CH 14

• Levels of Measurement


  • Nominal scale
  • Ordinal scale
  • Interval scale
  • Ratio scale
• Nominal scale


  Assigns items to two or more distinct categories that can be named using a shared feature, but does not quantify the items
• Nominal scale

  • Sorting pictures into attractive and unattractive categories
• Ordinal scale


  Measures the magnitude of the DV using ranks
• Ordinal scale


  • Marathon contestants assigned to places from first place to last place
• Interval scale


  Measures the magnitude of the DV using equal intervals between values with no absolute zero point
• Interval scale


  • Fahrenheit or Centigrade temperatures, Sarnoff and Zimbardo's 0-100 scale
• Ratio scale


  Measures the magnitude of the DV using equal intervals between values and an absolute zero
• Ratio scale


  • Distance in meters or time in seconds
• Nonparametric tests


  Use nominal or ordinal data
• Parametric tests


  Require interval or ratio data
• Chi square test


  Used when the data are nominal and the groups are independent
• Chi square test


  Determines whether the frequency of sample responses represents the frequencies we would expect in the population
• Chi square obtained (c2 obt)


  The actual frequency of responses
• Chi square critical value

  The minimum value required to reject the null hypothesis
• Cramer's coefficient Φ


  Analogous to r2 and indexes the degree of association between priming and the number of incorrect responses
• If our sample included every member of the population, we would have the maximum possible degrees of freedom and would know the exact population values of the mean and variance
• Deciding whether to accept or reject the null hypothesis for chi square

  If c2 obt > c2 critical, reject the null hypothesis
• Sample size and the t test

  The sample size determines the degrees of freedom, and there is a different t distribution for each value of degrees of freedom
• t distribution as sample size increases

  The t distribution approaches a normal curve as sample size increases
• Robustness of the t test


  The t test provides a valid test of the hypothesis when assumptions like normal distribution of population values are slightly to moderately violated
• Rejecting the null hypothesis for the t test

  We reject the null hypothesis when t obt > t crit
• Rejecting the null hypothesis for the t test

  • For 9 df, if t obt > 2.262, we would reject the null hypothesis
• Calculating effect size for a t test for independent groups


  First, calculate the t statistic (2.47), then enter it into the formula to calculate r
• Effect size r


  An r value of .50 is a large effect, and r2 reveals that the independent variable accounts for 44% of the variance in the dependent variable
• t test for matched groups

  Assigns the same subjects to both conditions or matches subjects and then randomly assigns them to either condition
• Advantage of t test for matched groups

  May use fewer subjects and achieve greater control over individual differences, making it potentially more powerful than a t test for independent groups
• When to use ANOVA


  When data are interval or ratio level and there is at least one independent variable with three or more levels
• Within-groups variability


  The degree to which the scores of subjects in the same treatment group differ from each other
• Between-groups variability


  The degree to which the scores of different treatment groups differ from one another or the grand mean
• Sources of within-groups variability

  Error due to individual differences and extraneous variables
• Sources of between-groups variability

  Error due to individual differences and extraneous variables, and treatment effects
• Significance of an F ratio

  Across all group means, there is a significant difference due to the independent variable
• Rejecting the null hypothesis for ANOVA


  When F obtained > F critical
• Post hoc tests


  Performed when an overall ANOVA is significant and no specific predictions have been made, to test all pairs of treatment groups
• Number of post hoc comparisons

  You may perform all possible pairwise comparisons without increasing the risk of Type 1 error
• A priori tests


  Used to test predictions of differences between groups, such as between two groups or between one group and the others
• Maximum number of a priori comparisons


  p - 1, where p is the number of treatment groups
• Advantage of a priori tests

  More powerful than post hoc tests, but you may perform fewer of them
• Effect size η2


  Proportion of the variability in the dependent variable that can be accounted for by the independent variable, indexing the strength of the relationship between the independent and dependent variables