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Statstics with Python

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01. Categorical Data

01 Identifying individuals, variables and categorical variables in a data set
02. Creating a bar graph
03 Reading bar charts - comparing two sets of data
04 Reading bar graphs movies
05 Two-way frequency tables and Venn diagrams
06 Two-way (column or row) relative frequency tables
07 Interpreting two-way tables
08 Marginal and conditional distributions
09 Mosaic plots and segmented bar charts
10 Analyzing mosaic plots
Categorical Data

02. Displaying and comparing quantitative data

01 Frequency tables & dot plots
02 Creating a histogram
03 Interpreting a histogram
04 Stem-and-leaf plots
05 Reading stem and leaf plots
06 Classifying shapes of distributions
07 Example - Describing a distribution
08 Example - Comparing distributions

03 Summarizing quantitative data

01 Statistics intro - Mean, median, & mode
02 Mean, median, & mode example
03 Median in a histogram
04 Missing value given the mean
05 Impact on median & mean - increasing an outlier
06 Impact on median & mean - removing an outlier
07 Estimating mean and median in data displays
08 Interquartile range (IQR)
09 Sample variance
10 Sample standard deviation and bias
11 Visually assessing standard deviation
12 Mean and standard deviation versus median and IQR
13 Review and intuition why we divide by n-1 for the unbiased sample variance
14 Why we divide by n - 1 in variance
15 Simulation showing bias in sample variance
16 Simulation providing evidence that (n-1) gives us unbiased estimate
17 Worked example - Creating a box plot (odd number of data points)
18 Worked example - Creating a box plot (even number of data points)
19 Reading box plots
20 Interpreting box plots
21 Judging outliers in a dataset

04 Modeling data distributions

01 Calculating percentile
02 Analyzing a cumulative relative frequency graph (optional)
02 Analyzing a cumulative relative frequency graph
03 Z-score introduction
04 Comparing with z-scores
05 How parameters change as data is shifted and scaled
06 Density Curves
07 Median, mean and skew from density curves
08 Density curve worked example
09 Worked example finding area under density curves
10 Qualitative sense of normal distributions (from ck12.org)
11 Normal distribution problems - Empirical rule (from ck12.org)
12 Standard normal table for proportion below
13 Standard normal table for proportion above
14 Standard normal table (optional)
15 Finding z-score for a percentile

05 Exploring bivariate numerical data

01 Constructing a scatter plot
02 Example of direction in scatterplots
03 Bivariate relationship linearity, strength and direction
04 Calculating correlation coefficient r
05 Example - Correlation coefficient intuition
06 Introduction to residuals and least-squares regression
07 Calculating residual example
08 Calculating the equation of a regression line
09 Interpreting slope of regression line
10 Interpreting y-intercept in regression model
11 Using least squares regression output
12 Residual plots
13 R-squared or coefficient of determination
14 Standard deviation of residuals or root mean square deviation (RMSD)
15 Interpreting computer regression data
16 Impact of removing outliers on regression lines

06 Study design

01 Identifying a sample and population
02 Generalizabilty of survey results example
03 Examples of bias in surveys
04 Example of undercoverage introducing bias
05 Techniques for generating a simple random sample
06 Techniques for random sampling and avoiding bias
07 Types of statistical studies
08 Worked example identifying experiment
09 Worked example identifying observational study
10 Introduction to experiment design
11 Matched pairs experiment design
12 Invalid conclusions from studies example
13 Can causality be established from this study

07 Probability

01 Intro to theoretical probability
02 Experimental versus theoretical probability simulation
03 Random number list to run experiment
04 Random numbers for experimental probability
05 Statistical significance of experiment
06 Probability with Venn diagrams
07 Addition rule for probability
08 Compound probability of independent events
09 Independent events example - test taking
11 Three-pointer vs free-throw probability
12 Dependent probability introduction
13 Coin flipping probability
14 Conditional probability and independence
15 Conditional probability with Bayes’ Theorem
16 Conditional probability tree diagram example
Untitled

08 Counting, permutations, and combinations

01 Count outcomes using tree diagram
02 Counting outcomes flower pots
03 Permutation formula
04 Zero factorial or 0!
05 Factorial and counting seat arrangements
06 Possible three letter words
07 Ways to arrange colors
08 Ways to pick officers
09 Intro to combinations
10 Combination formula
11 Handshaking combinations
12 Combination example 9 card hands
13 Probability using combinations
14 Probability & combinations (2 of 2)
15 Example Different ways to pick officers
16 Example Combinatorics and probability
17 Getting exactly two heads (combinatorics)
18 Exactly three heads in five flips
19 Generalizing with binomial coefficients (bit advanced)
20 Example Lottery probability
21 Conditional probability and combinations
22 Mega millions jackpot probability
23 Birthday probability problem

09 Random variables

01 Constructing a probability distribution for random variable
02 Valid discrete probability distribution examples
03 Probability with discrete random variable example
04 Mean (expected value) of a discrete random variable
05 Variance and standard deviation of a discrete random variable
06 Probabilities from density curves
07 Impact of transforming (scaling and shifting) random variables
08 Example - Transforming a discrete random variable
09 Mean of sum and difference of random variables
10 Variance of sum and difference of random variables
11 Intuition for why independence matters for variance of sum
12 Deriving the variance of the difference of random variables
13 Example - Analyzing distribution of sum of two normally distributed random variables
14 Example - Analyzing the difference in distributions
15 Binomial variables
16 Recognizing binomial variables
18 Binomial probability example
19 Generalizing k scores in n attempts
20 Free throw binomial probability distribution
21 Graphing basketball binomial distribution
22 Binompdf and binomcdf functions
23 Expected value of a binomial variable
24 Variance of a binomial variable
25 Finding the mean and standard deviation of a binomial random variable
26 Geometric random variables introduction
27 Probability for a geometric random variable
28 Cumulative geometric probability (greater than a value)
29 Cumulative geometric probability (less than a value)
30 TI-84 geometpdf and geometcdf functions
31 Proof of expected value of geometric random variable

