Videos for teaching and learning statistics

It delights me that several of my statistics videos have been viewed over half a million times each. As well there is a stream of lovely comments (with the odd weird one) from happy viewers, who have found in the videos an answer to their problems.

In this post I will outline the main videos available on the Statistics Learning Centre YouTube Channel. They already belong to 24,000 playlists and lists of recommended resources in textbooks the world over. We are happy for teachers and learners to continue to link to them. Having them all in one place should make it easier for instructors to decide which ones to use in their courses.

Philosophy of the videos

Early on in my video production I wrote a series of blog posts about the videos. One was Effective multimedia teaching videos. The videos use graphics and audio to increase understanding and retention, and are mostly aimed at conceptual understanding rather than procedural understanding.

I also wrote a critique of Khan Academy videos, explaining why I felt they should be improved. Not surprisingly this ruffled a few feathers and remains my most commented on post. I would be thrilled if Khan had lifted his game, but I fear this is not the case. The Khan Academy pie chart video still uses an unacceptable example with too many and ordered categories. (January 2018)

Before setting out to make videos about confidence intervals, I critiqued the existing offerings in this post. At the time the videos were all about how to find a confidence interval, and not what it does. I suspect that may be why my video, Understanding Confidence Intervals, remains popular.

Note to instructors

You are welcome to link to our YouTube channel, and we get a tiny amount of money from people clicking on the ads. Please do NOT download the videos, as it is against YouTube rules, and deprives us of income. Note that we also have a separate pay-to-view channel, with considerably more videos, at higher resolution, with no advertising. Email us at for free trial access to these videos, with a view to providing them for your students on a subscription basis. If you have trouble with reliable internet access, we can also provide the videos as files for your network as part of the licence.

Introducing statistics

Understanding Summary Statistics 5:14 minutes

Why we need summary statistics and what each of them does. It is not about how to calculate the statistics, but what they mean. It uses the shoe example, which also appears in the PPDAC and OSEM videos.

Understanding Graphs 6:06 minutes

I briefly explains the use and interpretation of seven different types of statistical graph. They include the pictogram, bar chart, pie chart, dot plot, stem and leaf, scatterplot and time series.


Analysing and commenting on Graphical output using OSEM 7:13 minutes

This video teaches how to comment on graphs and other statistical output by using the acronym OSEM. It is especially useful for students in NCEA statistics classes in New Zealand, but many people everywhere can find OSEM awesome! We use the example of comparing the number of pairs of shoes men and women students say they own.

Variation and Sampling error 6:30 minutes

Statistical methods are necessary because of the existence of variation. Sampling error is one source of variation, and is often misunderstood. This video explains sampling error, along with natural variation, explainable variation and variation due to bias. There is an accompanying video on non-sampling error.

Sampling methods 4:54 minutes 500,000 views

This video describes five common methods of sampling in data collection – simple random, convenience, systematic, cluster and stratified. Each method has a helpful symbolic representation.

Types of data 6:20 minutes 600,000 views

The kind of graph and analysis we can do with specific data is related to the type of data it is. In this video we explain the different levels of data, with examples. This video is particularly popular at the start of courses.

Important Statistical concepts 5:34 minutes 50,000 views

This video does not receive the views it deserves, as it covers three really important ideas. Maybe I should split it up into three videos. The ideas are the difference between significance and usefulness, evidence and strength of effect, causation and association.

Other videos complementary to these, but not on YouTube are:

  • The statistical enquiry process
  • Understanding the Box Plot
  • Non-sampling error

Videos for teaching hypothesis testing

Understanding Statistical inference 6:46 minutes 40,000 views

The most difficult concept in statistics is that of inference. This video explains what statistical inference is and gives memorable examples. It is based on research around three concepts pivotal to inference – that the sample is likely to be a good representation of the population, that there is an element of uncertainty as to how well the sample represents the population, and that the way the sample is taken matters.

Understanding the p-value 4:43 minutes 500,000 views

This video explains how to use the p-value to draw conclusions from statistical output. It includes the story of Helen, making sure that the choconutties she sells have sufficient peanuts. It introduces the helpful phrase “p is low, null must go”.

Inference and evidence 3:34 minutes

This is a newer video, based on a little example I used in lectures to help students see the link between evidence and inference. Of course it involves chocolate.

