Psych 300A: Final Review (Sampling Distribution of the Mean)

What are the 2 major problems with single participant designs

1 - No baseline for comparison

2 - Difference(s) could be due to to specific participant relative to the comparison

Sample distribution

Possible sample means that occur just due to sampling error

What are the 5 steps needed to generate a sample distribution

1 - List all possible outcomes of a random draw of 2 values for x

2 - Compute the mean for each pair of scores

3 - Compute the probability for each outcome

4 - Create a probability (frequency) table

5 - Create a graphic figure of the distribution of possible means

What is the problem with generating a sample distribution using the 5 steps

Will not be practical in large sample sizes, will help us to understand what the distribution is however

What are the two things actually need to generate the sampling distribution

1 - Characteristics of the population of individuals

2 - the number of scores in each sample

What are the 3 rules used to figure out the characteristics of the distribution of the sample mean

1 - Central tendency

2 - Variability

3 - Shape

Rule 1 (Central tendency)

The mean of the distribution of the sample mean is the same as the mean of the population because all possible combinations of means are included

μx̄= μ

Rule 2 (Variability)

We can calculate the standard error of the mean which tells us how much error on average is expected between a sample and population mean

SEM = σ / √N

What two principles define variance with regard to sample distributions

SEM varies directly with σ

As value for N increases, SEM decreases

Rule 3 (Shape)

Central limit theorem - Regardless of the shape of the population, as size N increases the sample distribution approaches a normally distributed

If population is normally distributed then sample distribution is normally distributed

How large does sample size need to be to approximate a normal distribution with regard to skewedness

Mild skew - N ≥ 10-12

Moderate skew - N ≥ 18-20

Strong/severe skew - N ≥ 25-30

What 3 things is the name of the sample distribution based on

1. Statistic being analyzed

2. Sample size

3. Whether parameters are known/unknown

What are the 5 assumptions amde when we engage in a single sample design

1. Can define the mean and SD of the population and therefore its related

sampling distribution

2. Population is finite, empirical

3. Sampling distribution of the mean is finite, empirical

4. Sample participants are randomly sampled from the population

5. Dependent variable is normally distributed in the population, if not we

need a sample N ≥ 25-30