Normal Sample Tool

Instructions for using Normal Sample Tool

Normal SampleTool: An online, printable lecture.

Normal Sample Tool Instructions

Note: These instructions are abstracted from and can be supplemented by the full web lecture on the Normal Probability Distribution available through another link on this page.

We will start with a short introduction to the vocabulary and symbols used in sampling from the Normal Distribution. These are standard concepts and symbols, so you can skip section 1 if you already are familiar with the distinction between population parameters and sample statistics.

1. Introduction to vocabulary and symbols
2. Normal Sample Tool Instructions

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1. Introduction to Vocabulary and Symbols

Achievement Test Example. Lets start again with an example. Let's say we have an infinite process, a child, happily playing in a tree, not knowing what's waiting for her, and then somebody shows up with a standardized achievement test at the end of second grade and she gets welcomed to the corporate world. So, she has to take a test which is designed to measure her achievement level for various culturally relevant school skills. When she's done the test is scored and she receives a number purported to measure her level of achievement. You are probably familiar with these sorts of tests since they are commonly given in most schools on a yearly basis.

We model the results of her test with the normal distribution. The graphic shows that the test has mu = 200 and sigma = 10. So we can summarize all this information as N(200, 10). For the moment you simply have to accept these parameters (mu = 100 and sigma = 10) which I've made up more or less arbitrarily for this example. We will call this normal distribution a population.

Population Parameters. In the statistical model we think that there is a population which is N(200, 10). We randomly sample 10 scores from that population to get our data. Mu and sigma are said to be the parameters of the population. Recall that we also said that we can call mu the "mean" of the population and we can call sigma the "standard deviation" of the population. We learned that the mean is the center of the population and the standard deviation indicates how spread out the population is.

Unfortunately we also use the terms mean and standard deviation in a related but distinct way. This use of mean and standard deviation to refer to different things can cause confusion unless a clear distinction is drawn.

Sample Statistics

On the graphic I've shown the sample mean to be 198.665. I didn't show how I calculated it so don't worry about how to find the sample mean. Just notice that the sample mean is a little different than the population mean. Mu is 200 but the sample mean (symbolized by M) is equal to 198.665. The population mean and the sample mean are highly related but distinct concepts.

Notice also on the graphic that the sample standard deviation (S) is equal to 8.530. Again, I've not shown how to calculate the sample standard deviation, so you don't need to know that right now. But S, the sample standard deviation, has a slightly different value (8.530) than does the population standard deviation (10). The population standard deviation and the sample standard deviation are related but distinct concepts.

The symbol we will use for the sample mean is M. The symbol we will use for the sample standard deviation is S.

Parameters refer to probability distributions (populations).

Statistics refer to sample data.

Now we are going to turn to a StatCenter tool which allows you to collect samples from a normal distribution.

2. Instructions of Normal Sample Tool

Normal Sample Tool is a tool for creating random samples from a normal population.

The current graphic (above) shows the Normal Sample Tool along with notes on how to use it. It will allow you to generate samples from any Normal Probability Distribution.

Setting Mu and Sigma. First, the Normal Sample Tool allows you to set the population parameters, mu and sigma. The graphic shows you where to type in the values of mu and sigma. Because our Achievement Test example uses N(200, 10), I have already typed in mu = 200 and sigma = 10. But if you have opened up the tool, you need to type in the correct parameters. Do that now.

Setting Sample Size (n). Next, the Normal Sample Tool allows you to set the number of data points in your sample. We use "n" to indicate how many scores we have in our sample. On the lecture graphic, I've set n to be 10.

Getting a sample. Simply clicking on the "Get Sample" button will give you a sample of the size you asked for from the normal population you defined. On the right hand side, upper panel, a normal distribution will appear with the mu and sigma you have set. On the right hand side, lower panel, a sample of scores will appear. The number of scores you get will depend on n, the sample size you set. The current lecture graphic shows a sample of size 10 taken from a population which is N(200, 10).

Each time you click the "Get Sample" button you will get a new sample with a different set of scores.

Sample Statistics. Notice that below the sample data the Normal Sample Tool automatically calculates the sample mean and standard deviation for you. Right now we haven't covered those topics yet, so just notice that the tool will make them available to you when, in the future, you will need them.

Click on the Get Data button several times and notice how the sample data (as well as the sample statistics) change each time you take a sample. You are exploring a statistical model in which you assume that data comes from normal probability distributions and that collecting data amounts to taking a sample from a normal population.