Standard Error
To have my sampling distribution, I then prepare a frequency distribution of the sample means (my last column of figures).
|
Sample Average |
Frequency |
Percent |
|
1.00 |
1 |
4.0 |
|
1.50 |
2 |
8.0 -> Look for the two 1.50 values above |
|
2.00 |
3 |
12.0 |
|
2.50 |
4 |
16.0 |
|
3.00 |
5 |
20. |
|
3.50 |
4 |
16.0 |
|
4.00 |
3 |
12.0 |
|
4.50 |
2 |
8.0 |
|
5.00 |
1 |
4.0 |
Total Number of Samples = 25
A Really Big Idea:
The Standard Deviation of a Sampling Distribution is called the Standard Error
Now, I graph this distribution and calculate its mean and standard deviation.
Big Point!!
- This distribution is the sampling distribution of the mean.
It's mean has to be the same as that of the population. Its standard deviation is the standard error of the mean. Look at the Graphic below.
Thus, we can see that most samples are close to 3.0 but there are some extreme sample means with values of 1.0, 1.5 and 4.5 and 5.0.
Sample Size of 3
Now I will redo the exercise with a sample size of 3.
Here is the list of all possible samples of size 3, with averages for each sample:
|
Subject 1 |
Subject 2 |
Subject 3 |
Average of Sample |
|
1.00 |
1.00 |
1.00 |
1.00 |
|
1.00 |
1.00 |
2.00 |
1.33 |
|
1.00 |
1.00 |
3.00 |
1.67 |
|
1.00 |
1.00 |
4.00 |
2.00 |
|
1.00 |
1.00 |
5.00 |
2.33 |
|
1.00 |
2.00 |
1.00 |
1.33 |
|
1.00 |
2.00 |
2.00 |
1.67 |
|
1.00 |
2.00 |
3.00 |
2.00 |
|
1.00 |
2.00 |
4.00 |
2.33 |
|
1.00 |
2.00 |
5.00 |
2.67 |
|
1.00 |
3.00 |
1.00 |
1.67 |
|
1.00 |
3.00 |
2.00 |
2.00 |
|
1.00 |
3.00 |
3.00 |
2.33 |
|
1.00 |
3.00 |
4.00 |
2.67 |
|
1.00 |
3.00 |
5.00 |
3.00 |
|
etc. |
etc. |
etc. |
etc. |
|
1.00 |
5.00 |
2.00 |
2.67 |
|
1.00 |
5.00 |
3.00 |
3.00 |
|
1.00 |
5.00 |
4.00 |
3.33 |
|
1.00 |
5.00 |
5.00 |
3.67 |
|
2.00 |
1.00 |
1.00 |
1.33 |
|
2.00 |
1.00 |
2.00 |
1.67 |
|
2.00 |
1.00 |
3.00 |
2.00 |
|
2.00 |
1.00 |
4.00 |
2.33 |
|
2.00 |
1.00 |
5.00 |
2.67 |
|
2.00 |
2.00 |
1.00 |
1.67 |
|
2.00 |
2.00 |
2.00 |
2.00 |
|
2.00 |
2.00 |
3.00 |
2.33 |
|
etc. |
etc. |
etc. |
etc. |
|
2.00 |
4.00 |
1.00 |
2.33 |
|
2.00 |
4.00 |
2.00 |
2.67 |
|
2.00 |
4.00 |
3.00 |
3.00 |
|
2.00 |
4.00 |
4.00 |
3.33 |
|
2.00 |
4.00 |
5.00 |
3.67 |
|
2.00 |
5.00 |
1.00 |
2.67 |
|
2.00 |
5.00 |
2.00 |
3.00 |
|
2.00 |
5.00 |
3.00 |
3.33 |
|
2.00 |
5.00 |
4.00 |
3.67 |
|
2.00 |
5.00 |
5.00 |
4.00 |
|
3.00 |
1.00 |
1.00 |
1.67 |
|
3.00 |
1.00 |
2.00 |
2.00 |
|
3.00 |
1.00 |
3.00 |
2.33 |
|
3.00 |
1.00 |
4.00 |
2.67 |
|
3.00 |
1.00 |
5.00 |
3.00 |
|
etc. |
etc. |
etc. |
etc. |
|
5.00 |
5.00 |
1.00 |
3.67 |
|
5.00 |
5.00 |
2.00 |
4.00 |
|
5.00 |
5.00 |
3.00 |
4.33 |
|
5.00 |
5.00 |
4.00 |
4.67 |
|
5.00 |
5.00 |
5.00 |
5.00 |
 |
 |