Hypothesis tests 7:38 minutes 350,000 views

This entertaining video works step-by-step through a hypothesis test. Helen wishes to know whether giving away free stickers will increase her chocolate sales. This video develops the ideas from “Understanding the p-value”, giving more of the process of hypothesis testing. It is also complemented by the following video, that shows how to perform the analysis using Excel.

Two-means t-test in Excel 3:54 minutes 50,000 views

A step-by-step lesson on how to perform an independent samples t-test for difference of two means using the Data Analysis ToolPak in Excel. This is a companion video to Hypothesis tests, p-value, two means t-test.

Choosing which statistical test to use 9:33 minutes 500,000 views

I am particularly proud of this video, and the way it links the different tests together. It took a lot of work to come up with this. First it outlines a process for thinking about the data, the sample and the thing you are trying to find out. Then it works through seven tests with scenarios based around Helen and the Choconutties. This video is particularly popular near the end of the semester, for tying together the different tests and applications.


Confidence Intervals

Understanding Confidence Intervals 4:02 minutes 500,000 views

This short video gives an explanation of the concept of confidence intervals, with helpful diagrams and examples. The emphasis is on what a confidence interval is and how it is used, rather than how they are calculated or derived.

Calculating the confidence interval for a mean using a formula 5:29 minutes 200,000 views

This video carries on from “Understanding Confidence Intervals” and introduces a formula for calculating a confidence interval for a mean. It uses graphics and animation to help understanding.

There are also videos pertinent to the New Zealand curriculum using bootstrapping and informal methods to find confidence intervals.


Introduction to Probability 2:54 minutes

This video explains what probability is and why we use it. It does NOT use dice, coins or balls in urns. It is the first in a series of six videos introducing basic probability with a conceptual approach. The other five videos can be accessed through subscription.

Understanding Random Variables 5:08 minutes 90,000 views

The idea of a random variable can be surprisingly difficult. In this video we help you learn what a random variable is, and the difference between discrete and continuous random variables. It uses the example of Luke and his ice cream stand.

Understanding the Normal Distribution 7:44 minutes

In this video we explain the characteristics of the normal distribution, and why it is so useful as a model for real-life entities.

There are also two other videos about random variables, discrete and continuous.

Risk and Screening 7:54 minutes

This video explains about risk and screening, and shows how to calculate and express rates of false positives and false negatives. An imaginary disease, “Earpox” is used for the examples.

Other videos

Designing a Questionnaire 5:23 minutes 40,000 views

This was written specifically to support learning in Level 1 NCEA in the NZ school system but is relevant for anyone needing to design a questionnaire. There is a companion video on good and bad questions.

Line-fitting and regression

Scatterplots in Excel 5:17 minutes

The first step in doing a regression in Excel is to fit the line using a Scatter plot. This video shows how to do this, illustrated by the story of Helen and the effect of temperature on her sales of choconutties

Regression in Excel 6:27 minutes

This video explains Regression and how to perform regression in Excel and interpret the output. The story of Helen and her choconutties continues. This follows on from Scatterplots in Excel and Understanding the p-value.

There are three videos introducing bivariate relationships in a more conceptual way.

There are also videos covering experimental design and randomisation, time series analysis and networks. In the pipeline is a video “understanding the Central Limit Theorem.”

Supporting our endeavours

As explained in a previous post, Lessons for a budding Social Enterprise, Statistics Learning Centre is a social enterprise, with our aim to build a world of mathematicians and enable people to make intelligent use of statistics. Though we get some income from YouTube videos, it does not support the development of more videos. If you would like to help us to create further videos contact us to discuss subscriptions, sponsorship, donations and advertising possibilities. or


On-line learning and teaching resources

Twenty-first century Junior Woodchuck Guidebook

I grew up reading Donald Duck comics. I love the Junior Woodchucks, and their Junior Woodchuck Guidebook. The Guidebook is a small paperback book, containing information on every conceivable subject, including geography, mythology, history, literature and the Rubaiyat of Omar Khayyam.  In our family, when we want to know something or check some piece of information, we talk about consulting the Junior Woodchuck Guidebook. (Imagine my joy when I discovered that a woodchuck is another name for a groundhog, the star of my favourite movie!) What we are referring to is the internet, the source of all possible information! Thanks to search engines, there is very little we cannot find out on the internet. And very big thanks to Wikipedia, to which I make an annual financial contribution, as should all who use it and can afford to.

