Exam 3

• Types of statistics/designs

  • Descriptive: summarizes data from a sample
  • Inferential: allows you to draw conclusions abt your data that can be applied to a broader population
• Measures of central tendency

  • mean: average
  • median: middle number
  • mode: most frequent score
• standard deviation (SD)


  average amount that scores in sample distribution deviate from the mean
• Sample vs Population in SD

  The population std dev is always smaller than the sample st dev
• Types of Variables

  • categorical: IV must be nominal or ordinal 
  • continuous: DV must be interval or ratio
• Types of hypothesis

  • alternative: differences between conditions (H0: u1 = u2)
  • null: NO differences between conditions  (H1: u1>u2 or H1: u1 doesn't = u2)
• Errors in statistical testing

  • Type I: rejecting the H0 when its true
  • Type II: failing to reject H0 that’s false
• Meaning of alpha

  Set at .05

  • >.05 = >.5% chance that differences between conditions were due to chance (significant)
• Meaning of T and F ratios in ANOVA

  • Smaller error results in larger t or F obtained, thus increasing chances of finding significance.
  • Larger treatment effects result in larger t or F obtained, thus increasing chances of finding significance.
  • Larger sample sizes result in smaller critical value (i.e., hurdle) thus increasing chances of finding significance.
• Types of Designs


  • Between
  • Within
  • longitudinal
  • cross-sectional
  • latin square
  • balanced latin square
• Between-subjects design

  Independent; separate group of Ps are selected to participate in one of two (or more) conditions (levels of IV)
• Within-subject design

  repeated; Same group of participants are selected to participate in all of the conditions (all levels of IV)
• Advantages of WS design over BS designs

  • no needs for equivalent groups
  • fewer participants
  • direct measuring variability due to statistical control of individual differences
  • provide ultimate ‘matched‘ group
  • MUST counterbalance
• Longitudinal design


  uses within-subjects approach (ex: measuring language performance in 3-year olds, then measuring the same group when 4 & then again when 5-years old)
• cross-sectional design


  similar to between-subjects design (ex: comparing children of ages 3, 4, and 5 on language performance)
• latin square


  Each condition appears once in any order position in the sequences

  • 1: ABCD
  • 2: DABC
  • 3: CDAB
  • 4: BCDA
• Balanced latin square

  Each condition appears once in each order position in the sequence, & precedes and follows every other condition an equal number of times
• Matching

  Typically used when sample size is small; correlating with DV
• counterbalance


  counterbalancing order of treatment to remove WS confounds (testing more than once per conditions or testing once per conditions)
• random assignment 


  Ps have an equal chance of being in one of conditions being formed
• Blocked randomization


  Ps are randomly assigned to conditions (levels of IV); a condition is not repeated a 2nd time until a Ps has been assigned to each condition
• Types of correlations

  • perfect positive (consistently upwards)
  • perfect negative (consistently downwards)
  • Zero correlation (scattered)
  • Weak positive (roughly upward)
  • Weak negative (roughly downwards)
• Problems related to causation

  • Directionality: if correlation between A & B. (A could have caused B, or B could have caused A, but no way of telling)
  • Third Variable: Correlational research does not attempt to control extraneous variables directly - so an extraneous variable may account for the correlation
• Coefficient of determination


  (r^2) indicates how much variability in A can be accounted for by B is found by squaring value of Pearson’s r
• Know How To Read SPSS Output!

  check notes
• Types of Experimental Design


  • independent groups (random assignment)
  • matched groups (matching procedure)
  • nonequivalent (different types of individuals)
  • repeated measures (IV manipulated within-subjects)
• One-tailed test


  Suggesting a direction of the interventions (greater or less than)
• Two-tailed 


  suggests a difference, but NOT a direction
• T-test for independent groups


  independent & nonequivalent groups design
• t-test for dependent groups 


  matched groups and repeated measure designs
• Example of Independent T-test Conclusion (reject)

  tobt of 3.99 was greater than the tcrit value of 1.697. Therefore, we reject the null hypothesis. The southern group that received the new drug recognized more words (M = 88.32) than the group that received the placebo (M = 69.97), t (30) = 3.99, p < .05.
• Example of Dependent t-test conclusions (reject)

  Using a t-test for dependent samples, we reject the null hypothesis because the tobt of 2.48 is greater than the tcrit of +1.812.  According to the dependent t-test, the treatment significantly reduced the number of anxiety attacks from the pre-test (M = 11.09, SD = 5.
• Outlier


  Data point that is so deviant from the data that researcher believes it is not representative of behavior & its inclusion distorts the results.
• Advantage of using a two-tailed t-test over a one-tailed t-test


  Allows you to test both ends of the sample distribution at the same time
• Correct (df) formula for t-test

  • independent: n1 + n2 - 2
  • dependent: n -1
• How do you justify excluding an ’outlier’ from the data analysis

  4 to 5 stan devs from the mean
• When to use independent samples vs dependent samples t-test?

  • independent: non-equivalent, independent
  • dependent: matched, repeated measures
• Theoretically, if an independent variable has no effect in an experiment (i.e. no treatment effect), the ANOVA, F or t ratio should be…


  less than or equal to 0
• F ratio in ANOVA

  [(treatment effect + error variance)/(error variance)]
• When should you use an ANOVA test instead of a t-test?

  When you want to compare more than two means