LAB 4.1 + 4.2

Key Concepts in Statistics

  • Central Tendency Measures:

    • Mean: Average of all data points.

    • Median: Middle value in ordered dataset.

    • Mode: Most frequently occurring value.

  • Distribution Types:

    • Symmetrical Distribution: Equal distribution around the mean.

  • Performance Metrics:

    • Evaluation of averages in various Wordle games based on attempts and win rates.

    • Example from Wordle performance: Average attempts vary, with significant scores for Sweden (3.72) and others like New Zealand (3.96).

Statistical Calculations

  • Guess Distribution Formula:

    • Example Calculation: (0×1)+(14×2)+(77×3)+(149×4)+(95×5)+(40×6)=1570(0 \times 1) + (14 \times 2) + (77 \times 3) + (149 \times 4) + (95 \times 5) + (40 \times 6) = 1570

    • Average: 1570395=3.97\frac{1570}{395} = 3.97

  • Standard Deviation (SD) is important for understanding variability:

    • In normal distributions, SD approximates to about 1.

Statistical Tests

  • t-test:

    • Used for comparing means between two groups (independent/dependent).

    • Example Format: t(df) = x.xx, p < .xx.

  • ANOVA:

    • Compares means among more than two groups.

    • Example Format: F(df1, df2) = x.xx, p < .xx.

  • Correlation:

    • Measures relationships between continuous variables, represented by r.

    • Ranges from -1.0 (perfect negative) to +1.0 (perfect positive).

Significance Testing

  • p-value Interpretation:

    • p < .05 indicates statistical significance; reject the null hypothesis.

  • Understanding Statistical Tests:

    • t-test for time vs. memory performance; ANOVA for studying environments; paired samples t-test for repeated measures.