You can learn just about anything on the internet. Problem is, how do you know what is good? And how do you help students find good stuff? And how do you use the internet wisely? And how can it help us as learners and teachers of statistics and operations research? These questions will take more than my usual 1000 words, so I will break it up a bit. This post is about the ways the internet can help in teaching and learning. In a later post I will talk about evaluating resources, and in particular multimedia resources.


Both the disciplines in which I am interested, statistics and operations research, apply mathematical and analytic methods to real-world problems. In statistics we are generally trying to find things out, and in operations research we are trying to make them better. Either way, the context is important. The internet enables students to find background knowledge regarding the context of the data or problem they are dealing with. It also enables instructors to write assessments and exercises that have a degree of veracity to them even if the actual raw data proves elusive. How I wish people would publish standard deviations as well as means when reporting results!


Which brings us to the second use for on-line resources. Real problems with real data are much more meaningful for students, and totally possible now that we don’t need to calculate anything by hand. Sadly, it is more difficult than first appears to find good quality raw data to analyse, but there is some available. You can see some sources in a previous post and the helpful comments.


If you are struggling to understand a concept, or to know how to teach or explain it, do a web search. I have found some great explanations, and diagrams especially, that have helped me. Or I have discovered a dearth of good diagrams, which has prompted me to make my own.


Videos can help with background knowledge, with explanations, and with inspiring students with the worth of the discipline. The problem with videos is that it takes a long time to find good ones and weed out the others. One suggestion is to enlist the help of your students. They can each watch two or three videos and decide which are the most helpful. The teacher then watches the most popular ones to check for pedagogical value. It is great when you find a site that you can trust, but even then you can’t guarantee the approach will be compatible with your own.

Social support

I particularly love Twitter, from which I get connection with other teachers and learners, and ideas and links to blogs. I belong to a Facebook group for teachers of statistics in New Zealand, and another Facebook group called “I love Operations Research”. These wax and wane in activity, and can be very helpful at times. Students and teachers can gain a lot from social networking.


There is good open-source software available, and 30-day trial versions for other software. Many schools in New Zealand use the R-based iNZight collection of programmes, which provide purpose-built means for timeseries analysis, bootstrapping and line fitting.

Answers to questions

The other day I lost the volume control off my toolbar. (Windows Vista, I’m embarrassed to admit). So I put in the search box “Lost my volume control” and was directed to a YouTube video that took me step-by-step through the convoluted process of reinstating my volume control! I was so grateful I made a donation. Just about any computer related question can be answered through a search.

Interactive demonstrations

I love these. There are two sites I have found great:

The National Library of Virtual Manipulatives, based in Utah.

NRich – It has some great ideas in the senior statistics area. From the UK.

A problem with some of these is the use of Flash, which does not play on all devices. And again – how do we decide if they are any good or not?

On-line textbooks

Why would you buy a textbook when you can get one on-line. I routinely directed my second-year statistical methods for business students to “Concepts and Applications of Inferential Statistics”. I’ve found it just the right level. Another source is Stattrek. I particularly like their short explanations of the different probability distributions.

Practice quizzes

There aren’t too many practice quizzes  around for free. Obviously, as a provider of statistical learning materials, I believe quizzes and exercises have merit for practice with immediate and focussed feedback. However, it can be very time-consuming to evaluate practice quizzes, and some just aren’t very good. On the other hand, some may argue that any time students spend learning is better than none.

Live help

There are some places that provide live, or slightly delayed help for students. I got hooked into a very fun site where you earned points by helping students. Sadly I can’t find it now, but as I was looking I found vast numbers of on-line help sites, often associated with public libraries. And there are commercial sites that provide some free help as an intro to their services. In New Zealand there is the StudyIt service, which helps students preparing for assessments in the senior high school years. At StatsLC we provide on-line help as part of our resources, and will be looking to develop this further. From time to time I get questions as a result of my YouTube videos, and enjoy answering them ,unless I am obviously doing someone’s homework! I also discovered “ShowMe” which looks like a great little iPad app, that I can use to help people more.

This has just been a quick guide to how useful the internet can be in teaching and learning. Next week I will address issues of quality and equity.

Open Letter to Khan Academy about Basic Probability

Khan academy probability videos and exercises aren’t good either

Dear Mr Khan

You have created an amazing resource that thousands of people all over the world get a lot of help from. Well done. Some of your materials are not very good, though, so I am writing this open letter in the hope that it might make some difference. Like many others, I believe that something as popular as Khan Academy will benefit from constructive criticism.

