Title: OA 5 Sampling Distribution SU
Course: PSYC 301 Statistical Methods in Psychol > Section: Second Part of Course

For this online assignment we are not going to work with jamovi because it is not suitable for exploring this topic.*

We will be using another GeoGebra app created by Steve Phelps.

The goal for this online assignment is for you to get insight into how the Standard Error of the Mean changes depending on the size of the individual samples used to create the sampling distribution of means. Remember the sampling distribution of means is the distribution that is created if you sample from a population a bunch of times and list all the means that result from those samples.

Below you will see a box that has a blue distribution of dots that represent a population of scores. (If you don't see that box with dot distribution, you may need to switch to a different device, possibly a laptop or desktop computer.) Think of each dot as a person who gave you a response on a measure of life satisfaction. Most people scored in the middle, as can be seen by the number of dots in middle scores around 50. Some scored high or low, but they were more rare, as can be seen by the few dots at the 'tails' of the distribution. The population of scores has a mean of 50 and a standard deviation of 10, as seen next to the blue dot distribution.

You will also see pink dots building up while it runs automatically. Each pink dot represents a mean of a sample that was drawn from the population. A random number generator picks one of the blue dots (a life satisfaction score), then another, and another... continuing until it has a sample. Each sample consists of the number of scores that are specified in the 'sample size' box to the right. Right now it is set for a sample size of 4. The collection of pink dots is building a sampling distribution of means. That is, it is a distribution of a bunch of means that were created by gathering many samples of 4 randomly drawn from the population.

Do these steps:

1. Stop the app by clicking the small circle and parallel lines in the lower left.
2. Click "Clear Sampling Data" and all the pink dots will vanish. Also the Mean and SD calculation next to the pink distribution will change to question marks.
3. Be prepared to mentally count the pink dots as they appear, which you may have noticed is pretty fast, but not faster than you can count.
4. Click the small circle and triangle in the lower left and begin counting up to 100, then click again to stop it. Don't worry about being perfect, we just want about 100 samples. Do not clear the distribution.
5. Write on paper the Mean and SD of the pink distribution labeling it: N = 4.

Then, do these steps:

1. Click in the box labeled Sample Size and remove the 4 (backspace) and type 100.
2. Repeat steps 2 through 4 above.
3. Write on paper the Mean and SD of the pink distribution labeling it: N = 100.

Below the app are the questions to answer.

In the text box for this assignment, submit responses for what is underlined in each step below:

1. A simple text (no fancy formatting) table that shows the sample size, mean, and standard deviation of the two sampling distributions you created. Remember, the standard deviation of a sampling distribution of means is called the Standard Error of the Mean (SEM). So, these two standard deviations is an estimate of the SEM. They are an estimate because they are generated from gathering data.
2. Calculate the theoretical SEM (which is the standard deviation of the theoretical sampling distribution of means) for the distribution based on N = 4 and also calculate an SEM for N = 100. The formula for the SEM is \(SEM\:=\frac{SD}{\sqrt{N}}\). SD is from the population and N is from the sample sizes. You will have two SEM values, one for N = 4 and one for N = 100.
3. Compare your calculated SEMs to the SEMs and answer this judgement call (no 'correct' numerical answer, because everyone has different values for the estimated SEMs): Are the estimated SEMs from the random selection of samples fairly close in value to the theoretical value calculated from the properties of the distribution and sample?

That's it. Submit.

*jamovi is a statistical analysis application for professional statisticians, not a statistical instruction application for students. It doesn't have systems specifically designed to illustrate concepts of statistics.