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Descriptive Statistics

arithmetic mean weighted mean median mode range variance standard deviation interquartile range

Probability

sample space and events addition rule multiplication rule conditional probability Bayes theorem independence expected value law of total probability

Distributions

Bernoulli distribution binomial distribution Poisson distribution uniform distribution normal distribution exponential distribution z-score standardization central limit theorem simulation

Sampling & Estimation

simple random sampling sampling distribution of mean standard error point estimate confidence interval for mean confidence interval for proportion margin of error bootstrap estimate

Hypothesis Testing

null and alternative hypotheses p-value one-sample z test one-sample t test two-sample t test paired t test chi-square independence test Type I and Type II errors

Relationships & Models

covariance Pearson correlation Spearman rank correlation simple linear regression coefficient of determination R² residual analysis multiple regression concept confounding variables

Statistics / Hypothesis Testing

Type I and Type II errors

Learn Type I and Type II errors in Statistics with a dedicated explanation, a concept-specific example, practical cautions, and a mastery check.

12 min read • Advanced

statistics-040.py

python

alpha=.05; p_value=.03
reject=p_value<alpha
print('reject H0' if reject else 'fail to reject H0')
print('Type I risk is controlled by alpha =',alpha)

What to watch

Content source & attribution

Original Syntaxis Content · Original Syntaxis Content

Lesson quizzes

Type I and Type II errors Mastery Check →

chi-square independence test