I fear that the reason that so many people like your mathematics videos so much is not because the videos are good, but because their experience in the classroom is so bad, and the curriculum is poorly thought out and encourages mechanistic thinking. This opinion is borne out by comments I have read from parents and other bloggers. The parents love you because you help their children pass tests.  (And these tests are clearly testing the type of material you are helping them to pass!) The bloggers are not so happy, because you perpetuate a type of mathematical instruction that should have disappeared by now. I can’t even imagine what the history teachers say about your content-driven delivery, but I will stick to what I know. (You can read one critique here)

Just over a year ago I wrote a balanced review of some of the Khan Academy videos about statistics. I know that statistics is difficult to explain – in fact one of the hardest subjects to teach. You can read my review here. I’ve also reviewed a selection of videos about confidence intervals, one of which was from Khan Academy. You can read the review here.

Consequently I am aware that blogging about the Khan Academy in anything other than glowing terms is an invitation for vitriol from your followers.

However, I thought it was about time I looked at the exercises that are available on KA, wondering if I should recommend them to high school teachers for their students to use for review. I decided to focus on one section, introduction to probability. I put myself in the place of a person who was struggling to understand probability at school.

Here is the verdict.

First of all the site is very nice. It shows that it has a good sized budget to use on graphics and site mechanics. It is friendly to get into. I was a bit confused that the first section in the Probability and Statistics Section is called “Independent and dependent events”. It was the first section though. The first section of this first section is called Basic Probability, so I felt I was in the right place. But then under the heading, Basic probability, it says, “Can I pick a red frog out of a bag that only contains marbles?” Now I have no trouble with humour per se, and some people find my videos pretty funny. But I am very careful to avoid confusing people with the humour. For an anxious student who is looking for help, that is a bit confusing.

I was excited to see that this section had five videos, and two sets of exercises. I was pleased about that, as I’ve wanted to try out some exercises for some time, particularly after reading the review from Fawn Nguyen on her experience with exercises on Khan Academy. (I suggest you read this – it’s pretty funny.)

So I watched the first video about probability and it was like any other KA video I’ve viewed, with primitive graphics and a stumbling repetitive narration. It was correct enough, but did not take into account any of the more recent work on understanding probability. It used coins and dice. Big yawn. It wastes a lot of time. It was ok. I do like that you have the interactive transcript so you can find your way around.

It dawned on me that nowhere do you actually talk about what probability is. You seem to assume that the students already know that. In the very start of the first video it says,

“What I want to do in this video is give you at least a basic overview of probability. Probability, a word that you’ve probably heard a lot of and you are probably just a little bit familiar with it. Hopefully this will get you a little deeper understanding.”

Later in the video there is a section on the idea of large numbers of repetitions, which is one way of understanding probability. But it really is a bit skimpy on why anyone would want to find or estimate a probability, and what the values actually mean. But it was ok.

The first video was about single instances – one toss of a coin or one roll of a die. Then the second video showed you how to answer the questions in the exercises, which involved two dice. This seemed ok, if rather a sudden jump from the first video. Sadly both of these examples perpetuate the common misconception that if there are, say, 6 alternative outcomes, they will necessarily be equally likely.


Then we get to some exercises called “Probability Space” , which is not an enormously helpful heading. But my main quest was to have a go at the exercises, so that is what I did. And that was not a good thing. The exercises were not stepped, but started right away with an example involving two dice and the phrase “at least one of”. There was meant to be a graphic to help me, but instead I had the message “scratchpad not available”. I will summarise my concerns about the exercises at the end of my letter. I clicked on a link to a video that wasn’t listed on the left, called Probability Space and got a different kind of video.

This video was better in that it had moving pictures and a script. But I have problems with gambling in videos like this. There are some cultures in which gambling is not acceptable. The other problem I have is with the term  “exact probability”, which was used several times. What do we mean by “exact probability”? How does he know it is exact? I think this sends the wrong message.

Then on to the next videos which were worked examples, entitled “Example: marbles from a bag, Example: Picking a non-blue marble, Example: Picking a yellow marble.” Now I understand that you don’t want to scare students with terminology too early, but I would have thought it helpful to call the second one, “complementary events, picking a non-blue marble”. That way if a student were having problems with complementary events in exercises from school, they could find their way here. But then I’m not sure who your audience is. Are you sure who your audience is?

