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Standard Error
Why is this Important?
You are going to generate lots of statistics as a researcher. There are basically two types:
Descriptive & Inferential
Descriptive statistics describe the data - like the mean and standard deviation.
Inferential statistics enable you to make decisions about your data and draw inferences such as:
A Big Idea:
Inferential statistics are based on the concept of making decisions using distributions of sample statistics. Such a distribution is called a sampling distribution. The reason to use samples is that populations are usually too large or impossible to test.
If one sets up a sampling distribution, you can judge the relative position of your sample statistic as compared to the population statistic. With this information, you can make a judgment called a hypothesis test. This is discussed in our next workshop.
In any case - there are different shapes of sampling distributions.
Some are bell shaped like the t-distribution. Some have asymmetrical shapes like the Chi-square and F-distributions (both related).
Another Big Idea:
You generate sampling distribution by:
An Example:
The Sampling Distribution and Standard Error of the Mean
We will use an artificial population of five numbers, which are 1, 2, 3, 4, 5 (I choose not to use some hypothetical distribution of all the students in the USA or the like). If you want, assume that it is after Y2K and only 5 people survive, they are the population. We test them on some variable. One person says 1, another says 2, etc.
So our population is: 1, 2, 3, 4, 5. Note that the mean (m) for this population is 3 and its standard deviation is 1.414.
I decide to take a sample size of 2. I pick a person at random. Then, I pick again. It is possible that I pick the same person twice. These would be all my possible samples. I have also calculated the mean of each of the samples. There are 25 possible samples.
|
Subject 1 |
Subject 2 |
Average of The Sample* |
|
1.00 |
1.00 |
1.00 |
|
1.00 |
2.00 |
1.50 |
|
1.00 |
3.00 |
2.00 |
|
1.00 |
4.00 |
2.50 |
|
1.00 |
5.00 |
3.00 |
|
2.00 |
1.00 |
1.50 *Average = (2 + 1)/2 = 1.50 |
|
2.00 |
2.00 |
2.00 |
|
2.00 |
3.00 |
2.50 |
|
2.00 |
4.00 |
3.00 |
|
2.00 |
5.00 |
3.50 |
|
3.00 |
1.00 |
2.00 |
|
3.00 |
2.00 |
2.50 |
|
3.00 |
3.00 |
3.00 |
|
3.00 |
4.00 |
3.50 |
|
3.00 |
5.00 |
4.00 |
|
4.00 |
1.00 |
2.50 |
|
4.00 |
2.00 |
3.00 |
|
4.00 |
3.00 |
3.50 |
|
4.00 |
4.00 |
4.00 |
|
4.00 |
5.00 |
4.50 |
|
5.00 |
1.00 |
3.00 |
|
5.00 |
2.00 |
3.50 |
|
5.00 |
3.00 |
4.00 |
|
5.00 |
4.00 |
4.50 |
|
5.00 |
5.00 |
5.00 |
|
|
