Statistics & Probability

Truth Check

• Axis manipulation (truncated scales) can mislead.
• Cherry-picked start/end dates distort trends.
• 3D charts and odd baselines exaggerate differences.

Center & Spread

• Mean, median, mode
• Range, IQR, variance, standard deviation

Shape

• Skewed left/right, symmetric
• Outliers: 1.5×IQR rule

Rules

• 0 ≤ P(A) ≤ 1; P(S) = 1
• Complement: P(Aᶜ) = 1 - P(A)
• Addition: P(A ∪ B) = P(A)+P(B)-P(A∩B)
• Independence: P(A∩B) = P(A)P(B)

Definition

Bayes: P(A|B) = [P(B|A)P(A)] / P(B)

Key Models

• Binomial: P(X=k) = C(n,k) p^k (1-p)^{n-k}
• Normal: Mean μ, sd σ; 68-95-99.7 rule
• Uniform & geometric (overview)

Common Biases

• Selection bias
• Nonresponse bias
• Convenience sampling
• Loaded/leading questions

Basics

For population mean (σ known): CI = x̄ ± z* (σ/√n)

Interpretation: If we repeated sampling, about C% of intervals would capture μ.

Framework

1. State hypotheses (H₀, H₁)
2. Choose test & conditions
3. Calculate statistic & p-value
4. Conclusion in context

Beware p-hacking and cherry-picking α.

Key Points

• Correlation r measures linear strength (-1 to 1)
• Correlation ≠ causation
• Least-squares line minimizes squared residuals
• Check residual plot for fit

Best Practices

• Report methods, sample size, limitations.
• Show full axes and raw data when possible.
• Avoid loaded language; state plain findings.
• Disclose conflicts of interest and funding sources.

Why Integrity Matters

• Misused statistics have justified harmful policies and deception.
• Believers must handle truth carefully; numbers are not neutral.
• Objective reality reflects the God of truth; data should serve truth, not agendas.

Bring It Together

• Describe → Infer → Decide → Communicate
• Check assumptions, avoid bias, report honestly
• Use statistics to reveal truth, not hide it