The first marble video was ok, though the terminology was sloppy.

The second marble video, called “Example: picking a non-blue marble”, is glacially slow. There is a point, I guess in showing students how to draw a bag and marbles, but… Then the next example is of picking numbers at random. Why would we ever want to do this? Then we come to an example of circular targets. This involves some problem-solving regarding areas of circles, and cancelling out fractions including pi. What is this about? We are trying to teach about probablity so why have you brought in some complication involving the area of a circle?

The third marble video attempts to introduce the idea of events, but doesn’t really. By trying not to confuse with technical terms, the explanation is more confusing.

Now onto some more exercises. The Khan model is that you have to get 5 correct in a row in order to complete an exercise. I hope there is some sensible explanation for this, because it sure would drive me crazy to have to do that. (As I heard expressed on Twitter)

What are circular targets doing in with basic probability?

The first example is a circular target one.  I SO could not be bothered working out the area stuff so I used the hints to find the answer so I could move onto a more interesting example. The next example was finding the probability of a rolling a 4 from a fair six sided die. This is trivial, but would have been not a bad example to start with. Next question involve three colours of marbles, and finding the probability of not green. Then another dart-board one. Sigh. Then another dart board one. I’m never going to find out what happens if I get five right in a row if I don’t start doing these properly. Oh now – it gave me circumference. SO can’t be bothered.

And that was the end of Basic probability. I never did find out what happens if I get five correct in a row.

Venn diagrams

The next topic is called “Venn diagrams and adding probabilities “. I couldn’t resist seeing what you would do with a Venn diagram. This one nearly reduced me to tears.

As you know by now, I have an issue with gambling, so it will come as no surprise that I object to the use of playing cards in this example. It makes the assumption that students know about playing cards. You do take one and a half minutes to explain the contents of a standard pack of cards.  Maybe this is part of the curriculum, and if so, fair enough. The examples are standard – the probability of getting a Jack of Hearts etc. But then at 5:30 you start using Venn diagrams. I like Venn diagrams, but they are NOT good for what you are teaching at this level, and you actually did it wrong. I’ve put a comment in the feedback section, but don’t have great hopes that anything will change. Someone else pointed this out in the feedback two years ago, so no – it isn’t going to change.

Khan Venn diagram

This diagram is misleading, as is shown by the confusion expressed in the questions from viewers. There should be a green 3, a red 12, and a yellow 1.

Now Venn diagrams seem like a good approach in this instance, but decades of experience in teaching and communicating complex probabilities has shown that in most instances a two-way table is more helpful. The table for the Jack of Hearts problem would look like this:

Jacks Not Jacks Total
Hearts 1 12 13
Not Hearts 3 36 39
Total 4 48 52

(Any teachers reading this letter – try it! Tables are SO much easier for problem solving than Venn diagrams)

But let’s get down to principles.

The principles of instruction that KA have not followed in the examples:

  • Start easy and work up
  • Be interesting in your examples – who gives a flying fig about two dice or random numbers?
  • Make sure the hardest part of the question is the thing you are testing. This is particularly violated with the questions involving areas of circles.
  • Don’t make me so bored that I can’t face trying to get five in a row and not succeed.

My point

Yes, I do have one. Mr Khan you clearly can’t be stopped, so can you please get some real teachers with pedagogical content knowledge to go over your materials systematically and make them correct. You have some money now, and you owe it to your benefactors to GET IT RIGHT. Being flippant and amateurish is fine for amateurs but you are now a professional, and you need to be providing material that is professionally produced. I don’t care about the production values – keep the stammers and “lellows” in there if you insist. I’m very happy you don’t have background music as I can’t stand it myself. BUT… PLEASE… get some help and make your videos and exercises correct and pedagogically sound.

Dr Nic

PS – anyone else reading this letter, take a look at the following videos for mathematics.

And of course I think my own Statistics Learning Centre videos are pretty darn good as well.

Other posts about concerns about Khan:

Another Open Letter to Sal ( I particularly like the comment by Michael Paul Goldenberg)

Breaking the cycle (A comprehensive summary of the responses to criticism of Khan

Difficult concepts in statistics

Recently someone asked: “I don’t suppose you’d like to blog a little on the pedagogical knowledge relevant to statistics teaching, would you? A ‘top five statistics student misconceptions (and what to do about them)’ would be kind of a nice thing to see …”

I wish it were that easy. Here goes:

Things that I have found students find difficult to understand and what I have done about them.


