Day 47-48: I’m 95% Confident Freshman Can Do Statistics

Back again for fun and frivolity.

Monday, my students were examining their mounted slides (made previously) of their embryos from their Tep3/cyoYFP x Tep3/cyoYFP cross. They were collecting data on how many of their embryos died (obviously before we bleached and mounted them) and how many survived. This was a test to see if they saw 25% or 50% of their offspring die as embryos, which they were thinking would happen in the Tep3/Tep3 and cyoYFP/cyoYFP individuals. The 25% would come from just the cyoYFP/cyoYFP dying and the 50% would be if the Tep3/Tep3 were dying too, along with the cyoYFP/cyoYFP individuals; the other 50% surviving would be from the Tep3/cyoYFP individuals. So students took to their microscopes and recorded their data in a table, seen below:

Individual A/P Normal Denticle Belts Present Early Lethal Notes Slide Number:
1 Date:
2 Scored by:

The A/P normal refers to organisms the appeared to have normal development of anterior and posterior portions, a first step for determining lethality. Then they checked for denticle belts (see Figure A and B below) which are easily seen in developmentally normal Drosophila and could also determine defects. The early lethal column was where students determined if after those 2 checkpoints if the embryos were dead before mounting. Those organisms looked like opaque embryos (compared to dark) and did not display normal signs of A/P or denticle belt development (such as Figures C-J below).

After they determined this we created a class-wide spreadsheet that students imputed the number of alive vs. dead embryos they started with/counted. That was Monday.

Then Monday night I got a weird idea…

…what if I tried teaching my freshman some statistics?*

Obviously our question from Monday, “Are 25% or 50% of our embryos dying?” begged for some statistics, and pretty common ones too. We have data of how many embryos lived or died and we have a question that asks do our results closely match 25% or 50% lethality? Is our 35% close enough to 25% or 50%? (There were differing opinions in the room: talk about entry points, they needed no help randomly suggesting whether they felt 10% or 15% off from a value was of significance to them) I then said we have a test to determine significance in our data. We need Chi-Square!** (At this point, I would like to acknowledge, that given time I would have loved to run through Brad’s chi-square excel model with them [check the AP Discussion Board], but we did not have the chance. Maybe later. That was just a plug for a great student exercise)

So, I presented the problem to them again, this time with our data. (Let’s say 350 dead out of 1,000 embryos just as an example) I asked them if 50% were dying due to the Tep3/Tep3 and cyoYFP/cyoYFP mutation, how many of the 1,000 embryos would we expect to be dead? Of course, 500. Then I asked, “Ok, how off or “different” from that 500 are we for both the dead and alive organisms?” At this point I told them it might be easiest to set up a table. So they set up a table with a 3 rows and initially 3 columns. Eventually, they created this.

Outcomes Observed (O) Expected (e) o-e (o-e)^2 (o-e)^2) (o-e)^2)/e

They knew observed and expected pretty easily and finding the difference between the two. Because this gives them negative values I asked them are we looking for magnitude of difference or general significant vs. non-significant? Again, we decided negative values aren’t telling us too much, so I introduce the squaring idea. We then divide by e (I had no idea how to explain this principle to students. I think e is also variance squared but this concept would destroy their minds, so I’m not sure how much of a disfavor I did to students by not explaining this)

Either way, we got significant results for both the 50% and 25% (Yes, I made some students who didn’t pass out do both***) which told us that our data was not close enough to 25% or 50% to be just random coincidence. Something else is at play in our research. We know cyoYFP/cyoYFP individuals die, because inheriting two balancer chromosomes is lethal. So what’s up with our Tep3/Tep3 mutation? Apparently, it is causing death in embryos, but not all, and larva, but not all.

Interesting…sounds like an experiment.

*Turns out if you Google “teaching freshman statistics” you get a bunch of college results back. Changing it to “teaching high school freshman statistics” only gave me more college results. Google never listens to me.

**They reacted something like this:

***Hey, the ones who did it twice loved it.



One thought on “Day 47-48: I’m 95% Confident Freshman Can Do Statistics”

  1. That GIF is possibly the best thing in the universe.

    Pretty impressive taking students into the statistics of the experiment. Every step we can take to remove the “boogyman” stigma from statistics as a discipline I think is a good one. I also agree that given infinite time Brad’s modeling would be well used here. Especially if they’ve seen other models before and can transfer some skills between lessons…

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