# Basic Statistics

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## Basic Statistics Coursera (CC) Provider rating: starstarstarstar_halfstar_border 7.2

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### Description

About this course: Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but also how to evaluate them. This course will also prepare you for the next course in the specialization - the course Inferential Statistics. In the first part of the course we will discuss methods of descriptive statistics. You will learn what cases and variables are and how you can compute measures of central tendency (mean, median and mode) and dispersion (standard deviation and variance). Next, we discuss how to assess relationships between variables, and we introduce the conce…

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About this course: Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but also how to evaluate them. This course will also prepare you for the next course in the specialization - the course Inferential Statistics. In the first part of the course we will discuss methods of descriptive statistics. You will learn what cases and variables are and how you can compute measures of central tendency (mean, median and mode) and dispersion (standard deviation and variance). Next, we discuss how to assess relationships between variables, and we introduce the concepts correlation and regression. The second part of the course is concerned with the basics of probability: calculating probabilities, probability distributions and sampling distributions. You need to know about these things in order to understand how inferential statistics work. The third part of the course consists of an introduction to methods of inferential statistics - methods that help us decide whether the patterns we see in our data are strong enough to draw conclusions about the underlying population we are interested in. We will discuss confidence intervals and significance tests. You will not only learn about all these statistical concepts, you will also be trained to calculate and generate these statistics yourself using freely available statistical software.

Created by:  University of Amsterdam
• Taught by:  Matthijs Rooduijn, Dr.

Department of Political Science
• Taught by:  Emiel van Loon, Assistant Professor

Institute for Biodiversity and Ecosystem Dynamics
Basic Info Course 3 of 5 in the Methods and Statistics in Social Sciences Specialization Level Beginner Commitment 8 weeks of study, week 1: 3-6 hours; week 2-8: 1-3 hours/week. Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what learners said Coursework

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University of Amsterdam A modern university with a rich history, the University of Amsterdam (UvA) traces its roots back to 1632, when the Golden Age school Athenaeum Illustre was established to train students in trade and philosophy. Today, with more than 30,000 students, 5,000 staff and 285 study programmes (Bachelor's and Master's), many of which are taught in English, and a budget of more than 600 million euros, it is one of the largest comprehensive universities in Europe. It is a member of the League of European Research Universities and also maintains intensive contact with other leading research universities around the world.

Syllabus

WEEK 1

Before we get started...

In this module we'll consider the basics of statistics. But before we start, we'll give you a broad sense of what the course is about and how it's organized. Are you new to Coursera or still deciding whether this is the course for you? Then make sure to check out the 'Course introduction' and 'What to expect from this course' sections below, so you'll have the essential information you need to decide and to do well in this course! If you have any questions about the course format, deadlines or grading, you'll probably find the answers here. Are you a Coursera veteran and ready to get started? Then you might want to skip ahead to the first course topic: 'Exploring data'. You can always check the general information later. Veterans and newbies alike: Don't forget to introduce yourself in the 'meet and greet' forum!

1 video, 11 readings, 1 practice quiz expand

1. Reading: Hi there!
2. Video: Welcome to Basic Statistics!
3. Reading: How to navigate this course
4. Reading: How to contribute
5. Reading: General info - What will I learn in this course?
6. Reading: Course format - How is this course structured?
7. Reading: Requirements - What resources do I need?
8. Reading: Grading - How do I pass this course?
9. Reading: Team - Who created this course?
10. Reading: Honor Code - Integrity in this course
11. Reading: Useful literature and documents
12. Reading: Research on Feedback
13. Practice Quiz: Use of your data for research

Exploring Data

In this first module, we’ll introduce the basic concepts of descriptive statistics. We’ll talk about cases and variables, and we’ll explain how you can order them in a so-called data matrix. We’ll discuss various levels of measurement and we’ll show you how you can present your data by means of tables and graphs. We’ll also introduce measures of central tendency (like mode, median and mean) and dispersion (like range, interquartile range, variance and standard deviation). We’ll not only tell you how to interpret them; we’ll also explain how you can compute them. Finally, we’ll tell you more about z-scores. In this module we’ll only discuss situations in which we analyze one single variable. This is what we call univariate analysis. In the next module we will also introduce studies in which more variables are involved.

