Unit 5 - Hypothesis Tests
In unit 5, we explore the complex world of variation amongst samples, recognising that many explorations can only be based on samples and that variation in these samples is to be expected and considered. Students will be asked to consider that whilst variation is to be expected, at a certain point it is unlikely. The concept is fascinating and sophisticated. The mathematics is excellent and its application takes us right in to the grey vagueries of the human sciences and the quest for knowledge. Students are quite likely to come across hypothesis tests in many academic pursuits and industries in their future.
....
What is this unit about?
The syllabus items in this unit are addressed as follows
Week 31 - 2 Sample T-tests - Start this unit with Samples Apples & T-tests from the SL T-test section of the site. The activity offers a concrete experience of sampling so that students can see first hand about variation in samples and the idea that the bigger the variation between two samples is, the less likely it is they came from the same population. This leads in to the excercise for practising T-tests.
Week 32 - Chi Squared Goodness of fit tests - As with the previous week, this Goodness of fit samples - Cinema Tickets task is a good exploration to help grab hold of the key idea behind the tests and then there are more practise resources here on the SL Chi Squared Tests page.
Week 33 - Chi Squared Tests of Independence - By now the common ground between these tests has been established and students can step in to this slightly more complex idea with the Independence Day activity aimed at getting the thinking right about independence tests. This can be explored further with Real independence tests that might fuel some exploration ideas and then the practise tasks on the SL Chi Squared Tests page.
Week 34 - More Chi Squared, Combining categories and Practise - This has probably gone quite quickly and there is a need to dwell for a bit longer on how GoF tests can involve Normal and Binomial distribution calculations and the important issue of Chi Squared - Combining Categories when expected frequencies are less than 5. Students will also want to make use of this SL Hypothesis testing at a glance page.
Week 35 - Revision and Unit Test - Finishing off the exam style questions and preparing for a summative assessment.
Why does it matter?
So easy and so complex to answer all at the same time. As mentoned above, Hypothesis tests are likely to cross most people's paths either in their day to day or as they read any report claiming discoveries about natural or human sciences. This topic is ToK gold! It draws on the reality that in any attempt to establish new knowledge about the world around us, we will often collect data and have to be satisfied that our data is only a sample of an often much bigger population. I will often refer back to the following 'Perhaps I will pick the 10 heaviest apples from the orchard as a sample. This will not be very representative, but it is also not very likely'. If I pick a sample from each of two orchards then they are most unlikely to be the same, but if they are signficantly different then I may have evidence to claim that apples from the two orchards are different.' It is a fundemantal statistical concept and crucial that DP students are exposed to it on this course. If this thinking is then applied to the myriad claims in the news about what is good for you, what works and so on, we understand that the evidence comes in the form of likelihoods.
Opportunities for broader goals of education
The IB philosophy as detailed under 'Approaches to teaching and learning' (ATTL and planning) , invites is to always be thinking about the broader goals of teaching these units. It can be really hard to detail all the things that we do, big and small, planned and spontaneous, to do this, but it is important to try and reference some of them so that we get a strong sense of how we are doing against these objectives. Each of the pages and activities referenced above will also include references specific to those activities.
Each of the links above have extensive details about the nature of the tasks and the opportunities within them to address the broader goals of teaching and learning. For example..
- Samples Apples & T-tests this draws on the need for concrete experieneces to help explore conceptual understanding and facilitates the path from concrete to pictorial to abstract nicely.
- Goodness of fit samples - Cinema Tickets this sets out to do the same as the above only with the different tests.
- Independence Day is a well thought through activity that draws students naturally to the idea of 'expected freqeuncy' in this context, helping it to be a natural development of understanding they already have rather than a new idea to be taught and memorised.
- Real independence tests invites students to explore some real data and offers inspiration for exploration as well.
Assessments
This is a test written for the fifth unit in this SL Scheme 2 that I have planned for this year. The unit is Unit 5 - Hypothesis tests - 60 marks over 8 questions varying from 4 to 10 marks. Solutions are here.
Help and support
Many of the tasks in the unit have different access points that should help students to engage at all levels. In addition, students have access to their text book and studyIB.net/mathapplications, where they can watch video lessons and get help and support. This is of course in addition to help from the teacher during lessons.