Research Modules 3: Distribution of Sample Means

Sampling error

Natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter

Determining whether a score is typical of a certain population or extreme

1. need a score for one sample (sample mean)

2. need a distribution made up of sample means, within which, we can examine out one sample mean

Distribution of Sample Means

Made up of sample means from all random samples of a certain size (n) that could be obtained from a population

Sampling distribution

Distribution of statistics obtained by selecting all possible samples of a specific size from a population

Distribution of sample means shape

will have a normal shape regardless of what the original population distribution shape was like

Central Limit Theorem

provides precise characteristics of the distribution of any distribution of sample means (tells precise characteristics of a distribution of sample means for samples of any size (n))

Mean of sample means

Same as the mean of the population sample it came from

central limit theorem: large sample size

for sample size of 30 or more the distribution of the sample means will have a normal shape

Standard Error

Standard deviation of the distribution of sample means, decreases as sample size increases (measures how well an individual sample mean represents the entire distribution)

Expected value of M

Mean of the distribution of sample means equal to the mean of the population scores (u)

standard error: as sample size increases

standard error decreases, when sample size is large enough its mean provides a reliable estimate of the population mean

Law of large numbers

States that the larger the sample size, the more probable the sample mean will be close to the population mean

standard error describes distribution of standard means

provides measure of how much difference is expected from one sample to another

when standard error is small

small sample means are close together and have similar values

when standard error is large

sample means are scattered over a wide range and there are big differences from one sample to another