Psychology 820 Chapters 10 - 11

1. Psychology 820Chapters 10 - 11 Statistical Inference: Sampling & Interval Estimation Introduction to Hypothesis Testing

2. Populations and Samples • Parameters • Characteristics of a population • Statistics • Characteristics of a sample

3. Random Sampling • Independence • Two events are independent if they have nothing to do with each other (uncorrelated). • Accidental or Convenience Samples • Systematic Sampling • While not true random sampling can be representative and generalizable.

4. Sampling Distributions • The distribution of a sample statistic that gives the probability associated with each value of the statistic over all possible samples of the same size that could be drawn from the population.

5. Central Limit Theorem • States the characteristics of the sampling distribution of the mean • One of the most important theorems in statistics • A Demonstration • Standard error of a statistic is the standard deviation of the sampling distribution of that statistic.

6. Properties of Estimators • Unbiased • The mean of the sampling distribution of the sample estimates equals the value of the parameter being estimated • Consistency • A consistent estimator tends to get closer and closer to the value of the parameter as the sample size becomes larger. • Relative Efficiency • Refers to the relative precision with which an estimator estimates a parameter.

7. Review of Statistical Inference • Scientific hypothesis • Statistical inference • Statistical hypothesis • Null hypothesis • Alternative hypothesis • Hypothesis testing

8. Test Statistics • Sample statistics – used to describe characteristics of samples or to estimate population parameters • Test statistics – used to test hypotheses about population parameters • z scores • t scores • degrees of freedom

9. Hypothesis Testing • Type I Errors • Type II Errors • Power • Correct acceptance • One-tailed & two-tailed tests and power • Determining sample size • Practical significance

10. Hypothesis Testing and The Interpretation of Significance • We must decide for ourselves whether we will regard any given event as rare enough to make us doubt that the null hypothesis is true. • American researchers have an informal agreement to regard as “statistically significant” t values with associated p levels of .05 or less.

11. When Is It Significant? • The most experienced data-analytic statisticians do not share the view of a fixed critical level of significance • They regard it as far wiser to report the actual p level obtained along with a statement of the size of the effect obtained. • It is important to remember that for any size of effect that is not precisely zero we can achieve any level of significance desired simply by adding to the size of the study (N).