Mastering Statistics: Fundamentals to Data Analysis

Apply t significance testing to assess if a target value, like zero, is plausible based on sample data; interpret p values and relate findings to confidence intervals using real data.

Explore p values, null hypothesis, and the risk of type I and type II errors in significance testing through one-sample t-tests and optical sample data.

Explore t significance tests with case studies, interpreting p-values, null hypotheses, false positives and false negatives, and the relation between confidence intervals and significance testing.

Identify common pitfalls in statistical inference, including sample bias, under coverage, and misinterpreting confidence intervals and significance tests. Predefine hypotheses before analysis to avoid p-hacking and the shotgun effect.

Estimate and interpret population proportions from binary data using one-sample proportions test. Learn about confidence intervals, continuity correction, and practical methods like Wilson score interval and the rule of three.

Perform significance testing for proportions on a binary variable from a 100-item sample, compare to 0.66, interpret the p-value, and construct a 95% confidence interval for the proportion.

Analyze one-sample proportions tests and 95% confidence intervals on survey data, focusing on education level completed and age under 35. Interpret p-values, null hypotheses like p=0.60, and potential sampling issues.

Apply chi-squared goodness-of-fit tests to assess whether categorical age distributions fit a hypothesized US distribution, interpreting p-values and omnibus results. Explore uniformity tests across categories and introductory Benford's law problems.

Analyze a towns dataset to test Benford's law using a chi-squared goodness-of-fit test, comparing observed first-digit frequencies to the Benford distribution and interpreting the p-value.

Explore statistical power and its effect on detecting true differences via confidence intervals and sample size choices. Learn when to perform power analysis and margins of error for proportions.

Learn core statistics concepts, including population, sample, parameter, statistic, and inference, and how confidence intervals and variability shape conclusions while guarding against bias and emphasizing data hygiene.

Explore two-sample testing with independent, not paired samples by comparing two product reviews, compute mean ratings, and assess whether observed differences reflect population effects or random sampling variability.

Learn to compute a Welch two-sample confidence interval for the difference in means using an A/B testing data set of product ratings, with 15 and 12 samples.

Assess whether the age difference between sales and research and development is statistically significant using a Welch two sample t test, p values, and the 0.05 cutoff.

Apply Welch two-sample tests to construct a 95% confidence interval and test differences in mean monthly income and rate between departments using t.test in the attrition dataset.

Compare attrition rates across departments and travel groups using two-sample binary data. Estimate the difference in proportions with confidence intervals and significance tests in R.

Demonstrates the dangers of repeated significance testing and data dredging, showing how multiple p values inflate type i error and blurs the line between exploratory analysis and statistical inference.

Analyze two-sample categorical data by comparing gender-based substance abuse diagnoses with a chi-squared test for homogeneity; test whether distributions are the same, examine cell counts, and interpret the goodness-of-fit result.

collapse psychiatric admissions into a yes/no indicator and compare diagnoses, anxiety, depression, psychosis, trauma, with a chi squared test for homogeneity, yielding p = 8.7e-5 and indicating different distributions.

Learn how to assess two-variable relationships with scatter plots and sample correlation, including the -1 to 1 scale, linear trends, and differences between sample and population correlations.

Learn to assess correlation with scatter plots and a line of best fit, perform a correlation test, and interpret p-values, confidence intervals, effect size, and significance while considering sample size.

Fit and interpret a regression line with a linear model, understanding the slope and intercept. Learn to predict within the data range (interpolation) and avoid extrapolation.

Explore the strong linear relationship between city and highway mileage in the mpg 2008 data, use a regression line and correlation test, and predict highway mileage for city 24.

Learn how ANOVA tests whether a categorical work life balance relates to a quantitative monthly rate, using box plots, p-values, and assumptions checks.

Explore advanced ANOVA techniques using the MPG 2008 data to compare highway mileage across drive types, interpret p-values, visualize data, and apply Tukey HSD post-hoc tests.

Explore independence testing of two categorical variables using a chi squared test on a contingency table of age and product categories, with interpretation of p-values and the null hypothesis.

Perform a chi-squared test on a contingency table to assess independence. For intervention patients, run anova with Tukey post-hoc to compare opioid and alcohol groups.