When I taught second year regression we would get students to collect data and fit their own multiple regressions. The interesting thing was that quite often students would collect unrelated data. The columns of the data would not be of the same observations. These students had made it all the way through first year statistics without really understanding about multivariate data.

So from them on when I taught about regression I would specifically begin by talking about observations (or data points) and explain how they were connected. It doesn’t hurt to be explicit. In the NZ curriculum materials for high school students are exercises using data cards which correspond to individuals from a database. This helps students to see that each card, which corresponds to a line of data, is one person or thing. In my video about Levels of measurement, I take the time to show this.

First suggestion is “Don’t assume”.  This applies to so much!

And this is also why it is vital that instructors do at least some of their own marking (grading). High school teachers are going, “Of course”. College professors – you know you ought to! The only way you find out what the students don’t understand, or misunderstand, or replicate by rote from your own notes, is by reading what they write. This is tedious, painful and sometimes funny in a head-banging sort of way, but necessary. I also check the prevalence of answers to multiple choice questions in my on-line materials. If there is a distracter scoring highly it is worthwhile thinking about either the question or the teaching that is leading to incorrect responses.


Well duh! Inference is a really, really difficult concept and is the key to inferential statistics. The basic idea, that we use information from a sample to draw conclusions about the population seems straight-forward. But it isn’t. Students need lots and lots of practice at identifying what is the population and what is the sample in any given situation. This needs to be done with different types of observations, such as people, commercial entities, plants or animals, geographical areas, manufactured products, instances of a physical experiment (Barbie bungee jumping), and times.

Second suggestion is “Practice”. And given the choice between one big practical project and a whole lot of small applied exercises, I would go with the exercises. A big real-life project is great for getting an idea of the big picture, and helping students to learn about the process of statistical analysis. But the problem with one big project is that it is difficult to separate the specific from the general. Context is at the core of any analysis in statistics, and makes every analysis different. Learning occurs through experiencing many different contexts and from them extracting what is general to all analysis, what is common to many analyses and what is specific to that example. The more different examples a student is exposed to, the better opportunity they have for constructing that learning. An earlier post extols the virtues of practice, even drill!


One of the most difficult things is for students to make connections between parts of the curriculum. A traditional statistics course can seem like a toolbox of unrelated but confusingly different techniques. It takes a high level of understanding to link the probability, data and evidence aspects together in a meaningful way. It is good to have exercises that hep students to make these connections. I wrote about this with regard to Operations Research and Statistics. But students need also to be making connections before they get to the end of the course.

The third suggestion is “get students to write”

Get students to write down what is the same and what is different between chi-sq analysis and correlation. Get them to write down how a poisson distribution is similar to and different from a binomial distribution. Get them to write down how bar charts and histograms are similar and different. The reason students must write is that it is in the writing that they become aware of what they know or don’t know. We even teach ourselves things as we write.

Graphs and data

Another type of connection that students have trouble with is that between the data and the graph, and in particular identifying variation and distribution in a histogram or similar. There are many different graphs, that can look quite similar, and students have problems identifying what is going on. The “value graph” which is produced so easily in Excel does nothing to help with these problems. I wrote a full post on the problems of interpreting graphs.

The fourth suggestion is “think hard”. (or borrow)

Teaching statistics is not for wusses. We need to think really hard about what students are finding difficult, and come up with solutions. We need to experiment with different ways of explaining and teaching. One thing that has helped my teaching is the production of my videos. I wish to use both visual and text (verbal) inputs as best as possible to make use of the medium. I have to think of ways of representing concepts visually, that will help both understanding and memory. This is NOT easy, but is extremely rewarding. And if you are not good at thinking up new ideas, borrow other people’s ideas. A good idea collector can be as good as or better than a good creator of ideas.

To think of a fifth suggestion I turned to my favourite book , “The Challenge of Developing Statistical Literacy, Reasoning and Thinking”, edited by Dani Ben-Zvi and Joan Garfield. I feel somewhat inadequate in the suggestions given above. The book abounds with studies that have shown areas of challenge or students and teachers. It is exciting that so many people are taking seriously the development of pedagogical content knowledge regarding the discipline of statistics. Some statisticians would prefer that the general population leave statistics to the experts, but they seem to be in the minority. And of course it depends on what you define “doing statistics” to mean.