8 videos, 5 readings expand

1. Reading: Data and visualisation
2. Video: 1.01 Cases, variables and levels of measurement
3. Video: 1.02 Data matrix and frequency table
4. Video: 1.03 Graphs and shapes of distributions
5. Reading: Measures of central tendency and dispersion
6. Video: 1.04 Mode, median and mean
7. Video: 1.05 Range, interquartile range and box plot
8. Video: 1.06 Variance and standard deviation
9. Reading: Z-scores and example
10. Video: 1.07 Z-scores
11. Video: 1.08 Example
12. Reading: Transcripts - Exploring data
14. LTI Item: R lab - Getting started (part 1)
15. LTI Item: R lab - Getting started (part 2)

Graded: R lab - Exploring data

WEEK 2

Correlation and Regression

In this second module we’ll look at bivariate analyses: studies with two variables. First we’ll introduce the concept of correlation. We’ll investigate contingency tables (when it comes to categorical variables) and scatterplots (regarding quantitative variables). We’ll also learn how to understand and compute one of the most frequently used measures of correlation: Pearson's r. In the next part of the module we’ll introduce the method of OLS regression analysis. We’ll explain how you (or the computer) can find the regression line and how you can describe this line by means of an equation. We’ll show you that you can assess how well the regression line fits your data by means of the so-called r-squared. We conclude the module with a discussion of why you should always be very careful when interpreting the results of a regression analysis.

8 videos, 6 readings expand

2. Video: 2.01 Crosstabs and scatterplots
3. Video: 2.02 Pearson's r
5. Video: 2.03 Regression - Finding the line
6. Video: 2.04 Regression - Describing the line
7. Video: 2.05 Regression - How good is the line?
9. Reading: Caveats and examples
10. Video: 2.06 Correlation is not causation
11. Video: 2.07 Example contingency table
12. Video: 2.08 Example Pearson's r and regression
14. Reading: Transcripts - Correlation and regression

Graded: Correlation and Regression
Graded: R lab - Correlation and Regression

WEEK 3

Probability

This module introduces concepts from probability theory and the rules for calculating with probabilities. This is not only useful for answering various kinds of applied statistical questions but also to understand the statistical analyses that will be introduced in subsequent modules. We start by describing randomness, and explain how random events surround us. Next, we provide an intuitive definition of probability through an example and relate this to the concepts of events, sample space and random trials. A graphical tool to understand these concepts is introduced here as well, the tree-diagram.Thereafter a number of concepts from set theory are explained and related to probability calculations. Here the relation is made to tree-diagrams again, as well as contingency tables. We end with a lesson where conditional probabilities, independence and Bayes rule are explained. All in all, this is quite a theoretical module on a topic that is not always easy to grasp. That's why we have included as many intuitive examples as possible.

11 videos, 5 readings expand

1. Reading: Probability & randomness
2. Video: 3.01 Randomness
3. Video: 3.02 Probability
4. Reading: Sample space, events & tree diagrams
5. Video: 3.03 Sample space, event, probability of event and tree diagram
6. Video: 3.04 Quantifying probabilities with tree diagram
7. Reading: Probability & sets
8. Video: 3.05 Basic set-theoretic concepts
9. Video: 3.06 Practice with sets
10. Video: 3.07 Union
11. Reading: Conditional probability & independence
12. Video: 3.08 Joint and marginal probabilities
13. Video: 3.09 Conditional probability
14. Video: 3.10 Independence between random events
15. Video: 3.11 conditional probability, decision trees and Bayes' Law
16. Reading: Transcripts - Probability

Graded: R lab - Probability

WEEK 4

Probability Distributions

Probability distributions form the core of many statistical calculations. They are used as mathematical models to represent some random phenomenon and subsequently answer statistical questions about that phenomenon. This module starts by explaining the basic properties of a probability distribution, highlighting how it quantifies a random variable and also pointing out how it differs between discrete and continuous random variables. Subsequently the cumulative probability distribution is introduced and its properties and usage are explained as well. In a next lecture it is shown how a random variable with its associated probability distribution can be characterized by statistics like a mean and variance, just like observational data. The effects of changing random variables by multiplication or addition on these statistics are explained as well.The lecture thereafter introduces the normal distribution, starting by explaining its functional form and some general properties. Next, the basic usage of the normal distribution to calculate probabilities is explained. And in a final lecture the binomial distribution, an important probability distribution for discrete data, is introduced and further explained. By the end of this module you have covered quite some ground and have a solid basis to answer the most frequently encountered statistical questions. Importantly, the fundamental knowledge about probability distributions that is presented here will also provide a solid basis to learn about inferential statistics in the next modules.

