understanding the scores from test 2 in-class exercise
TRANSCRIPT
Understanding the scores from Test 2 In-class exercise
Chapter 7Probability and Samples: The Distribution of Sample Means
Samples and sampling error
Probability of randomly selecting certain scores from a population
Probability of randomly selecting certain samples from a population
Consider the probability of randomly selecting Test #1 scores from our class Sampling error Sample size and sampling error Constructing a distribution of sample
means
Distribution of sample means
Distribution of sample means = sampling distribution of the mean = all possible random sample means (of a given size) from a given population
In-class exercise (watching sampling distributions develop)
Distribution of sample means
Characteristics Central limit theorem
Mean of sampling distribution = mean of population (M = )
Shape of sampling distribution is normal if n>30
Variability of sampling distribution < variability of population
Standard error of M = M = /n What does M tell you? Amount of sampling error depends on SD of
population and size of sample
Probability and distribution of sample means
Sampling distribution of mean approximates normal distribution
Can use concept of z-scores and apply to sample means
Compare z-score formula for x-score to z-score formula for sample mean (M)
Now we can play with the probabilities of sample means
More about standard error
Standard error of the mean (SE) is a measure of sampling error
Average error between a known sample mean and the unknown population mean it represents
SE often reported in research literature and often depicted on graphs
More about standard error
Compare these two graphs:
1.00 2.00
group
6.00
7.00
8.00
9.00
10.00
11.00
12.00
Mea
n +
- 1
SE
dv2
1.00 2.00
group
6
7
8
9
10
11
12
Mea
n +
- 1
SE
dv1
Looking ahead to inferential statistics
Can determine the probability (or percent chance) that a treated sample comes from a known untreated population
If the probability is relatively high, then we conclude no effect of treatment
If the probability is relatively low (<.05), then we conclude effect of treatment