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THE ESSENTIALS
Statistics, at a glance
The essentials · definitions, formulas & reminders
01The basics
Population: the complete group of interest.
Sample: a subset used to estimate a population.
Parameter: a population measure (μ, σ).
Statistic: a sample measure (x̄, s).
02Center & spread
Mean
Sample variance
Standard deviation:
IQR = Q₃ − Q₁; less sensitive to outliers.
03Probability rules
Complement:
Union:
Conditional:
If independent: .
04Normal distribution
Standard score:
About 68%, 95% and 99.7% of observations lie within 1, 2 and 3 standard deviations for a normal distribution.
Symmetric around μ; mean = median = mode.
05Confidence intervals
Mean, σ known
Mean, σ unknown
For a t interval, degrees of freedom = n − 1. Check sampling and distribution assumptions.
06Hypothesis testing
1. State H₀ and H₁.
2. Choose significance level α.
3. Check the test assumptions.
4. Calculate the test statistic and p-value.
5. If p ≤ α, reject H₀. Otherwise, fail to reject H₀.
A p-value is not the probability that H₀ is true.
07Correlation & regression
Correlation r: ranges from −1 to 1.
Linear model:
Residual: observed y − predicted ŷ.
R²: proportion of variation explained by the model.
Correlation alone does not establish causation.
08Remember
Check units and assumptions.
A larger sample reduces standard error.
Statistical significance ≠ practical importance.
A confidence level describes the long-run coverage of the method.
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