Pyschology Statistics (Chapter 7)

Distribution of Sample Means

the collection of sample means for ALL the possible
random samples of a set size (n) that can be collected from a population of interes

Sampling Error

the discrepancy or amount of error between a sample statistic and a population parameter

There will always be error between a computed statistic and the corresponding population parameter

Central Limit Theorem

a mathematical formula telling us what a distribution would
look like if we selected every possible sample, calculated the means, and constructed a
distribution

Expected Value of Mean

The average value of all the sample means will always be exactly equal to the population mean (μ)

M ​= μ

Shape of distribution of sample means

The distribution of sample means will be perfectly normal if:
a. The population from which the samples are selected is normal/bell curved (such as IQ, height, weight)

b. The number of scores (n) in each sample is large (around 30 or more)

Standard Error of M (σM)

the standard deviation of the distribution of sample means
which measures the standard amount of difference between M and μ

Standard Error of M (σM) Formula

σ / √n

OR

√(σ^2 / n)

2 factors influencing magnitute of standard error of M

Sample size – the larger the sample size the more accurate the value

Population standard variance

z-scores for a distribution of sample means formula

Z = M - μ/σM

Z-score formula for calculating sample mean that form boundaries

M = μ ± (Z * σM)