Causal Inference Basics: Why Prediction Accuracy Does Not Mean Real Effect
Causal inference separates prediction from effect. A model can predict who will buy without proving that an intervention will make them buy.
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How Do You Tell Goodness-of-Fit From Independence in Chi-Square Problems?
Chi-square tests compare observed counts with expected counts. First decide whether the problem is goodness-of-fit for one categorical variable or independence for two categorical variables.
When Should Bernoulli, Binomial, Normal, and Poisson Appear?
Distributions are names for data-generating situations, not formula cards. Learn when Bernoulli, Binomial, Poisson, and Normal distributions fit a problem.
How Do You Write Confidence Intervals Without Only Memorizing Bounds?
A confidence interval puts a point estimate back inside sampling fluctuation. Computing bounds is only the first step; you also need to explain standard error, critical values, and coverage.
When You See a Dataset, What Statistics Should You Check First?
Data type determines the statistical tools you can use. Start with categorical, numeric, count, and time-ordered data, then choose summaries that fit the question.
How Does the Delta Method Estimate Uncertainty for F1 and Ratio Metrics?
The delta method transfers uncertainty through a smooth function: the local derivative expands or shrinks the estimator's original standard error.
What Makes an Estimator Good: Bias, Variance, or MSE?
An estimator is a rule for using samples to infer a population parameter. To judge whether it is good, look at bias, variance, and MSE together.
When a Mixed Problem Appears, How Do You Pick the Tool in 30 Seconds?
At the final review stage, train problem recognition: identify data type, unknown quantity, and decision goal before choosing a formula and writing a contextual conclusion.
What Do Expectation and Variance Mean in Exams and Model Evaluation?
Expectation describes long-run center; variance describes fluctuation. This post computes E[X], E[X^2], and Var(X), then connects them to average loss and model stability.
How Does Experimental Design Make Results Interpretable Rather Than Merely Correlated?
Experimental design decides whether a result can be interpreted. Randomization, control, blocking, replication, blinding, and pre-specified outcomes give inference a usable foundation.
How Does Fisher Information Tell You Whether a Parameter Is Stable?
Fisher information uses likelihood curvature to measure how well the data locate a parameter; larger information usually means a smaller standard error for the MLE.
Confidence Intervals Are More Than t-Tables: What Is the General Construction?
A confidence interval is built by defining the target estimate, describing its sampling error, and choosing a rule that turns uncertainty into a range.
How Does a GLM Choose Distributions and Link Functions by Data Type?
A generalized linear model starts from the response type, chooses a suitable distribution, and uses a link function to connect the mean to a linear predictor.
From H0 to p-Values, What Decision Is a Hypothesis Test Making?
A hypothesis test is a decision process under uncertainty: write H0/H1, choose alpha, compute a test statistic and p-value, then decide whether the data is strong enough to challenge H0.
How Do Estimation, Testing, Likelihood, and Bayes Fit on One Inference Map?
The inference map starts with the question type: point estimate, uncertainty interval, decision test, likelihood model comparison, Bayesian update, or resampling.
How Does the Likelihood Ratio Test Compare Nested Models?
The likelihood-ratio test compares the log likelihood of a restricted model with a full model; the usual chi-square reference only makes sense under nested-model and approximation conditions.
When OLS Assumptions Fail, How Can the Regression Line Still Be Used?
OLS is a useful baseline, but coefficient interpretation, inference, prediction, and diagnosis depend on assumptions about linearity, errors, independence, and variance.
How Does Logistic Regression Move From Probability to Thresholds and Error Costs?
Logistic regression estimates probabilities first. Classification decisions come later, when thresholds turn those probabilities into actions under real error costs.
Why Should Classification Start With Log Odds?
Logistic regression connects a linear score to a probability between 0 and 1. Understanding odds, log odds, and odds ratios prevents wrong coefficient interpretations.
Why Does MAP Turn Priors Into Regularization?
MAP maximizes the posterior. After taking logs, the prior becomes a penalty term, which connects Bayesian estimation to L1, L2, and regularized ML objectives.