An Introduction to Sampling

A good portion of the remainder of this course relies on the use of sampling to try and understand population characteristics and various relationships that may exist. This latter half of this course is called inferential statistics – which means that we draw inferences about the population by using samples. In the end, we use the information from the sample to improve business decision-making.

What is a Random Sample and Why is it Important?

It is true that many of our beliefs about the characteristics of a population come from a relatively small sample of that population. The reason for sampling is quite simple:

• we often don’t have the time,
• money
• or the resources to measure the entire population.

We will also find that the amount of information and the accuracy associated with using sampling can be well defined leaving us with a good understanding of the population characteristics that are being studied.

Three Important Rules When Taking Random Samples

In taking a random sample from the population there are 3 important rules to remember:·

1.    We want the sample to be as representative as possible of the population.

2.    We need to try to avoid bias in our sampling

3.    A simple random sample means that each item in the population has an equal probability of being selected.

Importance of the Three rules

Why are these rules important how can they help us? They can:

• Can help us set up our study
• To ensure that we are not starting off with errors in our study.

Representative, Random, Non-Bias Samples (Examples)

Let us examine what it looks like for a sample to be random, representative and non-bias in our first example for this section below.

Example 42.1

Problem Setup: We are trying to conduct a study that has to do with ALL BCIT students, we need to consider the fact that we have day school, night school and various campuses throughout the Lower Mainland.

Question: How to we construct a representative sample of ALL BCIT students?

Solution:

1. We need to consider these different groups and locations of students.
2. Try to avoid bias is an important part of any quantitative study. For example, suppose you were conducting a taste test between 2 different items. It would be important not to include any information to the person about the two items being tested.
3. We need to sample randomly from each of the groups of students using a random sampling technique.

Example 42.2

Problem Setup: Suppose MacDonald’s Restaurants created a new Big Mac with some slight differences and they want to know if it would be preferred over the original one.

Question: How should MacDonald’s go about testing if there is a preference for the new Big Mac over the original one?

Solution:

1. It is important for MacDonald’s not to disclose information regarding the original and new burger to the people taking the taste test because they would be introducing a bias into their study.
2. They also need to try to conduct their sample in such a way that each type of person  in the population should have an equal probability of being selected.
3. They should go about this sampling in a strategic random way.

Random Sampling (Example)

Even though this sounds easy enough, it can be difficult to collect a sample in such a way that each type of person or item  in the population has an equal probability of being selected

This is a common error in carrying out sampling studies. See the example

Example 42.3

Problem Setup: Suppose your instructor wanted to randomly pick three people from the class.

Question: Would it be okay for your instructor to point at the first three people she sees or should she pick 3 people from different locations in the room (front; middle and back)?

Solution: The answer is neither option is ideal. To be truly random, remember –  each item has an equal likelihood of being selected. Thus, when creating a random sample of picking 3 people from a class of 100 students we could consider a number of approache:

1. First we start by ensuring that all students in the class correspond to one number (from 1 to 100).
2. Next we need a method of selecting randomly one of the 100 available numbers.

Some approaches may be as follows:

1. Put the numbers from 1 to 100 on individual small pieces of paper; put all the pieces of paper in a hat; mix the paper pieces thoroughly; randomly select a piece of paper for the hat.
2. Roll a massive dice with 100 sides to it!
3. Generate a random number from a computer (whereby the first 3 digits correspond to our group), or
4. Use your calculator to generate a random number
5. Use a Random Number Table
6. See more suggestions in the next section also.

Using Computers to Create Random Samples

There are many ways in which you can generate random numbers and probably the easiest is to use Excel or your calculator in selecting a truly random sample. One important technique that uses random samples to understand the operations of processes and activities is called Activity Sampling.

Activity Sampling

Activity Sampling is a technique in which a large number of observations are made over a period of time of one group of machines, processes or workers.

This technique will be further discussed when discussing the estimation of the proportion of a population.

Pseudo Random Sampling

When using computers to do random sampling, it’s important to know:

• Computers can’t really do random sampling.
• Instead, they can only do pseudo random, or “good enough” sampling.

Techniques in Excel

Some techniques that can used to sample using Excel are:

• Use Excel’s RAND() function to generate numbers. Then order and select your sample items/individuals using these numbers (see section below).
• Use stratified sampling (see section below).
• Cluster sampling.  

Simple Random Sampling (VIDEO)

We will use Excel’s RAND() function to perform Simple Random Sampling. See the video in the example below to step you through this method.

Example 42.4

Problem Setup: The registrar of a post-secondary institution would like to know more about the applicants why apply to enter their BBA program for the coming fall semester so that they can better target those customer segments.

Question: How do we perform a simple random sample to select 30 of their applicants?

Solution: Click here to download the Excel solutions shown in the video below.

Proportional Stratified Sampling (VIDEO)

We will now, sample according to the number individuals in each ‘strata’ or subgroup of a population. We will use several Excel functions for this sampling:

• RAND()
• COUNTIF()
• SORT
• FILTER
• PASTE SPECIAL
• FILTER UNIQUE VALUES

Example 42.5

Problem Setup: The registrar would like to know who is applying to enter their School of Business diploma programs for the coming fall semester so that they can better target that customer segments.

Question: How do we perform a proportional stratified random sample to select roughly 100 applicants from the program types below? Stratify by program code.

Solution: Click here to download the Excel solutions shown in the video below

Key Takeaways (EXERCISE)

Your Own Notes (EXERCISE)

• Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?
• These notes are for you only (they will not be stored anywhere)
• Make sure to download them at the end to use as a reference