Introduction to Mathematical Statistics

The study of math statistics includes the collection, analysis, presentation and interpretation of data. When data is collected, summarised and represented as graphs, we can look for trends and try to make predictions based on these facts.

This series of lessons will cover:

A. Collecting and summarizing data

• Data
• Frequency and Frequency Tables

B. Common ways to describe data

• Mode
• Median
• Mean
• Range

C. Different ways to represent data

• Pictograms / Pictographs
• Bar Charts
• Line Graphs
• Pie Charts / Pie Graphs / Circle Graphs
• Box and Whiskers Plot
• Stem-and-Leaf Plot

D. Frequency Tables

• Frequency Tables
• Frequency Table with Intervals
• Mode and Mean from Frequency Table
• Mean from Frequency Table with Intervals
• Median from Freqeuncy Table
• Histogram with Uniform Widths
• Histogram with Non-Uniform Widths

E. Cumulative Frequency

• Cumulative Frequency Table
• Cumulative Frequency Graph
• Median, Quartiles, Percentiles (Ungrouped Data)
• Median, Quartiles, Percentiles (Grouped Data)
  

F. More Advanced Statistics

• Population Mean and Sample Mean
• Populaton Variance and Sample Variance
• Standard Deviation
• Random Variable
• Probability Density Functions
• Binomial Distribution
• Expected Value
• Poisson Distribution
• Normal Distribution
• Z-Score
• Bayes' Theorem
• Normal Probability Plot Videos
• Confidence Interval Videos
• Chi-Square Test Videos
• ANOVA Test
• Central Limit Theorem videos
• Sampling Distribution videos
• Logistic Equations videos
• Chebychev's Theorem videos

A series of free Statistics Lectures in videos from Statslectures

Descriptive Statistics

The Basics: Descriptive and Inferential Statistics
Sampling Methods

Types of Variables
Independent and Dependent Variables
Variable Measurement Scales

Frequency Distributions and Cumulative Frequency Distributions
Bar Graphs and Pie Charts
Histograms and Stem & Leaf Plots

Arithmetic Mean for Samples and Populations
Central Tendency: Mean, Median, and Mode

Variance and Standard Deviation of a Population
Variance and Standard Deviation of a Sample
Percentiles and Quartiles
The Five Number Summary, Interquartile Range(IQR), and Boxplots
The Effects of Outliers

Skewness
The Normal Curve and Empirical Rule

Z-Scores
Extra Z-Score Problems

Probability

The Basics of Probability
Addition Rule (Probability "or")
Multiplication Rule (Probability "and")
Permutations
Combinations
Discrete and Continuous Random Variables
Discrete Probability Distributions

Probability Histograms
Mean and Expected Value of Discrete Random Variables
Variance and Standard Deviation of Discrete Random Variables

The Law of Large Numbers
Binomial Distribution
Mean and Standard Deviation of Binomial Random Variables
Poisson Distribution/Process
Mean and Standard Deviation of Poisson Random Variables
Bernoulli Distribution


Correlation
Scatter Plots
Pearson's r Correlation
Hypothesis Testing with Pearson's r
Linear Regression
Spearman Correlation
Correlation vs. Causation

Inferential Statistics

Parameters, Statistics, and Sampling Error
Distribution of the Sample Mean
The Central Limit Theorem
Sample Proportions
Confidence Intervals about the Mean, Population Standard Deviation Known
Calculating Required Sample Size to Estimate Population Mean
Student's t-Distribution
Confidence Intervals about the Mean, Population Standard Deviation Unknown
Confidence Intervals for Population Proportions
Calculating Required Sample Size to Estimate Population Proportions

Null and Alternative Hypotheses
Type I and Type II Errors
One-Tailed and Two-Tailed Tests
Effect Size
Power
Statistical vs. Practical Significance
Independent and Dependent Samples

One Sample z-Test
One Sample z-Test for Proportions
One Sample t-Test

Independent Samples t-Test
Confidence Intervals for Independent Samples t-Test
Effect Size for Independent Samples t-Test
Dependent Samples t-Test
Confidence Intervals for Dependent Samples t-Test
Effect Size for Dependent Samples t-Test
z-Test for Proportions, Two Samples
Confidence Intervals for the Difference of Two Proportions

Introduction to ANOVA
One-Way ANOVA
Effect Size for One-Way ANOVA
Post-Hoc Tests for One-Way ANOVA
Repeated-Measures ANOVA
Factorial ANOVA, Two Independent Factors
Factorial ANOVA, Two Dependent Factors
Factorial ANOVA, Two Mixed Factors

Chi-Square Test for Goodness of Fit
Chi-Square Test for Independence

Mann-Whitney U-Test
Wilcoxon Signed-Ranks Test
The Kruskal-Wallis Test
The Friedman Test

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