# 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: 3 4 5

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 Alive Dead

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.