The Distribution of Sample Means and Decision Errors

What is the distribution of sample means?

Separate samples are usually different even though they are taken from the same population. ---- especially when the sample size is small.

The distribution of sample means is the

collection of sample means for all possible random samples of a particular size that can be obtained from a population.

Characteristics of distribution of sample means

The values in the distribution are not scores, but statistics (sample means)

The sample means are more representative of the population than

raw scores.

The pile of sample means tend to form a normal shaped

distribution.

The larger the sample size, the closer the sample means are to the

population mean (µ)

The distribution of sample means is almost perfectly normal if either of the following two conditions is satisfied:

• 1) The population from which the samples are selected is a normal distribution.

• 2) The number of scores in each sample is relatively large, around 30 or more.

The Expected Value of Mean

The mean of the distribution of sample means is equal to the mean of the population of scores, and is called the expected value of mean. •µM = µ

The Standard Error of Mean

• The standard deviation of the distribution of sample means is called the standard error of mean. It is equal to the population standard deviation divided by square root of sample size

Central Limit Theorem

For any population with mean µ and standard deviation σ, the distribution of sample means for sample size n will have a mean of µ and a standard deviation of σ/ 𝑛 and will approach a normal distribution as n approaches infinity.

as n increases, the distribution is

more normal

Decision Errors

• Information from samples only provides limited or incomplete information about the whole population.

• There is possibility that an incorrect conclusion will be made when you draw conclusion about population from sample.

Two types of decision errors

Type I Error (False Alarm): You think there is an effect, but actually there is not.

Type II (Miss) Error: You think there is no effect, but actually effect exists.