Distribution of Sample Means
Collection of sample means for all the possible random samples for a size (n) that come from a population
1st Property of DSM
The average of the sample mean (grand mean) = the population mean
2nd Property of DSM
The sample mean’s distribution gets more normal as the sample size increases
3rd Property of DSM
The larger the sample size, the closer the sample mean will be to the population mean.
Central Limit Theorem
-The sampling distribution mean stays the same as the population mean
-Less variability
-Distribution is more normal as SS increases
Standard Error (σM)
It provides a measure of average expected distance between the sample mean (M) and population mean (μ)
1st Magnitude of Standard Error
As the sample size for each mean increases, the standard error decreases
2nd Magnitude of Standard Error
As the standard deviation for the population increases, the standard error decreases
Law of Large Numbers
The larger the sample size (n), the more likely it is that the sample mean will be closer to the population mean.
The Expected Value of M is equal to
The mean of population scores
The distribution is normal when
N is greater than or equal to 30
The Standard Error will always be
Less than or equal to the SD, and it will equal the SD when n=1
Find the Z-Score of a sample mean
Z=(raw score - mean)/SD divided by sqrt(n)
Larger Sample sizes…?
Reduce extreme scores/outliers (distribution becomes more normal)
Distribution of Means has…?
Less variability and the same mean as the population of scores
