18 September 2018

Understanding the Sampling Distribution

Population, Sample, Sampling distribution of the mean Among the many contenders for Dr Nic’s confusing terminology award is the term “Sampling distribution.” One problem is that it is introduced around the same time as population, distribution, sample and the normal distribution. A common confusion is between the standard error and the standard deviation. Here is how I explain it: Basic idea of inferential statistics Whenever we take a sample it will contain sampling error, which can also be described as sampling variation. No sample is a perfect representation of the population. When you calculate a sample mean, you do not […]
9 January 2018

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 […]
18 September 2017

Political polls – why they work – or don't

Political polls – why do they work – or don’t This is written in the week before the 2017 New Zealand General Election and it is an exciting time. Many New Zealanders are finding political polls fascinating right now. We wait with bated breath for each new announcement – is our team winning this time? If it goes the way we want, we accept the result with gratitude and joy. If not, then we conclude that the polling system was at fault. Many wonder how on earth asking 1000 people can possibly give a reading of the views of all […]
13 July 2017

Mathematics and statistics lessons about elections

Study elections in mathematics because it is important Too often mathematics is seen as pure and apolitical.  Maths teachers may keep away from concepts that seem messy and without right and wrong answers. However, teachers of mathematics and statistics have much to offer to increase democratic power in the upcoming NZ general elections (and all future elections really). The bizarre outcomes for elections around the world recently (2016/2017 Brexit, Trump) are evidence that we need a compassionate, rational, informed populace, who is engaged in the political process, to choose who will lead our country. Knowledge is power, and when people […]
24 April 2017

Graphs – beauty and truth

Graphs – beauty and truth (with apologies to Keats) A good graph is elegant I really like graphs. I like the way graphs turn numbers into pictures. A good graph is elegant. It uses a few well-placed lines to communicate what would take a paragraph of text. And like a good piece of literature or art, a good graph continues to give, beyond the first reading. I love looking at my YouTube and WordPress graphs. These graphs tell me stories. The WordPress analytics tell me that when I put up a new post, I get more hits, but that everyday […]
23 January 2017

STEM, STEM-Ed, STEAM and Statistics

STEM is a popular acronym in educational circles and is used to refer to careers and educational tasks. Though most know that the four letters stand for Science, Technology, Engineering and Mathematics, it can be difficult to pin down what exactly it means. In this post I suggest that there are two related uses of STEM as a description. STEM The term, STEM, originated in the USA in the late 1990s to describe specific careers and education for these careers. There seems to be no universally agreed-upon definition of STEM. From a careers perspective, the focus is on making sure that […]
6 September 2016

The nature of mathematics and statistics and what it means to learn and teach them

I’ve been thinking lately…. Sometimes it pays to stop and think. I have been reading a recent textbook for mathematics teachers, Dianne Siemon et al, Teaching mathematics: foundations to middle years (2011). On page 47 the authors asked me to “Take a few minutes to write down your own views about the nature of mathematics, mathematics learning and mathematics teaching.” And bearing in mind I see statistics as related to, but not enclosed by mathematics, I decided to do the same for statistics as well. So here are my thoughts: The nature of mathematics Mathematics is a way of modelling and […]
18 January 2016

The normal distribution – three tricky bits

There are several tricky things about teaching and understanding the normal distribution, and in this post I’m going to talk about three of them. They are the idea of a model, the limitations of the normal distribution, and the idea of the probability being the area under the graph. It’s a model! When people hear the term distribution, they tend to think of the normal distribution. It is an appealing idea, and remarkably versatile. The normal distribution is an appropriate model for the outcome of many natural, manufacturing and human endeavours. However, it is only a model, not a rule. […]
9 November 2015

Understanding Statistical Inference

Inference is THE big idea of statistics. This is where people come unstuck. Most people can accept the use of summary descriptive statistics and graphs. They can understand why data is needed. They can see that the way a sample is taken may affect how things turn out. They often understand the need for control groups. Most statistical concepts or ideas are readily explainable. But inference is a tricky, tricky idea. Well actually – it doesn’t need to be tricky, but the way it is generally taught makes it tricky. Procedural competence with zero understanding I cast my mind back […]
5 October 2015

Summarising with Box and Whisker plots

In the Northern Hemisphere, it is the start of the school year, and thousands of eager students are beginning their study of statistics. I know this because this is the time of year when lots of people watch my video, Types of Data. On 23rd August the hits on the video bounced up out of their holiday slumber, just as they do every year. They gradually dwindle away until the end of January when they have a second jump in popularity, I suspect at the start of the second semester. One of the first topics in many statistics courses is summary […]