Statistical inference

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Inferential statistics or statistical induction comprises the use of statistics to make inferences concerning some unknown aspect of a population. It is distinguished from descriptive statistics.

Two schools of inferential statistics are frequency probability and Bayesian inference.

See also

• Descriptive statistics
• Induction (philosophy)

Definition

Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time. It includes:

1. point estimation
2. interval estimation
3. hypothesis testing (or statistical significance testing)
4. prediction

There are several distinct schools of thought about the justification of statistical inference. All are based on some idea of what real world phenomena can be reasonably modeled as probability.

1. frequency probability
2. Bayesian probability
3. fiducial probability
4. eclectic probability

The topics below are usually included in the area of statistical inference.

1. Statistical assumptions
2. Likelihood principle
3. Estimating parameters
4. Statistical hypothesis testing
5. Revising opinions in statistics
6. planning statistical research
7. summarizing statistical data

v • d • e Statistics
Descriptive statistics	Mean (Arithmetic, Geometric) - Median - Mode - Power - Variance - Standard deviation
Inferential statistics	Hypothesis testing - Significance - Null hypothesis/Alternate hypothesis - Error - Z-test - Student's t-test - Maximum likelihood - Standard score/Z score - P-value - Analysis of variance
Survival analysis	Survival function - Kaplan-Meier - Logrank test - Failure rate - Proportional hazards models
Probability distributions	Normal (bell curve) - Poisson - Bernoulli
Correlation	Confounding variable - Pearson product-moment correlation coefficient - Rank correlation (Spearman's rank correlation coefficient, Kendall tau rank correlation coefficient)
Regression analysis	Linear regression - Nonlinear regression - Logistic regression

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