Statistics & Probability4 min read
Bayes' Theorem: Why a Positive Test May Mean Only 15%
A test that catches 90% of cases with a 5% false-alarm rate still gives only a 15.4% chance of disease when prevalence is 1%. Bayes' theorem shows why.
The Calcylator Blog
Big ideas for
everyday numbers.
Practical guides, clear examples, and smarter ways to calculate.
Statistics & Probability guides
22 articles
- Statistics & Probability4 min read
Exact Binomial Probability: Chance of Exactly k Successes
P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. A 60% free-throw shooter hits exactly 5 of 8 about 27.9% of the time; the guide shows each step.
- Statistics & Probability4 min read
Chi-Square Statistic: Computing χ² by Hand
χ² = Σ (observed − expected)² ÷ expected. A 30/70 split against an expected 50/50 gives χ² = 16, far beyond the 3.84 cut-off at the 5% level for 1 df.
- Statistics & Probability6 min read
Coefficient of Variation: Compare Spread Fairly
The coefficient of variation is SD ÷ mean. A 50 g SD on 5 kg bags (1%) is steadier than a 4 g SD on 200 g packs (2%), despite the larger SD.
- Statistics & Probability4 min read
Conditional Probability: P(A given B) with Examples
If 12 of the 40 sport players also play music, P(music | sport) is 30%. Learn P(A|B), the Bayes link, and the trap of reversing the condition.
- Statistics & Probability4 min read
Confidence Intervals: How to Calculate and Read Them
With mean 100, σ 15 and n = 100, the 95% interval is 97.06 to 102.94. Learn the z and t formulas, margin of error, and what 95% really means.
Put what you learn into practice.
Explore our free calculators and apply these concepts to your own numbers.