be performed, if 8 variables are involving factorial design will conduct 256 experiments.


Though, it is not always essential to conduct experimental research in factorial design format. But for the experiments involving a higher number of variables, factorial design is generally a good and efficient experimental approach. 


The reasons behind it are that the risk of missing non-linear relationships in between the process is generally minimized in factorial design and repetition allows the determination of confidence intervals.


Also Read | Guide to Market Research Analysis



Types of Factorial Design


For experimental research first the purpose of the experiment is studied. Later a list of variables is made. Once the investigation of a variable is done, an experimental design is chosen to estimate the influence of independent variables on dependent variables.


For the factor replication value, factorial design is chosen. The low level factors are denoted by (-) symbols and high level factors are represented by plus (+) symbols.


Factorial design is further classified into several types. The types of factorial design vary as the value of k fluctuates. In this blog, we will consider two cases of factorial design 22 design and 23 design. These two designs are also known as two level factorial design. The other variations of factorial design are quite difficult to discuss in literal terms.


  1. The 22 Design


The 22 design is the simple case of factorial design. It is the series that contains only two variables and most of the time factors run at two levels. It is also known as – factorial design. The 22 design has an arbitrary level of factors.


For example, consider an agro-industry process of producing caffeine pellets. The aim of the experiment is to produce a certain size of pellets, let us say laying between 0.71 mm to 1.4 mm and to obtain a yield higher than 95% of the total.


For this purpose, two variables are taken into consideration: amount of water in granulation (A) and spheronizer speed (B). A 22 factorial design approach is employed to conduct the research and evaluate the strength of the process. 


The level of the variables and yield response will be recorded by the process. The 22 design approach is widely used in the pharmaceuticals and food industry for pellet formation.


  1. The 23 Design


The 23 factorial design is quite similar to 22 factorial design. But the level of factors here can be arbitrary as well as fixed. In this series, the experimental design contains only three variables which can run at any level. A bit more complicated than 22 design, 23 design is quite simpler than other cases of factorial design.


For example, consider a pharmaceutical process that involves the formulation of the tablet. The aim of the experiment is to produce a tablet with consistent thickness and uniform size. The experiment also focusses to produce a universal amount of active drug ingredients in all the tablets.


For the experimental research, three variables will be considered, amount of active drug ingredient (A) which is responsible for the therapeutic value of the drug, amount of stearate (B) which is responsible for binding drug moiety, and amount of starch (C), that is responsible for the disintegration of tablet into GIT. For such cases a 23 factorial design is employed.


Also Read | Performance Testing



Advantages and Disadvantages of Factorial Design


Now let us conclude the blog by looking at the merits and limitations of Factorial Design.


Advantages of Factorial Design


The merits or advantages of factorial design are summed up as below:


  1. Factorial design helps in understanding the main effect of the experiment. A main effect is defined as the effect of one independent variable on a dependent variable, ignoring the effects of all other independent variables.


  1. Factorial designs are widely used by scientists, chemists and psychologists.


  1. Factorial design helps in preliminary studies, that further helps in developing and studying the link between several existing variables.


  1. Factorial design reduces the possibility of experimental error and confounding variables.


  1. Factorial design simplifies the research process and is cost-effective in nature.


  1. Factorial design highlights the relationships and causality between variables.


  1. Factorial design allows the effects of manipulating a single and isolated data.



Disadvantages of Factorial Design


The limitations of factorial design are as follows:


  1. Factorial design increases the total number of experiments to be performed.


  1. The increase in level and factors sometimes cause overlapping by three or more two factor interactions.


  1. It is difficult to conduct experiments involving more than two factors or multiple levels.


  1. Proper planning is required in factorial design.


  1. Any slight error in one of the levels can cause a systematic error in the whole data and analysis.


Also Read | Steps of Data Analysis



Other Important Tools of Experimental Design


Except factorial design there are several other tools and techniques employed for an experimental design. Here is a brief introduction to the major ones:


  1. Response surface methodology: Response surface methodology is used for the collection of mathematical, graphical, and statistical data for modeling a problem. Response surface methodology is a part of problem-solving assessment and is used to analyze the factors of a problem.


  1. D-Optimal design: D-optimal design is used for the construction of a quadratic model design for the conduct of scientific experiments.


  1. Historical design: Historical designs are employed to collect, verify and scenarize the past evidence to establish the facts to defend or protect a hypothesis.


  1. Optimization techniques: Optimization techniques are useful for finding the optimum solution or unconstrained maxima or minima of continuous or differentiable functions. It also includes basic SEO techniques for the collection and retrieval of data.


Experiments and research, especially in the medical field, are essential for the benefits of living beings. And for a proper experimental research, factorial design is essential as it governs the minimum chances of errors, overlapping and validates all the possible combinations.

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