1. Understanding the scores from Test 2 In-class exercise

2. Chapter 7 Probability and Samples: The Distribution of Sample Means

3. 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

4. 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) In-class exercise

5. 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

6. 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

7. 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

8. More about standard error Compare these two graphs:

9. 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