Mathtrackx: statistics (mooc)
Subject: Mathematics
Type: MOOC (massive open online course)
Taught by: The University of Adelaide
Where: edx.org
How long is it?
At a work rate of 3-6 hours per week, the course is designed to take 4 weeks.
Is it easy to understand?
It may be difficult for younger students who have never studied statistics in their mathematics lessons.
Who is it for?
There are no prerequisites for this introductory-level course. It is for anyone who wants to expand their understanding of statistics.
Section 0: Orientation
Orientation
Welcome to Statistics
Learning through MathTrackX
Certification
What do you already know?
Pre-course survey
Your course team
Course details
Introduce yourself
Discussions and support
Getting Started
Why study statistics?
Worked example: Using spreadsheets
Five number summaries and the boxplot
Five number summaries with your spreadsheet
Interpretation moment: Reporting factually
Summarise the patterns
Means and standard deviations
A warning about percentages
Quiz: Calculate the mean
Section 1: Sample means
Summarising random events
What is a random event?
Populations
Samples and statistical inference
Calculating sample statistics
Chat time: There is variability in everything
Variability and bias
Streak test 1.1: Sample means and standard deviations
Sampling
How to sample
Chat time: Lung disease in the Netherlands
How to recognise poor sampling
Discussion: Can you pick the flaw?
The sampling distribution
The sampling distribution of the sample mean is normal
Recap: Population versus sample
Summarising the sampling distribution
Some final reminders
Quiz: Summarising your data
Confidence intervals for population/sample means
What’s the deal with confidence intervals?
Estimating the population mean amount of active ingredient in tablets
Practice: Estimate the mean
Discussion: How did you go with the data sets?
Confidence intervals
Investigating confidence intervals
Calculating confidence intervals
Practice: Your turn to calculate confidence intervals
Interpretation and applications of confidence intervals
Interpretation moment: Reporting factually
Practice: Interpreting confidence intervals
Steak Test 1.2: Confidence intervals
Confidence intervals and uncertainty
Quiz: Confidence intervals
Section 2: Sample proportions
Proportions
Why proportions?
Population and sample proportions
Practice: Calculate proportions
Confidence intervals of population proportions
Interpretation and applications
Practice: Calculate a confidence interval for proportions
Quiz: Proportions
Section 3: Significance tests
Inference and Hypotheses
Inference
What is a research question?
Hypotheses
Hypotheses testing framework
Quiz: Inference and hypotheses
P-values
Introducing p-values
Evidence
Example: personality types
Error and importance
Discussion: Type I and Type II errors
Quiz: P-values
Testing hypotheses
The test statistic
Hypotheses for a sample proportion
The M&M’s example
Practice: Your turn to test a proportion
Hypotheses for a sample mean
The active ingredient in tablets example
Practice: Your turn to test a mean
Summary of hypothesis testing
Quiz: testing hypotheses
Section 4: Assessment
Exam overview
Exam 01 instructions
Exam 01
Exam 02 instructions
Exam 02
Next steps
My thoughts…
The importance of understanding probability
I think one of the most important scientific concepts to understand is probability because it is so easy to make mistakes with. Even mathematicians go wrong with probability. So, maybe we shouldn’t expect to become probability experts, but I think the complexity of probability is precisely why we must aim to grasp a basic understanding of it.
This is particularly important because we are exposed to probability figures on a daily basis, for example in the news, as so many people try to predict the future with mathematics. For instance, a newspaper said that when a women won the lottery twice in four months, there was a 1 in 17 trillion chance of it happening. However, this was the probability of this particular person buying the two winning tickets, not of anyone buying them. The probability of any person in America buying two winning lottery tickets in a four month period was actually 25%.
An understanding of probability can also be helpful at an arcade. For example, when playing a slot machine, if the probability of getting a jackpot is 1 in 10, people tend to assume that the probability of winning the next gamble increases if they’ve lost the last few gambles. However, this doesn’t work because each gamble is random; the probability is always 1 in 10, no matter what came before. This is called the gambler’s fallacy and it occurs because human brains are wired to spot patterns. This was an evolutionary advantage that helped us spot tigers in long grass, for example.
As well as this, I think that an understanding of probability can be helpful in understanding why we shouldn’t be scared of travelling by plane (although it’s bad for the environment) as it’s actually safer than travelling by car. For all of these reasons, I think probability is an incredibly important mathematical concept to get our heads round.