# Random Sampling And Random Assignment Examples Of Idioms

Random sampling is a technique used in selecting people or or items for research. There are many techniques that can be used; but, each technique makes sure that each person or item considered for the research has an equal opportunity to be chosen as part of the group.

## Common Random Sampling Techniques

### Random Number Table

Random number tables are created when every person or every item receives a number. The numbers are entered into a table with digits, starting with the number one and including a number for every person or item. The numbers are added onto the table in a random order.

To use this method for random sampling, each person in the population receives a unique number that is included on the table. Numbers are chosen at random from the table. The choice of one digit is unaffected by the choice of any other given digit.

An example of using a random number table is to assign a number to each of 100 people who have expressed interest in attending a special event. Individual numbers are chosen from the random number table. When a person's number is chosen, they are approved to attend the event.

- This is random sampling because any number can be chosen from the table. The numbers don't have to be chosen in numerical order.

- Each number has an equal opportunity to be chosen from the table.

### Replacement Sampling

#### With Replacement

Sampling with replacement is the act of choosing an individual once and then replacing their number or name into the original group of potential people such that the same person has the ability to be chosen more than once.

#### Without Replacement

This procedure is the same as sampling with replacement, except that the name or number of the individual is not replaced into the original group. This results in only one opportunity to be chosen, rather than multiple.

### Lottery

All of the names or assigned numbers of individuals are entered into a given group and then chosen at random.

### Using a Computer

Software and other programs are available for the purpose of making random samples.

## Real-World Examples of Random Sampling

- At a birthday party, teams are chosen by putting everyone’s name into a jar, then choosing names for each team.
- To test the quality of a river's water, samples of the water would be taken from multiple places in the river, on different dates and at different times of the day. All of the samples would be numbered with the numbers entered into a table. As numbers are chosen from the table, quality tests are run on the chosen sample.
- For a study, psychologists assign numbers to all volunteers for the trial. A number table is used to assign volunteers to the control group and to the four test groups.
- To determine what class to put students into at a school, names are entered into a software program, which then randomly places students in each class.
- To determine the quality of items produced on a factory line, a group of produced items would be removed from the line, each receiving a unique number and then the numbers would be entered into a table and selected one at a time until the quality control team has the number of items required for testing.
- At a fundraising event, every attendees name is entered for the chance to win a prize. Names are selected at random, then returned to the jar, giving individuals multiple opportunities to win prizes.
- Students are given an opportunity to win one of five prizes if they have displayed good behavior. Each child who has displayed good behavior throughout the marking period gets one ticket to put into a bowl. Then, five separate names are pulled from the bowl, without replacing them.
- In a warehouse with an assembly line operation, each employee is assigned a random number using computer software. The same software is used periodically to choose a number of one of the employees to be observed to ensure he is employing best practices.
- A company assigns random numbers using a number table to employees. Every week, a number is chosen and that employee is expected to go for blood tests to ensure sobriety.
- A restaurant leaves a fishbowl on the counter for diners to drop their business cards. Once a month, a business card is pulled out to award one lucky diner a discounted dinner.
- An organization uses a computer program to assign numbers to all of their clients. Once a week, the organization uses the computer program to choose a client for the firm to provide lunch for as a reward for their business.

Remember, there are many ways to implement random sampling. What they all have in common is that each person or item has an equal chance to be chosen.

## Do you have a good example to share? Add your example here.

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### By YourDictionary

Random sampling is a technique used in selecting people or or items for research. There are many techniques that can be used; but, each technique makes sure that each person or item considered for the research has an equal opportunity to be chosen as part of the group.

