Statistics

Statistics

Experiment Types
1. Levels of Constraint
  1. Correlational
  2. True Experimental
    1. Only one that can predict, rest are causality or description
  3. Quasi-Experimental
    1. No random assignment
  4. Observation
    1. Naturalistic
    2. with Intervention
2. Design
  1. Dependent Groups/Within Subject Design
    1. To find change in participant, eliminates individual differences, for rare cases
    2. Can't use with carry over effects (time, fatigue, etc.)
      1. Can be controlled for with counterbalancing, pre-training,rest or using a different design
  2. Independent Measures/Between Subject
    1. 2 samples are compared before and after
    2. Matched Samples
3. Scale of Measurement
  1. Interval
    1. Absolute 0
  2. Ratio
    1. Can be negative
  3. Ordinal
    1. Ranked Categories, not equally different
  4. Nominal
    1. Mutually Exclusive Categories, Collectively Exhaustive
Descriptive Statistics
1. Variabilitiy
  1. Range
    1. Continuous uses upper and lower real limit for calculations
    2. Semi-interquartile Range uses Middle 50% of scores
  2. Standard Deviation
    1. Z-Scores
      1. Distance from mean in SD
      2. Critical = 1.65
    2. Average Distance of a score form the mean
2. Central Tendency
  1. Mean
    1. Informative, but affected by outliers
  2. Median
    1. Central score when ordered (N+1/2)
  3. Mode
    1. Most frequent score (only one for nominal)
3. Graphs
  1. Histogram
    1. Ratio/Interval
    2. No Spaces
  2. Bar Graph
    1. Nominal/Ordinal
  3. Frequency Table
  4. Polygraph (line chart)
Inferential Statistics
1. Parametric Tests
  1. T-Tests
    1. One-sample t-test
      1. Use when know pop. mean, and can calc sample mean and SD
      2. To test whether a sample is significantly different from population
    2. Independent-Groups t-Test
      1. Test if two samples are significantly different from one another
    3. Dependent Groups t-Test
      1. Test changes in participants based on measurements from two times.
    4. Assumptions: Independent Observations, normal pop, homogenity of variance (variance of groups is similar, tested with Harthy FMAX test or Levene)
  2. ANOVA
    1. Oneway ANOVA
      1. Used with 1 factor, with independent groups
    2. Repeated-Measures ANOVA
      1. Assumption: Homogeneity of co-variance (Sphericity variances for each set of difference scores are equal)
        Mauchley Shpericity test; greenhouse geisser, hynn-feldt
    3. Factorial ANOVA
      1. Main Effects and Interaction between them
        Use simple main effects if there is an interaction
      2. 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
    4. Used to combat experiment-wise error rate which increases with each t-test.
    5. Assumptions: Normal distribution, homogenity of variance, ,independent observations.
    6. Post Hoc Tests
      1. Fisher's LSD (3 groups)
      2. Tukey's HSD (4 groups, conservative)
      3. Student-Neuman Keuls (4 groups, liberal)
      4. Dunnett's (somparing one group to series of experimetnal groups)
      5. Scheffe's Test (Complex contrasts)
    7. Planned Comparisons (a priori)
      1. Trend Analysis (Sequential Groups)
2. Non-Parametric Tests
  1. Chi-Square (Nominal Only)
    1. Goodness of Fit (1 group)
      1. Are individuals spread across cats evenly
      2. Are the number of cases distributed equally across categories
    2. Test of Independence (2 groups)
      1. Are groups equally distributed across categories
  2. Rank Test (Ordinal Only)
    1. Mann-Whitney U (Independent Measures)
    2. Wilcoxon T (Dependent Measures)
    3. Friedmann's Rank Test (3+ Groups
    4. Kruskall Wallis (3+ Groups)
  3. (Only for nominal/ordinal data)
  4. Less power than parametric
Indication of significance
1. Effect Size
  1. Measurement of the magnitude of treatment effect
2. Alpha Level
  1. One-tailed (directional) and two-tailed tests
  2. Type I Error: Concluding there is an effect when none exists
    1. Testwise Error: Error per test
    2. Experimentwise Error: Type I error in the test overall
  3. Type II Error: Concluding there is no significance when there is

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