Simple Random SampleSimple Random SampleHow to make sure your sample is good... How to make sure your sample is good...

or hopefully good...or hopefully good...

maybe...maybe...

DefinitionDefinition

The process of getting a simple random sample The process of getting a simple random sample simply means that every simply means that every unitunit in your sampling in your sampling frame has an equal probability of being frame has an equal probability of being selected for your sample, every selected for your sample, every groupgroup of the of the same size has the same probability of being same size has the same probability of being chosen, and you use some sort of chosen, and you use some sort of randomnessrandomness to select the units for your sample.to select the units for your sample.

This is a very common method of sample This is a very common method of sample selection, employed primarily for its ease of selection, employed primarily for its ease of implementation.implementation.

What does randomness What does randomness mean?mean?

Anything where the outcome is unpredictable Anything where the outcome is unpredictable can be considered random.can be considered random.

Examples: Flipping a fair coin, rolling a die, Examples: Flipping a fair coin, rolling a die, picking numbers out of a hat, picking a card picking numbers out of a hat, picking a card from a well shuffled deck, etc.from a well shuffled deck, etc.

This is a great tool for sampling because it This is a great tool for sampling because it greatly reduces the bias involved in human greatly reduces the bias involved in human sampling.sampling.

Why do we even sample Why do we even sample in the first place?in the first place?

Sampling gives us a way to use a small group Sampling gives us a way to use a small group of individuals to make inferences about a of individuals to make inferences about a whole population.whole population.

If we get a good, or representative, sample of a If we get a good, or representative, sample of a population, our inferences on that population population, our inferences on that population should be quite accurate.should be quite accurate.

The question is, should we sample just one The question is, should we sample just one time, or should we do it more than once?time, or should we do it more than once?

Sampling using Sampling using computer softwarecomputer software

We can use computer software to help us We can use computer software to help us simulatesimulate hundreds and hundreds of samples. hundreds and hundreds of samples.

Based on all of those samples, we can make a Based on all of those samples, we can make a very good guess about the actual population.very good guess about the actual population.

But in order to do this, we must be aware of But in order to do this, we must be aware of what our what our response variableresponse variable is. This is whatever is. This is whatever information we want to get from our individuals information we want to get from our individuals in the sample.in the sample.

Simulation ExampleSimulation Example

Suppose we wanted to see if a random number Suppose we wanted to see if a random number generator was actually random.generator was actually random.

We could randomly sample 10 numbers from We could randomly sample 10 numbers from the generator at a time, and record how many the generator at a time, and record how many of each we got.of each we got.

But using a computer, we could simulate But using a computer, we could simulate thousands of samples of size 10, and record thousands of samples of size 10, and record how many of each number we got in all those how many of each number we got in all those samples.samples.

Benefits of simulationBenefits of simulation

• This allows us to look at many more samples This allows us to look at many more samples than we would be able to get through by taking than we would be able to get through by taking samples by hand.samples by hand.

• Many companies use this to get a good idea of Many companies use this to get a good idea of certain demographics they are interested in.certain demographics they are interested in.

• But back to the matter at hand...But back to the matter at hand...

How can I get a random How can I get a random sample?sample?• There are many common, and practical, ways There are many common, and practical, ways

that researchers can generate random that researchers can generate random numbers.numbers.

• Microsoft Excel has a built in feature that will Microsoft Excel has a built in feature that will generate random numbers between two generate random numbers between two numbers that you decide, and you can just numbers that you decide, and you can just click and drag to get more random numbers.click and drag to get more random numbers.

• Many other computer programs will have built Many other computer programs will have built in functions like this.in functions like this.

Going old schoolGoing old school

• One of the oldest methods is the use a random One of the oldest methods is the use a random number or random digit table, which is just row number or random digit table, which is just row after row after row of random numbers. This after row after row of random numbers. This has been used for many, many years, and has has been used for many, many years, and has proven to be very useful and effective for proven to be very useful and effective for creating random samples.creating random samples.

• However, with the advent of computers, using However, with the advent of computers, using a random digit table to large samples would be a random digit table to large samples would be very time consuming and not worthwhile.very time consuming and not worthwhile.

Random Number TableRandom Number Table

• Here is an example of a random number tableHere is an example of a random number table

• You can start wherever You can start wherever

• you want to on the table.you want to on the table.

• This helps with your This helps with your

• sample being random.sample being random.

Identifying your unitsIdentifying your units• To be able to use a random number table or To be able to use a random number table or

random number generator, you need to have random number generator, you need to have numbers assigned to each of your units in your numbers assigned to each of your units in your sampling frame.sampling frame.

• It is usually easiest to start at 1,2,3,... all the It is usually easiest to start at 1,2,3,... all the way up to however many units there are in your way up to however many units there are in your sampling frame. sampling frame.

• This might be slightly different depending on This might be slightly different depending on what method you are using (random number what method you are using (random number table, random number generator, etc).table, random number generator, etc).

Easy exampleEasy example• Say we have 5 units in our sample...well, go Say we have 5 units in our sample...well, go

on, say it! Good.on, say it! Good.

• We would give each unit a number 1-5.We would give each unit a number 1-5.

• If we want a simple random sample of size 2, If we want a simple random sample of size 2, we can go to any row of a random number we can go to any row of a random number table, and pick the first two single digits that table, and pick the first two single digits that are between 1 and 5.are between 1 and 5.

• This can be extended to bigger sampling This can be extended to bigger sampling frames and sample sizes.frames and sample sizes.