10 Sampling distributions

01 Introduction to sampling distributions
02 Sample statistic bias worked example
03 Sampling distribution of sample proportion part 1
04 Sampling distribution of sample proportion part 2
05 Normal conditions for sampling distributions of sample proportions
06 Probability of sample proportions example
07 Central limit theorem
08 Sampling distribution of the sample mean
09 Sampling distribution of the sample mean 2
10 Standard error of the mean
11 Example - Probability of sample mean exceeding a value

11 Confidence intervals

01 Confidence intervals and margin of error
02 Confidence interval simulation
03 Interpreting confidence level example
04 Interpreting confidence levels and confidence intervals
05 Confidence interval example
06 Margin of error 1
07 Margin of error 2
08 Conditions for valid confidence intervals
09 Conditions for confidence intervals worked examples
10 Reference Conditions for inference on a proportion
11 Critical value (z) for a given confidence level
12 Example constructing and interpreting a confidence interval for p
13 Interpreting a z interval for a proportion
14 Determining sample size based on confidence and margin of error
15 Introduction to t statistics
16 Simulation showing value of t statistic
17 Conditions for valid t intervals
18 Reference Conditions for inference on a mean
19 Example finding critical t value
20 Example constructing a t interval for a mean
21 Confidence interval for a mean with paired data
22 Making a t interval for paired data
23 Interpreting a confidence interval for a mean
24 Sample size for a given margin of error for a mean
25 T-statistic confidence interval
26 Small sample size confidence intervals

12 Significance tests (hypothesis testing)

01 Simple hypothesis testing
02 Idea behind hypothesis testing
03 Examples of null and alternative hypotheses
04 P-values and significance tests
05 Comparing P-values to different significance levels
06 Estimating a P-value from a simulation
07 Using P-values to make conclusions
08 Introduction to Type I and Type II errors
09 Type 1 errors
10 Examples identifying Type I and Type II errors
11 Introduction to power in significance tests
12 Examples thinking about power in significance tests
13 Consequences of errors and significance
14 Constructing hypotheses for a significance test about a proportion
15 Conditions for a z test about a proportion
16 Reference Conditions for inference on a proportion
17 Calculating a z statistic in a test about a proportion
18 Calculating a P-value given a z statistic
19 Making conclusions in a test about a proportion
20 Writing hypotheses for a significance test about a mean
21 Conditions for a t test about a mean
22 Reference Conditions for inference on a mean
23 When to use z or t statistics in significance tests
24 Example calculating t statistic for a test about a mean
25 Using TI calculator for P-value from t statistic
26 Using a table to estimate P-value from t statistic
27 Comparing P-value from t statistic to significance level
28 Free response example Significance test for a mean
29 Hypothesis testing and p-values
30 One-tailed and two-tailed tests
31 Z-statistics vs. T-statistics
32 Small sample hypothesis test
33 Large sample proportion hypothesis testing

13 Inference comparing two groups or populations (AP)

01 Confidence intervals for the difference between two proportions
02 Examples identifying conditions for inference on two proportions
03 Calculating a confidence interval for the difference of proportions
04 Hypothesis test for difference in proportions
05 Constructing hypotheses for two proportions
06 Hypothesis test for difference in proportions example
07 Comparing P value to significance level for test involving difference of proportions
08 Confidence interval for hypothesis test for difference in proportions
09 Conditions for inference for difference of means
10 Constructing t interval for difference of means
11 Calculating confidence interval for difference of means
12 Hypotheses for a two-sample t test
13 Example of hypotheses for paired and two-sample t tests
14 Two-sample t test for difference of means
15 Conclusion for a two-sample t test using a P-value
16 Conclusion for a two-sample t test using a confidence interval
Untitled

13 Two-sample inference for the difference between groups

01 Comparing population proportions 1
02 Comparing population proportions 2
03 Hypothesis test comparing population proportions
04 Statistical significance of experiment
05 Statistical significance on bus speeds
06 Difference of sample means distribution
07 Confidence interval of difference of means
08 Clarification of confidence interval of difference of means
09 Hypothesis test for difference of means

14 Inference for categorical data (chi-square tests)

01 Chi-square distribution introduction
02 Pearson’s chi square test (goodness of fit)
03 Chi-square statistic for hypothesis testing
04 Chi-square goodness-of-fit example
05 Filling out frequency table for independent events
06 Contingency table chi-square test
07 Introduction to the chi-square test for homogeneity
08 Chi-square test for association (independence)

15 Advanced regression (inference and transforming)

01 Conditions for inference on slope
02 Introduction to inference about slope in linear regression
03 Confidence interval for the slope of a regression line
04 Calculating t statistic for slope of regression line
05 Using a P-value to make conclusions in a test about slope
06 Using a confidence interval to test slope
07 Comparing models to fit data example
08 Transforming nonlinear data
09 Worked example of linear regression using transformed data

16 Analysis of variance (ANOVA)

01 ANOVA 1 Calculating SST (total sum of squares)
02 ANOVA 2 Calculating SSW and SSB (total sum of squares within and between)
03 ANOVA 3 Hypothesis test with F-statistic

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