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 […]
2 February 2015

Don't teach significance testing – Guest post

The following is a guest post by Tony Hak of Rotterdam School of Management. I know Tony would love some discussion about it in the comments. I remain undecided either way, so would like to hear arguments. GOOD REASONS FOR NOT TEACHING SIGNIFICANCE TESTING It is now well understood that p-values are not informative and are not replicable. Soon null hypothesis significance testing (NHST) will be obsolete and will be replaced by the so-called “new” statistics (estimation and meta-analysis). This requires that undergraduate courses in statistics now already must teach estimation and meta-analysis as the preferred way to present and analyze empirical […]
19 November 2014

Nominal, Ordinal, Interval, Schmordinal

Everyone wants to learn about ordinal data! I have a video channel with about 40 videos about statistics, and I love watching to see which videos are getting the most viewing each day. As the Fall term has recently started in the northern hemisphere, the most popular video over the last month is “Types of Data: Nominal, Ordinal, Interval/Ratio.” Similarly one of the most consistently viewed posts in this blog is one I wrote over a year ago, entitled, “Oh Ordinal Data, what do we do with you?”. Understanding about the different levels of data, and what we do with […]
4 September 2014

Sampling error and non-sampling error

The subject of statistics is rife with misleading terms. I have written about this before in such posts as Teaching Statistical Language and It is so random. But the terms sampling error and non-sampling error win the Dr Nic prize for counter-intuitivity and confusion generation. Confusion abounds To start with, the word error implies that a mistake has been made, so the term sampling error makes it sound as if we made a mistake while sampling. Well this is wrong. And the term non-sampling error (why is this even a term?) sounds as if it is the error we make from […]
18 August 2014

Teaching random variables and distributions

Why do we teach about random variables, and why is it so difficult to understand? Probability and statistics go together pretty well and basic probability is included in most introductory statistics courses. Often maths teachers prefer the probability section as it is more mathematical than inference or exploratory data analysis. Both probability and statistics deal with the idea of uncertainty and chance, statistics mostly being about what has happened, and probability about what might happen. Probability can be, and often is, reduced to fun little algebraic puzzles, with little link to reality. But a sound understanding of the concept of […]
25 June 2014

It is so random! Or is it? The meaning of randomness

The concept of “random” is a tough one. First there is the problem of lexical ambiguity. There are colloquial meanings for random that don’t totally tie in with the technical or domain-specific meanings for random. Then there is the fact that people can’t actually be random. Then there is the problem of equal chance vs displaying a long-term distribution. And there is the problem that there are several conflicting ideas associated with the word “random”. In this post I will look at these issues, and ask some questions about how we can better teach students about randomness and random sampling. […]
31 March 2014

Teaching Confidence Intervals

If you want your students to understand just two things about confidence intervals, what would they be? What and what order When making up a teaching plan for anything it is important to think about whom you are teaching, what it is you want them to learn, and what order will best achieve the most important desired outcomes. In my previous life as a university professor I mostly taught confidence intervals to business students, including MBAs. Currently I produce materials to help teach high school students. When teaching business students, I was aware that many of them had poor mathematics […]
16 December 2013

Deterministic and Probabilistic models and thinking

The way we understand and make sense of variation in the world affects decisions we make. Part of understanding variation is understanding the difference between deterministic and probabilistic (stochastic) models. The NZ curriculum specifies the following learning outcome: “Selects and uses appropriate methods to investigate probability situations including experiments, simulations, and theoretical probability, distinguishing between deterministic and probabilistic models.” This is at level 8 of the curriculum, the highest level of secondary schooling. Deterministic and probabilistic models are not familiar to all teachers of mathematics and statistics, so I’m writing about it today. Model The term, model, is itself challenging. […]
21 October 2013

Proving causation

Aeroplanes cause hot weather In Christchurch we have a weather phenomenon known as the “Nor-wester”, which is a warm dry wind, preceding a cold southerly change. When the wind is from this direction, aeroplanes make their approach to the airport over the city. Our university is close to the airport in the direct flightpath, so we are very aware of the planes. A new colleague from South Africa drew the amusing conclusion that the unusual heat of the day was caused by all the planes flying overhead. Statistics experts and educators spend a lot of time refuting claims of causation. […]