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: Outline for Samples 1000
TIMING
This session is 15 mins.
RESOURCES
A set of data cards of Kumeti Middle School for the presenter.
Each pair of participants needs two copies of one sample. Altogether there are 17 samples, enough for up to 34 people. Print the document: Samples 1000.doc and make two copies.
Electronic resources available online at HYPERLINK "http://www.censusatschool.org.nz" www.censusatschool.org.nz:
Fathom files sampleheight14middleschool1000.ftm, sampleheightMS1000diffrecord.ftm
Workshop resources Outline for Samples 1000.doc; Samples 1000.doc
PLAN
Setting the scene
Moved to a larger population. A dataset made up of 14 middle schools from the same region as Kumeti Middle School. Too hard to make the population now, but due to technology can access samples from this bigger group electronically. (Keep the bag of Kumeti Middle School to refer back to, it is like dipping into a big bag with all the students from the 14 middle schools and pulling out a sample of ...)
Look at the heights question again.
Do the heights of boys in the 14 middle schools tend to be taller than the heights of girls in the 14 middle schools?
What are we going to do? This time we are going to take a larger sample of boys and a larger sample of girls... say 1000. Why dont we just look at the whole population? Well for every student you select it is going to cost you 10c. The whole population is around 8000, so that would cost $80. We are a bit cheap; cost is an issue, so we will settle for samples of 1000 at $20 (two samples of 1000).
Predict what will happen if we take bigger samples and graph the results.
For the purpose of what we are doing today, we are going to give you a template which already has the dot and box plots drawn for you. Each pair will have copies of the same samples, but different pairs have different samples. As there are 30 of us, there will be 15 samples (simulating what happens in the class).
Activity
Hand out the samples to the pairs. As you can see by looking at the template, the problem, plan and data part has been done for you, PPD. In pairs complete the analysis and the conclusion. You have about 5 mins to do this.
Just quickly we want to pull together the collective from the group of what the samples were telling us.
Can I get a show of hands (one per pair) for those groups who could make a call what was the call?
Can I get a show of hands (one per pair) for those groups who it was too close to call?
For those that were too close to call, a show of hands for boys median bigger?
Girls median bigger?
Medians the same?
So if we summarise around the group, of the 15 samples, all are too close to call. All of them have boys median higher than girls median.
All the samples had both the medians inside the overlap. So using the level 5 guide for samples of about 30 we would say they are too close to call. The shift is not big enough. I know this because the boxes overlap a lot, the medians are both inside the overlap and if I was to take another sample I could quite possibly get the medians the other way around.
But by collating our evidence we see that all groups, while too close to call, all had the boys median higher. Does this hold for more samples?
Use technology
Using Fathom sampleheightMS1000diffrecord.ftm take repeated samples of 1000. Currently it is set up to take 20 samples of at least 1000 boys and at least 1000 girls. The table on the right records the medians and then boys median minus girls median. If the result is positive then boys median higher, result negative then girls median is higher. This can be repeated by clicking on the collect more measures button.
What happens, boys median is always higher...
Wrap Up
Cognitive conflict, our year 10 (level 5) guide doesnt seem to work for a larger sample size when it is too close to call, that is in this example all our samples gave the same median higher, whereas with smaller samples (n=30) the medians swapped around.
The level 5 guide works for samples of about 30. So we need to refine or develop our guides further to account for different sample sizes.
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