The Argument for Using Statistics Weighing the Evidence Statistical Inference: An Overview

1. The Argument for Using Statistics Weighing the Evidence Statistical Inference: An Overview Applying Statistical Inference: An Example Going Beyond Testing the Null Hypothesis The Odds of Finding Significance Test Statistics Organizing and Summarizing Data

2. Statistics are quantitative measurements of samples. What are statistics? The Argument for Using Statistics

3. Descriptive statistics describe sample central tendency and variability. Inferential statistics allow us to draw conclusions about a parent population from a sample. What do statistics tell us? Weighing the Evidence

4. Just as Detective Katz can at best show that Ms. Adams is probably guilty, in statistics we can only state that the independent variable probably affected the dependent variable. What point does the Ms. Adams story make about evaluating experimental data? Weighing the Evidence

5. While we cannot prove that the independent variable definitely caused the change in the dependent variable, we can state the probability that our conclusion is correct. What point does the Ms. Adams story make about evaluating experimental data? Weighing the Evidence

6. A populationis a set of people, animals, or objects that share at least one characteristic in common (like college sophomores). A sample is a subset of the population that we use to draw inferences about the population. Define sample and population. Statistical Inference: An Overview

7. Statistical inferenceis the process by which we make statements about a parent population based on a sample. What is statistical inference? Statistical Inference: An Overview

8. The differences in scores obtained from separate treatment groups are not significantly greater than what we might expect between any samples randomly drawn from this population. When researchers report this outcome, it means that were was no treatment effect. What does it mean when we conclude that our scores probably came from the same population? Statistical Inference: An Overview

9. For a set of dependent variable measurements, there isvariabilitywhen the scores are different. Variability “spreads out” a sample of scores drawn from a population. What is variability? Statistical Inference: An Overview

10. Which sample shown below has the most variability? What is variability? Statistical Inference: An Overview

11. The null hypothesis (H0) is the statement that the scores came from the same population and the independent variable did not significantly affect the dependent variable. What is the null hypothesis? Statistical Inference: An Overview

12. Results are statistically significantwhen the difference between our treatment groups exceeds the normal variability of scores on the dependent variable.Statistical significance means that there is a treatment effect at an alpha levelwe have preselected, like .01 or .05. What is statistical significance? Statistical Inference: An Overview

13. The alternative hypothesis (H1) is the statement that the scores came from different populations the independent variable significantly affected the dependent variable. Explain the alternative hypothesis. Statistical Inference: An Overview

14. We may reject the null hypothesis when the differences between treatment groups exceed the normal variability in the dependent variable at our chosen level of significance. When may we reject the null hypothesis? Statistical Inference: An Overview

15. The frequency distributiondisplays the number of individuals contributing a specific value of the dependent variable in a sample. What does a frequency distribution of scores reveal? Statistical Inference: An Overview

16. The values of the dependent variable are indicated on the horizontal X-axis (abscissa)and the frequencies of these values are indicated on the vertical Y-axis (ordinate). You can calculate the total number of participants by adding the frequencies. What does a frequency distribution of scores reveal? Statistical Inference: An Overview

17. The decision to accept or reject the null hypothesis depends on whether the differences we measure between treatment groups are significantly greater than the normal variability among people in the population. Why does rejecting the null hypothesis depend on data variability? Applying Statistical Inference: An Example

18. The greater the normal variability in the population, the larger the difference between groups required to reject the null hypothesis. Why does rejecting the null hypothesis depend on data variability? Applying Statistical Inference: An Example

19. A directional hypothesis predicts the “direction” of the difference between two groups on the dependent variable. For example: The experimental group will lower their systolic blood pressure more than the control group. Contrast directional and nondirectional hypotheses. Applying Statistical Inference: An Example

20. A nondirectional hypothesispredicts that the two groups will have different values on the dependent variable: For example: The experimental group and control group will achieve different systolic blood pressure reductions. Contrast directional and nondirectional hypotheses. Applying Statistical Inference: An Example

21. The significance level(alpha)is our criterion for deciding whether to accept or reject the null hypothesis. Psychologists do not use a significance level larger than .05. What is a significance level and how do we select one? Applying Statistical Inference: An Example

22. A significance level of .05 means that a pattern of results is so unlikely that it could have occurred by chance fewer than 5 times out of 100. What is a significance level and how do we select one? Applying Statistical Inference: An Example

23. A Type 1 error (a) is rejecting the null hypothesis when it is correct. The experimenter determines the risk of a Type 1 error by selecting the alpha level. A Type 2 error (b) is accepting the null hypothesis when it is false. What are Type 1 and Type 2 errors? Applying Statistical Inference: An Example

24. An American Psychological Association task force recommended that researchers include estimates of effect size and confidence intervals, in addition to p values. When you calculate a p value that is statistically significant, this means that your results are unlikely to be due to chance (are probably real). How should we support null hypothesis testing? Going Beyond Testing the Null Hypothesis

25. Effect sizeestimates the strength of the association between the independent and dependent variable—the percentage of the variability in the dependent variable is due to the independent variable. How should we support null hypothesis testing? Going Beyond Testing the Null Hypothesis

26. A confidence intervalis a range of values above and below a sample mean that is likely to contain the population mean (usually 95% or 99% of the time). How should we support null hypothesis testing? Going Beyond Testing the Null Hypothesis

27. A critical regionis a region of the distribution of a test statistic sufficiently extreme to reject the null hypothesis. For example, if our criterion is the .05 level, the critical region consists of the most extreme 5% of the distribution. What is a critical region? The Odds of Finding Significance

28. To reject the null hypothesis, the test statistic would have to fall within the shaded critical region. What is a critical region? The Odds of Finding Significance

29. A one-tailed testhas a critical region at one tail of the distribution. We use a one-tailed test with a directional hypothesis. A two-tailed testhas two critical regions, found at opposite ends of the distribution. We use a two-tailed test with a nondirectional hypothesis. What are one-tailed and two-tailed tests? The Odds of Finding Significance

30. Inferential statisticsallow us to predict the behavior of a population from a sample. Examples of inferential statistics are the t testand F test. What is the function of inferential statistics? Test Statistics