10. Statistics
Course Description:
This course introduces students to the collection and analysis of data by rational principles. We will discuss how to recognize sources of bias in data presented in the real world, and how to collect unbiased data ourselves. We will study how best to present and summarize data, using Microsoft Excel as our basic tool. We will study basic probability in depth as it is a foundation for Statistical reasoning. Finally, most of the second semester will be spent studying the bread-and-butter of statistics: confidence intervals, margins of error, hypothesis testing, and regression analysis in a wide variety of contexts.
The prerequisite for this class is Algebra 2, although it is generally recommended that students take Precalculus before taking Statistics.
The textbook is:
Barr, Diez, Dorazio, Cetinkaya-Rundel: Advanced High School Statistics, 1st Edition
The teacher is:
Detailed Course Topic List:
Data collection
Population vs. parameter, parameter vs. statistic
Observational study vs. experiment
Sources of bias when collecting data
Correlation vs. causation and lurking variables
Control and randomization in experiments
Placebo effect
Summarizing data
Intro to Microsoft Excel
Visual displays of data: histograms, scatterplots, dot plots, etc.
Shape of data: skew, modality, outliers
Measures of center: mean, median and relations between them
Measures of spread: standard deviation, range, and IQR
Mapping data
Summarizing categorical data: two-way tables, bar charts
Probability
Definition of probability
Law of Large Numbers
Addition and Multiplication rules for probability
Conditional probability and relation to independence
Visualizing probability with tree diagrams
Bayes' Theorem
Binomial Formula
Simulations
Probability distributions
Definition of a random variable
Probability distribution of a random variable
Expected value, variance, standard deviation
Discrete vs. continuous distributions
Binomial distribution
Normal distribution
Central Limit Theorem
Geometric distribution (if time)
Foundations of Statistical Inference
Point estimate of a statistics
Definition of a confidence interval and margin of error
Choosing a confidence level
Basic terminology of hypothesis testing
Type I and Type II errors
Inference for Categorical Data
Conditions for applying a normal approximation to categorical data
Inference for a single proportion and difference of two proportions
Testing Goodness of Fit and independence of data with the Chi-square distribution
Inference for Numerical Data
The t-distribution: definition and use in statistics
Calculating confidence intervals and margins of error using the t-distribution
Hypothesis testing for a single mean, paired data, and difference of two means
Comparing many means with ANOVA (if time)
Introduction to Regression analysis
Definition of the least-squares fit line
Correlation coefficient and strength of fit
Using the regression line for interpolation
Dangers of extrapolation
Effect of outliers on linear regression
Conditions for inference in linear regression
Interpretation of slope and intercept in context
Transforming non-linear data to apply linear regression