# Statistics

Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!).

• ##### Statistics: The Average
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Introduction to descriptive statistics and central tendency. Ways to measure the average of a set: median, mean, mode.

• ##### Sample vs. Population Mean
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The difference between the mean of a sample and the mean of a population.

• ##### Variance of a Population
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Variance of a population.

• ##### Sample Variance
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Using the variance of a sample to estimate the variance of a population.

• ##### Standard Deviation
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Review of what we've learned. Introduction to the standard deviation.

• ##### Alternate Variance Formulas
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Playing with the formula for variance of a population.

• ##### Introduction to Random Variables
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Introduction to random variables and probability distribution functions.

• ##### Probability Density Functions
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Probability density functions for continuous random variables.

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• ##### Expected Value: E(X)
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Expected value of a random variable.

• ##### Poisson Process 1
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Introduction to Poisson Processes and the Poisson Distribution.

• ##### Poisson Process 2
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More of the derivation of the Poisson Distribution.

• ##### Law of Large Numbers
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Introduction to the law of large numbers.

• ##### Normal Distribution Excel Exercise
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(Long-26 minutes) Presentation on spreadsheet to show that the normal distribution approximates the binomial distribution for a large number of trials.

• ##### Introduction to the Normal Distribution
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Exploring the normal distribution.

• ##### Qualitative Sense of Normal Distributions
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Discussion of how "normal" a distribution might be.

• ##### Z-Score
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Z-score practice.

• ##### Emperical Rule
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Using the empirical rule (or 68-95-99.7 rule) to estimate probabilities for normal distributions.

• ##### Standard Normal Distribution and the Empirical Rule
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Using the Empirical Rule with a standard normal distribution.

• ##### More Emperical Rule and Z-Score Practice
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More Empirical Rule and Z-score practice.

• ##### Central Limit Theorem
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Introduction to the central limit theorem and the sampling distribution of the mean.

• ##### Sampling Distribution of the Sample Mean Part 1
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The central limit theorem and the sampling distribution of the sample mean.

• ##### Sampling Distribution of the Sample Mean Part 2
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More on the Central Limit Theorem and the Sampling Distribution of the Sample Mean.

• ##### Standard Error of the Mean
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Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean.

• ##### Sampling Distribution of the Sample Mean
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Figuring out the probability of running out of water on a camping trip.

• ##### Mean and Variance of Bernoulli Distribution Example
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Mean and Variance of Bernoulli Distribution Example.

• ##### Bernoulli Distribution Mean and Variance Formulas
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Bernoulli Distribution Mean and Variance Formulas.

• ##### Margin of Error 1
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Finding the 95% confidence interval for the proportion of a population voting for a candidate.

• ##### Margin of Error 2
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Finding the 95% confidence interval for the proportion of a population voting for a candidate.

• ##### Confidence Interval Example
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Confidence Interval Example.

• ##### Small Sample Size Confidence Intervals
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Constructing small sample size confidence intervals using t-distributions.

• ##### One-Tailed and Two-Tailed Tests
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One-Tailed and Two-Tailed Tests.

• ##### Z-statistics vs. T-statistics
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Z-statistics vs. T-statistics.

• ##### Type 1 Errors
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Type 1 Errors.

• ##### Small Sample Hypothesis Test
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Small Sample Hypothesis Test.

• ##### T-Statistic Confidence Interval
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T-Statistic Confidence Interval (for small sample sizes).

• ##### Large Sample Proportion Hypothesis Testing
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Large Sample Proportion Hypothesis Testing.

• ##### Variance of Differences of Random Variables
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Variance of Differences of Random Variables.

• ##### Difference of Sample Means Distribution
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Difference of Sample Means Distribution.

• ##### Confidence Interval of Difference of Means
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Confidence Interval of Difference of Means.

• ##### Clarification of Confidence Interval of Difference of Means
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Clarification of Confidence Interval of Difference of Means.

• ##### Hypothesis Test for Difference of Means
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Hypothesis Test for Difference of Means.

• ##### Comparing Population Part 1
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Comparing Population Proportions 1.

• ##### Comparing Population Part 2
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Comparing Population Proportions 2.

• ##### Hypothesis Test Comparing Population Proportions
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Hypothesis Test Comparing Population Proportions.

• ##### Squared Error of Regression Line
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Introduction to the idea that one can find a line that minimizes the squared distances to the points.

• ##### Minimizing Squared Error to Regression Line Part 1
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Proof (Part 1) Minimizing Squared Error to Regression Line.

• ##### Minimizing Squared Error to Regression Line Part 3
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Proof (Part 3) Minimizing Squared Error to Regression Line.

• ##### Minimizing Squared Error to Regression Line Part 4
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Proof (Part 4) Minimizing Squared Error to Regression Line.

• ##### Regression Line Example
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Regression Line Example.

• ##### Minimizing Squared Error to Regression Line 2
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Proof Part 2 Minimizing Squared Error to Line.

• ##### R-Squared or Coefficient of Determination
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R-Squared or Coefficient of Determination.

• ##### Second Regression Example
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Second Regression Example.

• ##### Calculating R-Squared
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Calculating R-Squared to see how well a regression line fits data.

• ##### Covariance and the Regression Line
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Covariance, Variance and the Slope of the Regression Line.

• ##### Chi-Square Distribution Introduction
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Chi-Square Distribution Introduction.

• ##### Pearson's Chi Square Test (Goodness of Fit)
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Pearson's Chi Square Test (Goodness of Fit).

• ##### Contingency Table Chi-Square Test
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Contingency Table Chi-Square Test.

• ##### Calculating SST (Total Sum of Squares)
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Analysis of Variance 1 - Calculating SST (Total Sum of Squares).

• ##### Calculating SSW and SSB (Total Sum of Squares Within and Between)
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Analysis of Variance 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).

• ##### Hypothesis Test with F-Statistic
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Analysis of Variance 3 -Hypothesis Test with F-Statistic.