Statistics
MTH1495 ccs
Introduction to Statistics

This course will begin with a brief overview of the discipline of statistics and will then quickly focus on descriptive statistics, introducing graphical methods of describing data. You will learn about combinatorial probability and random distributions, the latter of which serves as the foundation for statistical inference. On the side of inference, we will focus on both estimation and hypothesis testing issues. We will also examine the techniques to study the relationship between two or more variables; this is known as regression. By the end of this course, you should gain a sound understanding about what statistics represent, how to use statistics to organize and display data, and how to draw valid inferences based on data by using appropriate statistical tools.

Unit 1: Statistics and Da...

Upon successful completion of this unit, you will be able to: describe various types of sampling methods to data collection, and apply these methods; create and interpret frequency tables; display data graphically and interpret the following types of graphs: stem plots, histograms, and boxplots; identify, describe, and calculate the following measures of the location of data: quartiles and percentiles; identify, describe, and calculate the measures of the center of mean, median, and mode; and identify, describe, and calculate the following measures of the spread of data: variance, standard deviation, and range.

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Statistics: Sample vs. Population Mean

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Statistics: Sample Variance

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Sample Mean versus Population Mean

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Sample Variance

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Statistics intro: Mean, median, & mode

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Mean, median, & mode example

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Variance of a population

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Review and intuition why we divide by n-1 for the ...

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Introduction to Statistics Chapter 1: Introduction

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Introduction to Statistics Chapter 4: Describing B...

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What are Statistics?

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Importance of Statistics

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Descriptive Statistics

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Inferential Statistics

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Statistics: Basic Definitions and Concepts

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Introduction to Statistics: Variables

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Data Collection

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Presentation of Data

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Graphical Methods for Describing Quantitative Data

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Three Popular Data Displays

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Numerical Measures of Central Tendency and Variabi...

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Measures of Central Location

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Measures of Variability

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Percentiles

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Scatterplot/Bivariate Data

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Methods for Describing Bivariate Relationships

Unit 2: Elements of Proba...

apply simple principles of probability, and use common terminology of probability; calculate conditional probability, and determine whether two events are mutually exclusive and whether two events are independent; calculate probabilities using the addition rules and multiplication rules; construct and interpret Venn diagrams; apply useful counting rules in the context of combinatorial probability; identify and use common discrete probability distribution functions; calculate and interpret expected values; identify the binomial probability distribution, and apply it appropriately; identify the Poisson probability distribution, and apply it appropriately; identify and use continuous probability density functions; and identify the normal probability distribution, and apply it appropriately.

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Probability with venn diagrams

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Expected Value of Binomial Distribution

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Introduction to the Normal Distribution

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Addition Rule for Probability

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Free throw binomial probability distribution

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Graphing basketball binomial distribution

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Visualizing a binomial distribution

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Binomial Distribution

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Events, Sample Spaces, and Probability

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Basic Concepts of Probability

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Permutations and Combinations

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Common Discrete Random Variables

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Binomial Distribution and Probabilities

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The Standard Normal Distribution

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Normal Distribution

Unit 3: Sampling Distribu...

apply the central limit theorem to approximate sampling distributions; describe the role of sampling distributions in inferential statistics; interpret and create graphs of a probability distribution for the mean of a discrete variable; describe a sampling distribution in terms of repeated sampling; define and compute the mean and standard deviation of the sampling distribution of population proportion p; identify or approximate a sampling distribution based on the properties of the population; compare and evaluate the sampling distributions of different sample sizes; and compare and evaluate the performance of different estimators based on their sampling distributions.

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Statistics: Standard Deviation

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Central Limit Theorem

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Sampling Distribution of the Sample Mean

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Standard Error of the Mean

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Continuous Random Variables

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Introduction to Sampling Distributions

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The Sampling Distribution of Sample Mean

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The Mean and Standard Deviation of the Sample Mean

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Sampling Distribution of Pearson's r

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Sampling Distribution of p

Unit 4: Estimation with C...

explain the central limit theorem, and use it to construct confidence intervals; compare t-distributions and normal distributions; apply and interpret the central limit theorem for sample averages; calculate, describe, and interpret confidence intervals for population averages and one population proportions; and interpret the student-t probability distribution as the sample size changes.

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Confidence Interval Example

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Small Sample Size Confidence Intervals

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Introduction to Estimation and Degrees of Freedom

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Characteristics of Estimators

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Confidence Intervals for Mean

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Confidence Interval Demonstration

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t Distribution Demonstration

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Correlation and Proportion

Unit 5: Hypothesis Test

differentiate between type I and type II errors, and find the probability of these errors; describe and conduct hypothesis testing, calculate the p-value, and accept or reject the null hypothesis; and explain how to conduct hypothesis tests for a single population mean and population proportion, when the population standard deviation is unknown; perform this task; and interpret the results.

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Hypothesis Testing and P-values

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One-Tailed and Two-Tailed Tests

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Difference of Sample Means Distribution

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Hypothesis Test for Difference of Means

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Comparing Population Proportions I

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Comparing Population Proportions II

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Hypothesis Test Comparing Population Proportions

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Chi-Square Distribution Introduction

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Pearson's Chi Square Test (Goodness of Fit)

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Contingency Table Chi-Square Test

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Setting up Hypotheses

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The Observed Significance of a Test

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Interpreting Hypotheses Testing Results

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Type I and Type II Errors

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Steps in Hypothesis Testing and Its Relation to Co...

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Testing Single Mean

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Testing Hypotheses

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Testing the Difference between Two Means

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Contingency Tables

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Chi-Square Distribution

Unit 6: Linear Regression

discuss and apply basic ideas of linear regression and correlation; identify the assumptions that inferential statistics in regression are based on; compute the standard error of a slope; test a slope for significance; construct a confidence interval on a slope; and calculate and interpret the coefficient of determination and the correlation coefficient.

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VIDEO

Squared Error of Regression Line

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Regression Line Example

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ANOVA 1: Calculating SST (total sum of squares)

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ANOVA 2: Calculating SSW and SSB (total sum of squ...

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ANOVA 3: Hypothesis test with F-statistic

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Chapter 12: Linear Regression and Correlation

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Introduction to Statistics Chapter 15: Analysis of...

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Introduction to Linear Regression

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The Linear Correlation Coefficient

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Partitioning Sums of Squares

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Standard Error of the Estimate

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Inferential Statistics for b and r

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Statistical Inferences About β1

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Influential Observations

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Correlation and Regression: A Complete Example