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What do you think, could hypothesis testing be taught, in some way (probably informal) to that age group of kindergarten to 4th grade? Ideas, some resources, published papers, and so on? This would definitely be after they have been exposed to statistics in projects with collecting and presenting some data. Myself, I am skeptical, but what do you think?

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    $\begingroup$ What do you mean by "K4"? $\endgroup$ – DavidButlerUofA May 19 '15 at 20:04
  • $\begingroup$ K1-K12 usually means grades 1 through 12 (maybe only in US?) so K1 is first year of school, K2 second year and so on. $\endgroup$ – kjetil b halvorsen May 19 '15 at 20:10
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    $\begingroup$ Oh. I have never seen that ever, even in American materials. I have seen "K-12" (ie Kindergarten to 12), but never a K attached to both. Perhaps just say "grades 1 to 4" to avoid confusion. $\endgroup$ – DavidButlerUofA May 19 '15 at 20:36
  • $\begingroup$ Kjetil, I think the convention in the US is that "K" is "kindergarten", and the other grades do not have prefix "K". So "1-4" might be what you want. $\endgroup$ – paul garrett May 19 '15 at 20:36
  • $\begingroup$ Thanks, @paul garrett English is a foreign language ... will edit. $\endgroup$ – kjetil b halvorsen May 19 '15 at 21:12
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Basic hypothesis testing is something kids do lots every day, so it is just a matter of tapping into that and giving them a way of talking about it.

Testing with non-overlapping ranges

Basic hypothesis testing would involve comparing ranges of values from 2 groups to see if the values of one group or another group is higher. If the 2 groups have non-overlapping ranges of values, it is possible for even a Kindergartener to use that to make a valid inference.

You could hypothesise that adults are taller than primary school children. You could get a sample of adults (teachers) and a sample of children (the class), get their heights and plot them on a number line (they could be marked directly on the ruler/number line that was used to measure the people). You would use 2 different colours for teachers and children. The range of heights from the adult sample will be higher than the range of heights for the children, likely with no overlap. It is fair to infer that the hypothesis has been confirmed.

You could then test whether boys are taller than girls with the same method. It is likely that there will be a large overlap so that no inference can be made, and the hypothesis is not supported.

Testing with Monte Carlo matches

A more advanced method that kids might understand is to use Monte Carlo methods to test for differences between to groups. If you use boys vs girls the kids would come up with lots of hypotheses. Match up a random pair, one from each team. For each match up, give a point to the team whose representative matches the hypothesis. At the end of 10 random match-ups, has the "boys team" won all (or all except one), has the "girls team" won nearly all, or are the results mixed?

Keep in mind that with a large number of tests, even 8/10 could allow several apparent positives in support of false hypotheses so only 10/10 or 9/10 should be used to support a hypothesis. They need to understand it is not about which team "won" this time, hypothesis testing is about whether that team will (almost) always win.

When the score is 7/10, we could imagine that with different match ups from different classes the score will sometimes be 9/10, but it might also sometimes be only 4/10, so the other team will sometimes win. But if the score is 9/10 or 10/10 it is unlikely that the other team will ever win. This concept might be too hard for your year levels, but it might be worth a shot.

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There was a nice example I learned the other day from someone who was affiliated with a short film some students made following the theme of "discovery".

The students directed and shot the film with little or no adult involvement. They decided to "discover the real Santa Claus", and went to various locations where people who looked like Santa Claus were seen. (I imagine this was shot in early December.)

They had some criteria for determining if Santa Claus was real: he had to have a beard, and he had to know that caribou were reindeer (and so of course he had caribou). The first Santa they filmed had a fake beard, and the second did not admit to having caribou. The third Santa had a real beard and played well into the caribou question; they must have found the real thing!

Even if their tests were not conclusive, the idea of preliminary validation testing struck me as quite apt, and I imagine similar examples would lend themselves to students coming up with creative tests. Even just thinking up tests is a worthy exercise.

Gerhard "It Was Documented On Film" Paseman, 2015.05.25

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