Inferential Statistics: Used to infer properties about a population from a sample.
Descriptive Statistics: A tool for summarizing and describing data.
Parametric vs Non-parametric Techniques
8. Definitions
a. Parametric Techniques
Applicable under specific conditions:
Data on interval scales.
Normal distribution of data.
Homogeneity of variance (similar variability among groups).
b. Non-parametric Techniques
Used when one or more of the parametric assumptions do not hold.
Selecting Statistical Tests
9. Test Selection Criteria
a. Type of Test
Two-tailed vs One-tailed tests.
b. Considerations in Experimental Design
Types of subjects (between/within).
Aim of the experiment (A causes B).
Number of conditions being tested.
10. Decision Trees for Statistical Tests
a. Non-parametric Decision Tree
Choose based on:
Type of analysis required (i.e., Difference between conditions).
Specific techniques for dependent variables.
Non-parametric Tests
11. Specific Techniques
a. Mann-Whitney Test
When: Used for two independent conditions.
Analysis Method: Ranks scores and examines total for calculations.
Formula:
$U = n1n2 + (n1(n1 + 1)/2) - T1$, where $T1$ is the sum of ranks for one group.
12. Wilcoxon Test
When: Within subject analysis for two dependent conditions.
Mechanism includes:
Compare ranks to analyze differences (Negative ranks, Positive ranks).
Summation of negative/positive ranks for test statistic.
13. Friedman Test
When: Within subjects for more than two conditions.
Mechanism: Rank within rows; compare sums to check for non-random differences.
14. Kruskal-Wallis Test
When: Between subjects for more than two conditions.
Mechanism: Rank totalizes and checks for variability in ranks across conditions.
Correlation Analysis
15. Spearman Correlation Coefficient
Examines relationships between variables without asserting causation:
Formula:
R = 1 - \frac{6 \sum{d^2}}{n(n^2 - 1)}
Important to rank the data for comparison.
16. Chi-square Test
Application: Used to assess categorical data.
Mechanism: Compares observed with expected frequencies.
Formula:
\chi^2 = \sum \frac{(O - E)^2}{E}
where $O$ is observed frequency and $E$ is expected frequency.
Requires a minimum of 5 expected observations per category for reliability.
17. Outro: Fundamentals of Statistics
Goals include providing an introduction to statistics, applying decision trees for test selection, and focusing on non-parametric, inferential statistics.