8 videos, 5 readings expand

1. Reading: Probability distributions
2. Video: 4.01 Random variables and probability distributions
3. Video: 4.02 Cumulative probability distributions
4. Reading: Mean and variance of a random variable
5. Video: 4.03 The mean of a random variable
6. Video: 4.04 Variance of a random variable
7. Reading: The normal distribution
8. Video: 4.05 Functional form of the normal distribution
9. Video: 4.06 The normal distribution: probability calculations
10. Video: 4.07 The standard normal distribution
11. Reading: The binomial distribution
12. Video: 4.08 The binomial distribution
13. Reading: Transcripts - Probability distributions

Graded: R lab - Probability distributions

WEEK 5

Sampling Distributions

Methods for summarizing sample data are called descriptive statistics. However, in most studies we’re not interested in samples, but in underlying populations. If we employ data obtained from a sample to draw conclusions about a wider population, we are using methods of inferential statistics. It is therefore of essential importance that you know how you should draw samples. In this module we’ll pay attention to good sampling methods as well as some poor practices. To draw conclusions about the population a sample is from, researchers make use of a probability distribution that is very important in the world of statistics: the sampling distribution. We’ll discuss sampling distributions in great detail and compare them to data distributions and population distributions. We’ll look at the sampling distribution of the sample mean and the sampling distribution of the sample proportion.

7 videos, 5 readings expand

1. Reading: Sample and sampling
2. Video: 5.01 Sample and population
3. Video: 5.02 Sampling
4. Reading: Sampling distribution of sample mean and central limit theorem
5. Video: 5.03 The sampling distribution
6. Video: 5.04 The central limit theorem
7. Video: 5.05 Three distributions
9. Reading: Sampling distribution of sample proportion and example
10. Video: 5.06 Sampling distribution proportion
11. Video: 5.07 Example
12. Reading: Transcripts - Sampling distributions

Graded: R lab - Sampling distributions

WEEK 6

Confidence Intervals

We can distinguish two types of statistical inference methods. We can: (1) estimate population parameters; and (2) test hypotheses about these parameters. In this module we’ll talk about the first type of inferential statistics: estimation by means of a confidence interval. A confidence interval is a range of numbers, which, most likely, contains the actual population value. The probability that the interval actually contains the population value is what we call the confidence level. In this module we’ll show you how you can construct confidence intervals for means and proportions and how you should interpret them. We’ll also pay attention to how you can decide how large your sample size should be.

7 videos, 4 readings expand

1. Reading: Inference and confidence interval for mean
2. Video: 6.01 Statistical inference
3. Video: 6.02 CI for mean with known population sd
4. Video: 6.03 CI for mean with unknown population sd
5. Reading: Confidence interval for proportion and confidence levels
6. Video: 6.04 CI for proportion
7. Video: 6.05 Confidence levels
8. Reading: Sample size and example
9. Video: 6.06 Choosing the sample size
10. Video: 6.07 Example
11. Reading: Transcripts - Confidence intervals

Graded: R lab - Confidence intervals

WEEK 7

Significance Tests

In this module we’ll talk about statistical hypotheses. They form the main ingredients of the method of significance testing. An hypothesis is nothing more than an expectation about a population. When we conduct a significance test, we use (just like when we construct a confidence interval) sample data to draw inferences about population parameters. The significance test is, therefore, also a method of inferential statistics. We’ll show that each significance test is based on two hypotheses: the null hypothesis and the alternative hypothesis. When you do a significance test, you assume that the null hypothesis is true unless your data provide strong evidence against it. We’ll show you how you can conduct a significance test about a mean and how you can conduct a test about a proportion. We’ll also demonstrate that significance tests and confidence intervals are closely related. We conclude the module by arguing that you can make right and wrong decisions while doing a test. Wrong decisions are referred to as Type I and Type II errors.

7 videos, 4 readings expand

1. Reading: Hypotheses and significance tests
2. Video: 7.01 Hypotheses
3. Video: 7.02 Test about proportion
4. Video: 7.03 Test about mean
5. Reading: Step-by-step plan and confidence interval
6. Video: 7.04 Step-by-step plan
7. Video: 7.05 Significance test and confidence interval
8. Reading: Type I and Type II errors and example
9. Video: 7.06 Type I and Type II errors
10. Video: 7.07 Example
11. Reading: Transcripts - Significance tests

Graded: R lab - Significance tests

WEEK 8

Exam time!

This is the final module, where you can apply everything you've learned until now in the final exam. Please note that you can only take the final exam once a month, so make sure you are fully prepared to take the test. Please follow the honor code and do not communicate or confer with others while taking this exam. Good luck!