Summary
Highlights
This unit introduces the concept of variables, distinguishing between categorical and quantitative (discrete and continuous). It outlines how to describe quantitative data using the acronym CUSS (Center, Unusual Features, Shape, Spread), detailing measures like mean, median, outliers, gaps, and types of distributions (unimodal, bimodal, skewed). Graphs like dot plots, stem-and-leaf plots, histograms, and box plots are discussed, along with the five-number summary and methods for identifying outliers. The section also covers z-scores and the normal distribution, including the 68-95-99.7 rule and the effects of adding/subtracting or multiplying/dividing constants on data sets.
Focusing on quantitative data, this unit explains how to describe relationships in scatter plots using the acronym SCUFF (Strength, Context, Unusual Features, Form, Direction). It covers the correlation coefficient (R) and coefficient of determination (R-squared), emphasizing linear regression, interpolation vs. extrapolation, and residual plots. The properties of the least squares regression line (LSRL) and the interpretation of computer-generated regression tables are also discussed.
This unit delves into proper data collection methods. It contrasts censuses with samples, emphasizing the necessity of random sampling for generalizability. Different sampling techniques, such as simple random, stratified, cluster, and systematic sampling, are explained. Common biases in sampling (undercoverage, non-response, volunteer, convenience, etc.) are reviewed. The distinction between observational studies (showing correlation) and experiments (allowing for causation) is highlighted, along with the four principles of good experimental design (Random, Comparisons, Replication, Control).
This unit covers the fundamentals of probability, including basic probability rules, complements, mutually exclusive events, and independent events. Formulas for 'or' and 'and' probabilities are presented, along with permutations and combinations. The concept of random variables (discrete and continuous), expected value, and standard deviation for random variables is introduced. Finally, it examines various probability distributions: uniform, normal, binomial (using BINS conditions and PDF/CDF calculations), and geometric (using BIFFS conditions).
This unit differentiates between parameters (population values) and statistics (sample values) and introduces sampling distributions for proportions and means. It explains the conditions for a valid sampling distribution (Random, 10% condition, Large Counts for proportions, and Central Limit Theorem for means). The unit emphasizes how increasing sample size decreases variability and how the Central Limit Theorem allows for approximately normal distributions for sample means and proportions under certain conditions.
This unit introduces inferential statistics, focusing on confidence intervals and hypothesis tests for proportions. It defines a confidence interval, its components (point estimator, margin of error), and how confidence level and sample size affect the margin of error. The process for conducting one-proportion Z-intervals and one-proportion Z-tests is detailed, including setting up null and alternative hypotheses, checking conditions, and interpreting p-values against significance levels (alpha) for rejecting or failing to reject the null hypothesis. Types of errors (Type I and Type II) and the concept of power are also explained.
Similar to unit 6, this unit applies inferential techniques to means. The key difference is the use of t-distributions instead of z-distributions, requiring degrees of freedom (n-1). The conditions for inference are similar: random sampling, 10% condition, and the Central Limit Theorem (n>=30 or a normal/no outliers distribution). The performance of one-sample and two-sample t-intervals and t-tests is outlined, following the same four C's structure (Choose, Conditions, Calculate, Conclude) as for proportions.
This unit covers three types of Chi-squared (χ²) tests, which are used to analyze categorical data: goodness-of-fit, homogeneity, and association/independence. The common conditions for these tests include random sampling, 10% condition, and all expected counts being greater than 5. It explains how to calculate the χ² statistic and degrees of freedom for each test (n-1 for goodness-of-fit, (rows-1)*(cols-1) for homogeneity and association), and how to identify which test to use based on the data structure (one-way vs. two-way frequency tables, number of samples/variables).
This final unit revisits linear regression from unit 2, but from an inferential perspective. It focuses on making inferences about the true slope (beta) of the population regression line. The conditions for inference (Linear, Independent, Normal, Equal Variance, Random - LINER) are crucial. Unlike previous units, calculations often rely on computer-generated output tables rather than direct calculator functions. The process for constructing confidence intervals and conducting significance tests for the slope is detailed, including interpreting coefficients, standard errors, t-values, and p-values from these tables, with degrees of freedom defined as N-2.