Statistical Analysis Fundamentals for Psychology

1. Type I and Type II Errors

Type I Error (α): Occurs when a researcher rejects a true null hypothesis (a "false positive").

Type II Error (β): Occurs when a researcher fails to reject a false null hypothesis (a "false negative").

The goal of statistical testing is to minimize both errors simultaneously.

2. Parametric vs. Non-Parametric Statistics

Parametric Tests: These assume data is normally distributed and use interval/ratio scales (e.g., t-test, ANOVA).

Non-Parametric Tests: These are "distribution-free" tests used for nominal/ordinal data or small samples (e.g., Chi-square, Mann-Whitney U).

Parametric tests are generally more powerful if their assumptions are met.

3. Null Hypothesis (H₀) vs. Alternative Hypothesis (H₁)

Null Hypothesis (H₀): A statement of no effect or no difference between groups.

Alternative Hypothesis (H₁): A statement that there is a significant effect or difference.

Statistical tests are designed to determine if H₀ can be rejected.

4. Level of Significance (α)

The probability of committing a Type I error, usually set at 0.05 or 0.01 in psychology.

A 0.05 level means there is a 5% chance the results occurred by random accident. It serves as the threshold (critical value) for rejecting the null hypothesis.

5. Degrees of Freedom (df)

Refers to the number of values in a final calculation that are free to vary.

In ANOVA, df is split into:

• Between Groups: (K-1)
• Within Groups: (N-K)

It is essential for locating the correct critical value in statistical tables.

6. Assumptions of ANOVA

To ensure valid results, ANOVA requires:

• Normality: The dependent variable should be normally distributed within each group.
• Homogeneity of Variance: The variance (spread) should be roughly equal across all groups.
• Independence: Observations must be independent of one another.

7. One-Tailed vs. Two-Tailed Tests

One-Tailed: Used when the researcher predicts a specific direction of the effect (e.g., Group A will be higher than Group B).

Two-Tailed: Used when the researcher predicts a difference exists but does not specify the direction.

Two-tailed tests are more conservative and are commonly used in psychology.

8. Kruskal-Wallis Test

The non-parametric alternative to a One-Way ANOVA.

Used to compare three or more independent groups when data is ordinal or not normally distributed. It is based on ranking the data rather than using raw means.

9. Advantages of Using SPSS in Data Analysis

• Efficiency: Can process large datasets much faster than manual calculation.
• Accuracy: Reduces human error in complex mathematical formulas.
• Visualization: Easily generates professional graphs, charts, and distribution plots.

10. Normal Probability Curve (NPC)

A bell-shaped, symmetrical theoretical distribution where the mean, median, and mode coincide at the center.

The total area under the curve is equal to 1.00 or 100%. Specific percentages of data fall within standard deviations (e.g., 68.26% within ±1 SD).