# 3 Experimentation

Learning Objectives

After completing this session, you will be able to:

• define experiment.
• Identify the characteristics of a basic experiment.
• discuss the relationship between dependent and independent variables in experiments.

Although can be formally defined in different ways, depending on the context, for a Business Management Student, it can be defined as trying out different things to get the best result. In fact, we do experiments in our daily life also. While cooking, we often change the ingredients or change their proportion or change time of cooking etc. Our objective is to get a better taste. A company can introduce promotional offer or discounts to increase sales. Experiments are conducted at the Causal Stage of a Research where we try to identify factors that influence Response (result).

In an experiment there is one dependent variable (Y) and one or more independent variables (X). Let’s take a simple example. In order to decide the price at which we want to launch a new product, we decided to try out three different prices in randomly chosen stores (in one store only one price). So, my X variable is Price. If P1, P2 and P3 are the three prices we are trying, these will be called Level of the Variable (or Factor) X. Here dependent variable Y is the sales of the product at each of the three prices.

In experimental research we study effect of one or more variables (typically they are called independent variables or Factors) on another variable (called dependent variable or Response). Different values of independent variables are tried to check how they impact the dependent variables. For example, suppose in a research we want to determine what should be the price of a product to increase sales. So, independent variable (or Factor) is Price. Sales is the Response. Our objective is to determine the best price for higher sales. So, we choose three different values of Price, say P1, P2 and P3 (these are known as Levels of the Factor) and try to sell the product at different locations. This is a simple experiment involving only one Factor (as we are trying only one independent variable). This is also called Primary experiment.

In Business Research, we often study attitude of people. Data are collected from individuals. In the above example, some buyers prefer P1 price, some P2 and so on. This is due to their preference, perception etc. The individuals from whom we collect the data are called ‘Subjects’.

There are three types of primary experimental research depending on how subjects are allocated to different conditions. These are Pre-experimental, Quasi-experimental and True experimental research. In these experiments one or more groups of subjects are used. They are often called “” (Group in which no change is allowed) and “Experimental Group” (Group which receives experimental conditions or ‘Treatments’).

Pre-experimental Research: One or more groups of subjects are kept under observation after implementing a factor. This is to understand whether further investigation may be conducted. For example, new recruits in a company are given a special training for a period and observed their on-job performance. There are different types of Pre-experimental Research. Some of them are mentioned below,

• One-shot Case Study (After only design): As the name suggest, here we have only one group of subjects, which is Experimental Group. They receive Treatment (denoted by ‘X’). Response (O1) is measured. Pictorially this is shown as below.
 Group Treatment Post-Test Experimental X O1

The example of new recruits and training mentioned above is a example of this design.

• One Group Pre-Test Post-Test Design: Here also we have one group only – Experimental group. Response is measured before and after they receive the Treatment. The difference indicates the effect of the treatment.
 Group Pre-Test Treatment Post-Test Experimental O1 X O2

For example, a few of the employees are selected for a training. They are assessed before start of the training (O1). Then they receive the training (X) and again assessed at the end of the training (O2). So, the difference O2 – O1 is the measure of Treatment Effect.

• Static-Group Design: Here we have one Control Group and one Experimental Group. There is no Pre-Test done.
 Group Treatment Post-Test Control O1 Experimental X O2

This is often very useful as we may not get a Pre-Test opportunity in certain situation. Hence, based on some criteria we split a group into two part – call one as Control Group and other as Experimental Group. Continuing with the example of training of employees, we may form an Experimental Group with those scoring low in Annual Appraisal and they are given special training for improving their performance.

True Experiments: True experimental research has a strong base of statistical analysis to prove or disprove a hypothesis. This can establish a cause-effect relationship between the Response and independent variables.

In a True Experiment, followings are required

• Control Group and Experimental Group
• Use of Treatment on Experimental Group
• Pre and Post Test measurement
 Group Pre-Test Treatment Post-Test Control O1 O2 Experimental O3 X O4

O2-O1 measures change in performance in Control Group. This change may be due to self-learning / experience or any other self-motivating factor. O4-O1 is the change in performance of Experimental Group. This is expected to be due to the Treatment and all factors mentioned in the Control Group. So, the difference of (O4-O3) and (O2-O1) is due to the Treatment only.

: Quasi experiment is similar to True experiment and tries to establish a cause- effect relation between independent and dependent variables. However, unlike a true experiment, a quasi-experiment does not follow sound statistical principles of . Subjects are assigned to groups based on non-random criteria. Though it has this drawback, it is a useful in situations where true experiments cannot be done for practical reasons.

The experiments described above try to establish a Cause-Effect relation between a Dependent and Independent variable. However, as we have seen earlier in Correlation-Regression, that in reality one variable usually depends on multiple variables (Factors here). So, to execute an experiment meaningfully to arrive at the best possible result, often we need to consider multiple Factors simultaneously. These are called Statistical Design of Experiment (DOE). We will learn a few such designs here.

• Completely Randomized Design (CRD)
• Randomized Block Design (RBD)
• Latin Square Design (LSD)
• Full Factorial Design.

There are many more designs available and also many variations of the above are there.

Completely Randomized Design: A completely randomized design (CRD) is a design where Treatments are assigned “at random” to the experimental units, so that each has the same probability of receiving a treatment. So, CRD is appropriate for experiments with homogeneous experimental units.

In CRD, one Factor is tried with different Levels on experimental units and Response is measure. Suppose we are trying 3 different Price and we have chosen 12 stores to try. Hence each price can be tried at 4 stores. Write P1 in four pieces of papers, P2 on another 4 and P3 on 4 more. So, we have 12 pieces of papers with either P1 or P2 or P3. Label 12 stores with 1 – 12 numbers and thus create another 12 pieces of papers with store number. Draw one store number and one chit with price written and make an allocation. Thus, we decide which price to try at which store. Once the allocation is done, collect the Response data (i.e. Sales). The data is analyzed using one-way                                                                                                                                 and optimum Price is determined.

Randomized Block Design (RBD): In CRD we assume that the experimental units are homogeneous. In the above example, we assumed the 12 stores, selected for the experiments are homogeneous i.e. no different impact of stores. However, this may not be a right assumption. If the store selected is in a posh locality and another store at the fringe of the city limit – they cannot be treated as ‘similar’ (with respect to the type of customers they receive and hence their perception on product-price etc.). Thus, ‘Locality’ may be a Factor, which may influence our study. In an RBD, this external influencing Factor is called a Blocking Factor and the design blocks its impact on the Response. All Levels of the Factor under study are tried in each Block and analyzed using a two-way ANOVA.

Latin-Square Design (LSD): LSD has two blocking factors (RBD has one blocking factor). The fundamental idea of blocking is extended to more dimensions. Blocking simultaneously with complete blocks in two directions is done with a Latin Square design. However, there are certain limitations of LSD. The limitation is that the Latin Square experimental layout will only be possible if the number of Row blocks = number of Column blocks = number of treatment levels.

Full Factorial Design: Factorial design is one of the most useful design in industry, as it helps estimate effect of multiple factors and their combined impact on Response simultaneously. Suppose, three Factors are tried simultaneously in a Full Factorial Design, each having two Levels as given below.

 Factors Promotions Discounts Home Delivery Level-1 Nil Nil No Level-2 Free movie ticket (2) 10% for bill above Rs 2000 Free for bill above Rs 5000

The response for this trial is the sales figure. A total of 23 = 8 trials will be required to cover all Factor Level Combinations. That’s why this is called Full Factorial Design. The data is analyzed using ANOVA and also other methods.