CH 13

• Statistics


  Quantitative measurements of samples
• What statistics tell us

  • Descriptive statistics describe sample central tendency and variability
  • Inferential statistics allow us to draw conclusions about a parent population from a sample
• 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
• 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
• Population


  A set of people, animals, or objects that share at least one characteristic in common (like college sophomores)
• Sample


  A subset of the population that we use to draw inferences about the population
• Statistical inference


  The process by which we make statements about a parent population based on a sample
• 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 there was no treatment effect
• Variability


  For a set of dependent variable measurements, there is variability when the scores are different. Variability "spreads out" a sample of scores drawn from a population
• Which sample shown below has the most variability?
• Null hypothesis (H0)


  The statement that the scores came from the same population and the independent variable did not significantly affect the dependent variable
• Statistical significance


  Results are statistically significant when 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 level we have preselected, like .01 or .05
• Alternative hypothesis (H1)


  The statement that the scores came from different populations the independent variable significantly affected the dependent variable
• 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
• Frequency distribution


  Displays the number of individuals contributing a specific value of the dependent variable in a sample
• 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
• 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
• The greater the normal variability in the population


  The larger the difference between groups required to reject the null hypothesis
• Directional hypothesis


  Predicts the "direction" of the difference between two groups on the dependent variable
• Nondirectional hypothesis


  Predicts that the two groups will have different values on the dependent variable
• Significance level (alpha)


  The criterion for deciding whether to accept or reject the null hypothesis. Psychologists do not use a significance level larger than .05
• 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
• Type 1 error (a)

  Rejecting the null hypothesis when it is correct. The experimenter determines the risk of a Type 1 error by selecting the alpha level
• Type 2 error (b)


  Accepting the null hypothesis when it is false
• 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)
• Effect size


  Estimates 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
• Confidence interval


  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)
• Critical region


  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
• To reject the null hypothesis, the test statistic would have to fall within the shaded critical region
• One-tailed test


  Has a critical region at one tail of the distribution. We use a one-tailed test with a directional hypothesis
• Two-tailed test


  Has two critical regions, found at opposite ends of the distribution. We use a two-tailed test with a nondirectional hypothesis
• Inferential statistics


  Allow us to predict the behavior of a population from a sample. Examples of inferential statistics are the t test and F test