Course Updates for High School Statistics in July 2021

Conditional distributions and relationships

Identifying bias in samples and surveys

The language of experiments

Principles of experiment design

Random sampling vs. random assignment (scope of inference)

Conditional probability and independence

Tree diagrams and conditional probability

Calculating mean and median from data displays

Estimating mean and median in data displays

Sample standard deviation

Visually assess standard deviation

Identifying outliers

Calculate percentiles

Calculating z-scores

Normal distribution: Area above or below a point

Normal distribution: Area between two points

Normal calculations in reverse

Identify marginal and conditional distributions

Marginal distributions

Conditional distributions

Calculating and interpreting residuals

Residual plots

Identify the population and sample

Generalizability of results

Types of studies

Bias in samples and surveys

Simple random samples

Sampling methods

Sampling method considerations

Experiment designs

Experiment design considerations

Conclusions in observational studies versus experiments

Finding errors in study conclusions

Two-way tables, Venn diagrams, and probability

Probability with general multiplication rule

Interpret probabilities of compound events

Calculate conditional probability

Interpret results of simulations

Graph probability distributions

Probability with discrete random variables

Develop probability distributions: Theoretical probabilities

Develop probability distributions: Empirical probabilities

Use probabilities to make fair decisions

Mean (expected value) of a discrete random variable

Interpret expected value

Find expected payoffs

Median in a histogram

Estimating mean and median in data displays

Sample variance

Sample standard deviation and bias

Visually assessing standard deviation

Mean and standard deviation versus median and IQR

Worked example: Creating a box plot (odd number of data points)

Worked example: Creating a box plot (even number of data points)

Judging outliers in a dataset

Example: Comparing distributions

Calculating percentile

Z-score introduction

Comparing with z-scores

Standard normal table for proportion below

Standard normal table for proportion above

Standard normal table for proportion between values

Finding z-score for a percentile

Threshold for low percentile

Two-way frequency tables and Venn diagrams

Marginal and conditional distributions

Bivariate relationship linearity, strength and direction

Interpreting slope of regression line

Interpreting y-intercept in regression model

Introduction to residuals and least-squares regression

Calculating residual example

Residual plots

Identifying a sample and population

Generalizabilty of survey results example

Types of studies

Worked example identifying observational study

Invalid conclusions from studies example

Examples of bias in surveys

Example of undercoverage introducing bias

Techniques for generating a simple random sample

Techniques for random sampling and avoiding bias

Systematic random sampling

Introduction to experiment design

Matched pairs experiment design

Statistical significance of experiment

Can causality be established from this study?

General multiplication rule example: independent events

General multiplication rule example: dependent events

Interpreting general multiplication rule

Conditional probability and independence

Conditional probability with Bayes' Theorem

Conditional probability tree diagram example

Experimental versus theoretical probability simulation

Random number list to run experiment

Random numbers for experimental probability

Factorial and counting seat arrangements

Zero factorial or 0!

Probability using combinations

Example: Lottery probability

Probability with permutations & combinations example: taste testing

Probability with combinations example: choosing groups

Probability with combinations example: choosing cards

Constructing a probability distribution for random variable

Valid discrete probability distribution examples

Probability with discrete random variable example

Theoretical probability distribution example: tables

Theoretical probability distribution example: multiplication

Probability distributions from empirical data

Using probabilities to make fair decisions example

Mean (expected value) of a discrete random variable

Interpreting expected value

Expected payoff example: lottery ticket

Expected payoff example: protection plan

Comparing range and interquartile range (IQR)

The idea of spread and standard deviation

Calculating standard deviation step by step

Two-way frequency tables

Two-way relative frequency tables and associations

Positive and negative associations in scatterplots

Samples and surveys

Observational studies and experiments

Probability: the basics

Theoretical and experimental probability: Coin flips and die rolls

Expected value (basic)

Binomial probability (basic)

Shape of distributions

Mean, median, and mode

Missing value given the mean

Standard deviation of a population

Create two-way relative frequency tables

Constructing scatter plots

Making appropriate scatter plots

Positive and negative linear associations from scatter plots

Describing trends in scatter plots

Valid claims

Making inferences from random samples

Types of statistical studies

Simple probability

Experimental probability

Making predictions with probability

Comparing probabilities

Probability models

Adding probabilities

Probabilities of compund events

Independent probability

Dependent probability

The counting principle

Shapes of distributions

Mean, median, & mode example

Missing value given the mean

Impact on median & mean: removing an outlier

Impact on median & mean: increasing an outlier

Effects of shifting, adding, & removing a data point

Measures of spread: range, variance & standard deviation

Constructing a box plot

Comparing distributions with dot plots (example problem)

Interpreting a trend line

Constructing a scatter plot

Example of direction in scatterplots

Reasonable samples

Types of statistical studies

Appropriate statistical study example

Intro to theoretical probability

Simple probability: yellow marble

Simple probability: non-blue marble

Experimental probability

Theoretical and experimental probabilities

Making predictions with probability

Intuitive sense of probabilities

Probability models example: frozen yogurt

Free-throw probability

Independent & dependent probability

Dependent probability: coins

Counting outcomes: flower pots

Count outcomes using tree diagram

Probability with counting outcomes

Example: All the ways you can flip a coin

Example: Combinatorics and probability

Binomial probability example

Generalizing k scores in n attempts

Free throw binomial probability distribution

Graphing basketball binomial distribution