Subtopic 1.1

1.1

Principle of Experimental Design

Introduction

The foundation of any successful experiment lies in its design. Experimental design is a structured approach that enables researchers to systematically investigate relationships between variables while minimizing errors and biases. Understanding the basic principles of experimental design is crucial for ensuring the validity and reliability of findings. In this subtopic, we will explore key concepts of experiment and examine how to select participants, assign treatments, and manage external factors that could influence results, allowing us to draw meaningful and accurate conclusions from the data.

Learning Outcome (LO)

Upon completion of this lesson, you should be able to: LO1: Identify the basic principles of experimental design

1.1

Principle of Experimental Design

Do you remember learning about this back in high school or junior high even? What were those steps again? Decide what phenomenon you wish to investigate. Specify how you can manipulate the factor and hold all other conditions fixed, then measure your chosen response variable at several (at least two) settings of the factor under study. If changing the factor causes the phenomenon to change, then you conclude that there is indeed a cause-and-effect relationship at work. This is the concept of experimental design that we will address in this course.

If we had infinite time and resource budgets there probably wouldn't be a big fuss made over designing experiments. In production and quality control we want to control the error and learn as much as we can about the process or the underlying theory with the resources at hand. From an engineering perspective we're trying to use experimentation for the following purposes:

• reduce time to design/develop new products & processes
• improve performance of existing processes
• improve reliability and performance of products
• achieve product & process robustness
• perform evaluation of materials, design alternatives, setting component & system tolerances, etc.

We always want to fine-tune or improve the process. In today's global world this drive for competitiveness affects all of us both as consumers and producers.

In general, experiments are used to study the performance of processes and systems. The process or system can be represented by the model shown in Figure 1.1. We can usually visualize the process as a combination of operations, machines, methods, people, and other resources that transforms some input (often a material) into an output that has one or more observable response variables.

Some of the process variables and material properties x1, x2, . . . , xp are controllable, whereas other variables z1, z2, . . . , zq are uncontrollable (although they may be controllable for purposes of a test).

The objectives of the experiment may include the following:1) Determining which variables are most influential on the response y 2) Determining where to set the influential x’s so that y is almost always near the desired nominal value 3) Determining where to set the influential x’s so that variability in y is small 4) Determining where to set the influential x’s so that the effects of the uncontrollable variables z1, z2, . . . , zq are minimized.

FIGURE 1.1 General model of a process or system

Usually, an objective of the experimenter is to determine the influence that these factors have on the output response of the system. The general approach to planning and conducting the experiment is called the strategy of experimentation. This strategy serves as a framework for systematically addressing research questions and optimizing experimental outcomes. At its core, the strategy relies on basic principles of experimentation, such as 1) randomization 2) replication 3) blocking These principles ensure that the experiment is not only well-structured but also robust, minimizing bias and enhancing the reliability and validity of the results.

There are three basic principles of experimental design are randomization, replication, and blocking.

Randomization

Replication

Blocking

1) Randomization

This is an essential component of any experiment that is going to have validity. The aspect of recording observations in an experiment in a random order is referred to as randomization. Specifically, randomization is the process of assigning the various levels of the investigated factors to the experimental units in a random fashion. An experiment is said to be completely randomized if the probability of an experimental unit to be subjected to any level of a factor is equal for all the experimental units. The importance of randomization can be illustrated using an example.

Consider an experiment where the effect of the speed of a lathe machine on the surface finish of a product is being investigated. In order to save time, the experimenter records surface finish values by running the lathe machine continuously and recording observations in the order of increasing speeds.

The analysis of the experiment data shows that an increase in lathe speeds causes a decrease in the quality of surface finish. However the results of the experiment are disputed by the lathe operator who claims that he has been able to obtain better surface finish quality in the products by operating the lathe machine at higher speeds. It is later found that the faulty results were caused because of overheating of the tool used in the machine. Since the lathe was run continuously in the order of increased speeds the observations were recorded in the order of increased tool temperatures.

This problem could have been avoided if the experimenter had randomized the experiment and taken reading at the various lathe speeds in a random fashion. This would require the experimenter to stop and restart the machine at every observation, thereby keeping the temperature of the tool within a reasonable range. Randomization would have ensured that the effect of heating of the machine tool is not included in the experiment.

