Statistics

Statistics

1. Experiment Types

   • Levels of Constraint
     • Correlational
     • True Experimental
       • Only one that can predict, rest are causality or description
     • Quasi-Experimental
       • No random assignment
     • Observation
       • Naturalistic
       • with Intervention
   • Design
     • Dependent Groups/Within Subject Design
       • To find change in participant, eliminates individual differences, for rare cases
       • Can't use with carry over effects (time, fatigue, etc.)
         • Can be controlled for with counterbalancing, pre-training,rest or using a different design
     • Independent Measures/Between Subject
       • 2 samples are compared before and after
       • Matched Samples
   • Scale of Measurement
     • Interval
       • Absolute 0
     • Ratio
       • Can be negative
     • Ordinal
       • Ranked Categories, not equally different
     • Nominal
       • Mutually Exclusive Categories, Collectively Exhaustive

2. Descriptive Statistics

   • Variabilitiy
     • Range
       • Continuous uses upper and lower real limit for calculations
       • Semi-interquartile Range uses Middle 50% of scores
     • Standard Deviation
       • Z-Scores
         • Distance from mean in SD
         • Critical = 1.65
       • Average Distance of a score form the mean
   • Central Tendency
     • Mean
       • Informative, but affected by outliers
     • Median
       • Central score when ordered (N+1/2)
     • Mode
       • Most frequent score (only one for nominal)
   • Graphs
     • Histogram
       • Ratio/Interval
       • No Spaces
     • Bar Graph
       • Nominal/Ordinal
     • Frequency Table
     • Polygraph (line chart)

3. Inferential Statistics

   • Parametric Tests
     • T-Tests
       • One-sample t-test
         • Use when know pop. mean, and can calc sample mean and SD
         • To test whether a sample is significantly different from population
       • Independent-Groups t-Test
         • Test if two samples are significantly different from one another
       • Dependent Groups t-Test
         • Test changes in participants based on measurements from two times.
       • Assumptions: Independent Observations, normal pop, homogenity of variance (variance of groups is similar, tested with Harthy FMAX test or Levene)
     • ANOVA
       • Oneway ANOVA
         • Used with 1 factor, with independent groups
       • Repeated-Measures ANOVA
         • Assumption: Homogeneity of co-variance (Sphericity variances for each set of difference scores are equal)
           • Mauchley Shpericity test; greenhouse geisser, hynn-feldt
       • Factorial ANOVA
         • Main Effects and Interaction between them
           • Use simple main effects if there is an interaction
         • Types of Factorial ANOVA
           • Simple 2 factors with 2-3 levels
           • Higher order ANOVA 3+ factors
             • 3 2-way interactions
             • 1 3-way interactions
           • Mixed ANOVA 1 between and 1 within subjects factors
           • 2-way repeated measure tested two separate times twice
       • Used to combat experiment-wise error rate which increases with each t-test.
       • Assumptions: Normal distribution, homogenity of variance, ,independent observations.
       • Post Hoc Tests
         • Fisher's LSD (3 groups)
         • Tukey's HSD (4 groups, conservative)
         • Student-Neuman Keuls (4 groups, liberal)
         • Dunnett's (somparing one group to series of experimetnal groups)
         • Scheffe's Test (Complex contrasts)
       • Planned Comparisons (a priori)
         • Trend Analysis (Sequential Groups)
   • Non-Parametric Tests
     • Chi-Square (Nominal Only)
       • Goodness of Fit (1 group)
         • Are individuals spread across cats evenly
         • Are the number of cases distributed equally across categories
       • Test of Independence (2 groups)
         • Are groups equally distributed across categories
     • Rank Test (Ordinal Only)
       • Mann-Whitney U (Independent Measures)
       • Wilcoxon T (Dependent Measures)
       • Friedmann's Rank Test (3+ Groups
       • Kruskall Wallis (3+ Groups)
     • (Only for nominal/ordinal data)
     • Less power than parametric

4. Indication of significance

   • Effect Size
     • Measurement of the magnitude of treatment effect
   • Alpha Level
     • One-tailed (directional) and two-tailed tests
     • Type I Error: Concluding there is an effect when none exists
       • Testwise Error: Error per test
       • Experimentwise Error: Type I error in the test overall
     • Type II Error: Concluding there is no significance when there is