Types of Statistical Inference

Estimation

INFO

Techniques that allows analysts to approximate population parameters using sample data while accounting for uncertainty

• point estimation
• confidence intervals
  • provide range of plausible values for a parameter
  • offer insights into the reliability of an estimate
• Common Employed Methods
  • Maximum Likelihood Estimation (MLE): focus on finding the parameter values that maximize the probability of observed data
  • Bayesian estimation: incorporates prior knowledge to update beliefs based on new evidence

Hypothesis Testing

INFO

enables data scientists to assess the validity of claims or assumptions about population characteristics

• formulates null and alternative hypothesis
  • uses statistical tests to determine whether observed patterns are due to chance or reflect significant underlying relationships
    • t-test
    • chi-square test
    • ANOVA
    • correlation
    • regression-based tests
  • selection of appropriate test depends on factors
    • sample size
    • distribution assumptions
    • nature of variables under investigation
  • p-values and confidence intervals helps quantify the strength of evidence against the null hypothesis, guiding decision-making
• Essential to account for potential errors, which can influence the reliability of inferences
  • Type I (false positives)
  • Type II (false negatives)
• Hypothesis

INFO

• testable statement about the relationship between 2 or more variables or a proposed explanation for some observed phenomenon
• brief summation of the researcher’s prediction of the study’s findings, which may or may not be supported by the outcome

IMPORTANT

Core of scientific method

• statistical hypothesis

INFO

method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis

• In business analytics
  • provides a structured framework for evaluating whether observed data significantly deviate from established norms or expectations → guiding strategic decisions
• In marketing
  • helps to determine if changes in strategy lead to significant differences in consumer behavior to identify variations in manufacturing processes and assess their impact on product quality
• Approaches to Hypothesis Testing
  • modern statistical inference techniques
    • leveraged computational advancements
      • enhance accuracy and scalability
  • Resampling methods
    • bootstrapping and permutation testing
    • provide robust alternatives when parametric assumptions are difficult to meet
  • Bayesian inference
    • gained prominence in machine learning applications
      • probabilistic modeling and reinforcement learning
  • Integration of statistical inference with artificial intelligence techniques enables more sophisticated analyses
    • Monte Carlo methods
    • Markov Chain Monte Carlo (MCMC) simulations
  • Allowed to
    • quantify uncertainty
    • make probabilistic predictions
    • refine models dynamically based on new data
    • reinforcing the critical role of statistical inference in driving data-driven decision-making