## Parametric and Resampling Statistics (cont):

## Random Sampling and Random Assignment

The major assumption behind traditional parametric procedures--more fundamental than normality and homogeneity of variance--is the assumption that we have randomly sampled from some population (usually a normal one). Of course virtually no study you are likely to run will employ true random sampling, but leave that aside for the moment. To see why this assumption is so critical, consider an example in which we draw two samples, calculate the sample means and variances, and use those as estimates of the corresponding population parameters. For example, we might draw a random sample of anorexic girls (potentially) given one treatment, and a random sample of anorexic girls given another treatment, and use our statistical test to draw inferences about the parameters of the corresponding populations from which the girls were randomly sampled. We would probably like to show that our favorite treatment leads to greater weight gain than the competing treatment, and thus the mean of the population of all girls given our favorite treatment is greater than the mean of the other population. But statistically, it makes no sense to say that the sample means are estimates of the corresponding population parameters unless the samples are drawn randomly from that (those) populations(s). (Using the 12 middle school girls in your third period living-arts class is not going to give you a believable estimate of U. S. (let alone world) weights of pre-adolescent girls.) That is why the assumption of random sampling is so critical. In the extreme, if we don't sample randomly, we can't say anything meaningful about the parameters, so why bother? That is part of the argument put forth by the resampling camp.

Of course, those of us who have been involved in statistics for any length of time recognize this assumption, but we rarely give it much thought. We assume that our sample, though not really random, is a pretty good example of what we would have if we had the resources to draw truly random samples, and we go merrily on our way, confident in the belief that the samples we actually have are "good enough" for the purpose. That is where the parametric folks and the resampling folks have a parting of the ways.

The parametric people are not necessarily wrong in thinking that on occasion nonrandom sampling is good enough. If we are measuring something that would not be expected to vary *systematically* among participants, such as the effect of specific stimulus variations on visual illusions, then a convenience sample may give acceptable results. But keep in mind that any inferences we draw are not statistical inferences, but logical inferences. Without random sampling we cannot make a statistical inference about the mean of a larger population. But on nonstatistical grounds it may make good sense to assume that we have learned something about how people in general process visual information. But using that kind of argument to brush aside some of the criticisms of parametric tests doesn't diminish the fact that the resampling approach legitimately differs in its underlying philosophy.

The resampling approach, and for now I mean the randomization test approach, and not bootstrapping, really looks at the problem differently. In the first place, people in that area don't give a "population" the centrality that we are used to assigning to it in parametric statistics. They don't speak as if they sit around fondly imagining those lovely bell-shaped distributions with numbers streaming out of them, that we often see in introductory textbooks. In fact, they hardly appear to think about populations at all. And they certainly don't think about drawing random samples from those imaginary populations. Those people are as qualified as you could wish as statisticians, but they don't worry too much about estimating parameters, for which you really do need random samples. They just want to know the likelihood of the sample data falling as they did if treatments were equally effective. And for that, they don't absolutely need to think of populations.

In the history of statistics, the procedures with which we are most familiar were developed on the assumption of random sampling. And they were developed with the expectation that we are trying to estimate the corresponding population mean, variance, or whatever. This idea of "estimation" is central to the whole history of traditional statistics--we estimate population means so that we can (hopefully) conclude that they are different and that the treatments have different effects.

But that is not what the randomization test folks are trying to do. They start with the assumption that samples are probably not drawn randomly, and assume that we have no valid basis (or need) for estimating population parameters. This, I think, is the best reason to think of these procedures as *nonparametric* procedures, though there are other reasons to call them that. But if we can't estimate population parameters, and thus have no legitimate basis for retaining or rejecting a null hypothesis about those parameters, what basis do we have for constructing any statistical test. It turns out that we have legitimate alternative ways for testing our hypothesis, though I'm not sure that we should even be calling it a null hypothesis.

This difference over the role of random sampling is a critical difference between the two approaches. But that is not all. The resampling people, in particular, care greatly about *random assignment*. The whole approach is based on the idea of random assignment of cases to conditions. That will appear to create problems later on, but take it as part of the underlying rationale. Both groups certainly think that random assignment to conditions is important, primarily because it rules out alternative explanations for any differences that are found. But the resampling camp goes further, and makes it the center point of their analysis. To put it very succinctly, a randomization test works on the logical principle that if cases were randomly assigned to treatments, and if treatments have absolutely no effect on scores, then a particular score is just as likely to have appeared under one condition than under any other. Notice that the principle of random assignment tells us that if the null hypothesis is true, we could validly shuffle the data and expect to get essentially the same results. This is why random assignment is fundamental to the statistical procedure employed.

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dch:

David C. Howell

University of Vermont

David.Howell@uvm.edu

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