But the ship of statistical protectionism has sailed, and it is up to statisticians and statistical educators to do our best to teach statistics in such a way that each student can understand and apply their knowledge confidently, correctly and appropriately.


In statistical analysis the word “significant” means that there is evidence that effect found in the sample exists in the population from which the sample was drawn. The choice of the word “significant” is unfortunate, as it is used to mean something different in common language. Reporters hear a scientist say that there is a significant effect, and tend to think big. Results gets reported as significant, meaning big, and we have effect inflation.

Where do p-values come from?

In reality, if we take a large enough sample, even a small effect will show up as significant. Because the sample is large, it is easier to detect and be sure of the existence of small effects in the population. However, this does not mean that the effect is notable or makes any difference.

Unfortunately this confusion is rife in the reporting of medical and educational research. A drug may have a statistically significant effect, which means that there is evidence that it exists in the population, but it may be to reduce incidence from 2 in a thousand to 1 in a thousand, which isn’t really much of a difference. To make matters worse a result like this can also be stated as a 50% decrease, which makes it seem even more miraculous.

This post is more about learning statistics, but those who teach it really need to be alert for this misconception. We have just posted our latest YouTube video explaining significance and usefulness, evidence and strength, association and causation.

Within the video I have tried to give memorable images, which students will hold onto, even if they don’t quite remember the reasoning. The p-value shrinking as the Evidence label grows, aims to help students understand that a small p means more evidence to reject the null. I’m also really pleased with my “p-machine”, turning the mean, standard deviation and sample size into a t statistic, which is then converted to a p-value.

There are just a few really big ideas in statistics, and these are some of them. This forms part of statistical literacy, which is important to all citizens. I hope you may find the video useful in helping students remember.

Effective multimedia teaching videos

I have converted lectures into considerably shorter videos that students view at their own time and pace, and as many times as they like. Hosted on YouTube, they are open to an international audience and have proved popular. Here are some tips that may be useful to other instructors interested in doing likewise. (Though teachers of statistics, Excel or linear programming are welcome to use ours!)

Pictures and words

As much as possible two channels, pictures and words are used. Narration and illustrations complement each other. There are no talking heads.

There is considerable research regarding the effectiveness of multimedia instruction. Mayer shows in his experiments that “students learn more deeply from a multimedia explanation presented in words and pictures than in words alone”, which he calls “the multimedia effect.”

Levels of Measurement

Illustrations complement the narrative

Mayer developed a framework, based on aspects of cognitive science, which helps to explain this multimedia effect. The framework assumes that humans process pictures and words using different parts of working memory, both of which are limited. However, the total amount of information that can be taken in is increased by using both input channels (pictures and words), which appear to have independent capacities.

Fast conversational narrative

Conversational narrative is used, which Mayer suggests is more effective. In addition the rate of speech is fast. This is based on the premise that students can stop, pause and go back if they didn’t understand something, but will lose interest in a slow and ponderous delivery. All the narrative is tightly scripted so that there is no wasted time, and the best possible explanations are used.

Avoid extraneous material

Though I accept that generally extraneous material must be avoided, we do add humour to our videos, as we believe it keeps people’s attention, and lightens the atmosphere. Diagrams are developed carefully to aid memory and support the message, rather than distract from it.

Diagrams are used to aid memory and understanding

No summaries

In general we do not have summaries at the ends of the videos. The videos are less than ten minutes long, so students can go back and watch them again. From examining the YouTube viewer statistics we found that the viewing levels plummeted when we began the summary.

Keep them short

We try to keep videos between 5 and 7 minutes, although one has grown to 10 minutes. Define a small set of knowledge or skills and focus on that. If there is too much material, make two videos. There is a lot of padding in a traditional lecture, whereas our videos are scripted to say exactly and effectively what we want to say; consequently so you can fit at least 30 minutes of lecture content into about five to seven minutes of video.

Think REALLY hard

The time limit on the explanation means that you need to examine what makes the material difficult to grasp, and what are some ways to make it clearer. There are well-known Youtube mathematics videos that use a rambling approach with little or no prior preparation. We can do better than that. Each of our videos is the product of years of experience of explanations to thousands of students, accompanied by deep thought and experimentation to find ways to explain things.

Try new things – be creative – have fun

To begin with our videos under the UCMSCI banner were quite primitive and quirky, focussing mainly on Excel implementation. Our later videos as Creative Heuristics are more polished, and also use diagrams and animations to get our material across. And the best is yet to come!