Completely Randomize Design (CRD)

A Completely Randomized Design (CRD) is one of the simplest experimental designs where subjects are assigned to treatment groups purely by chance. In CRD, every subject has an equal chance of being placed in any of the treatment groups, ensuring random allocation.Key Characteristics of CRD:

• Simple Structure: The experimental units (participants) are randomly assigned to different treatment groups.
• No Restriction: The random assignment is not restricted by any factors such as age, gender, or baseline conditions.
• Homogeneous Population: Assumes that the population from which participants are drawn is relatively homogeneous or that randomization balances differences.

The CRD will be discussed further in the topic "Analysis of Variance."

2) Replication

Replication is the basic issue behind every method we will use in order to get a handle on how precise our estimates are at the end. We always want to estimate or control the uncertainty in our results. We achieve this estimate through replication.It refers to the repetition of the experiment under identical conditions to estimate the experimental error and increase the precision of the results. Replicating an experiment ensures that the results are not due to random chance or external factors, and provides a more reliable estimate of the effects of the variables being studied.

There are 3 key aspects of replication:

• Error Estimation: By repeating the experiment, you can calculate the variation in the results and assess the consistency of the findings.
• Increased Precision: It reduces the noise in the data and increases the ability to detect a true effect.
• Generalizability: Replication allows the results to be more generalizable because it shows that the findings can be repeated and are not just a one-time occurrence.

In an experiment to study the effects of fertilizer and water on plant growth, replication is applied to ensure reliable and accurate results. The experiment involves testing three levels of fertilizer (Low, Medium, High) and two levels of water (1L, 2L), resulting in six different combinations. To improve the precision of the findings, the experiment is replicated three times for each combination, making a total of 18 trials (6 combinations × 3 replications). Replication allows the researchers to assess the variability in plant growth under the same conditions, helping to identify whether the results are consistent across different trials. By repeating the experiment, they can estimate experimental error, reduce random variations, and ensure that the effects observed are due to the treatments themselves and not external factors.

3) Blocking

Many times a factorial experiment requires so many runs that not all of them can be completed under homogeneous conditions. This may lead to inclusion of the effects of nuisance factors into the investigation. Nuisance factors are factors that have an effect on the response but are not of primary interest to the investigator.For example, two replicates of a two factor factorial experiment require eight runs. If four runs require the duration of one day to be completed, then the total experiment will require two days to be completed. The difference in the conditions on the two days may introduce effects on the response that are not the result of the two factors being investigated. Therefore, the day is a nuisance factor for this experiment. Nuisance factors can be accounted for using blocking.

In blocking, experimental runs are separated based on levels of the nuisance factor. For the case of the two factor factorial experiment (where the day is a nuisance factor), separation can be made into two groups or blocks: runs that are carried out on the first day belong to block 1, and runs that are carried out on the second day belong to block 2. Thus, within each block conditions are the same with respect to the nuisance factor. As a result, each block investigates the effects of the factors of interest, while the difference in the blocks measures the effect of the nuisance factor.

For example, in human studies, the gender of the subjects is often an important factor. Age is another factor affecting the response. Age and gender are often considered nuisance factors which contribute to variability and make it difficult to assess systematic effects of a treatment. By using these as blocking factors, you can avoid biases that might occur due to differences between the allocation of subjects to the treatments, and as a way of accounting for some noise in the experiment. We want the unknown error variance at the end of the experiment to be as small as possible. Our goal is usually to find out something about a treatment factor (or a factor of primary interest), but in addition to this, we want to include any blocking factors that will explain variation.

Steps for Planning, Conducting and Analyzing an Experiment

The practical steps needed for planning and conducting an experiment include: recognizing the goal of the experiment, choice of factors, choice of response, choice of the design, analysis and then drawing conclusions. This pretty much covers the steps involved in the scientific method. What this course will deal with primarily is the choice of the design. This focus includes all the related issues about how we handle these factors in conducting our experiments.

1. Recognition and statement of the problem 2. Choice of factors, levels, and ranges 3. Selection of the response variable(s) 4. Choice of design 5. Conducting the experiment 6. Statistical analysis 7. Drawing conclusions, and making recommendations

Now that you've mastered the basics principle of experimental design, let’s dive into the next exciting subtopic and discover how design factors shape the outcomes of your experiments!

- Dr. Nurulhuda