It's Not a Race! Or Is It?

I recently gave a biology exam to twelve students, and I was alarmed at the pace they set in completing it.  Actually, my students surprised me in multiple ways, and here I’ll share the experience and a vague recap of the results to show you what I mean.

This was the second exam of the semester, and a few students who were particularly fast on the first exam again finished the earliest.  In fact, by simple observation of the extreme cases the relative speed at which students worked was fairly similar.  The fastest workers were the same, the slowest workers were the same in either case.

On the other hand, the absolute speed at which students worked was startling.  Based on the extremes again, the fastest students were done in just 10 minutes while the last student still finished in under 40 minutes.  I had students working for up to 80 minutes on the first exam, so the pace of the class overall was startling.  Though my observations are driven by the extreme cases for clarity, the students in-between submitted their exams at a relatively steady pace (fairly balanced, overall).

I was curious to know if I had written an anomalously easy exam, and I even asked a student who finished surprisingly early, “Too easy?”  The response seemed to suggest that the exam had been just that.  This was early on (less than 20 minutes), and I kept the exams sorted in order of completion to see if there would be any difference between those who spent less than a minute with each question and those who took more time to think.

To my increasing surprise, though, exam after exam was submitted in fairly rapid succession.  There was a detectably confident air in the room as folks packed up to leave.  And none of my students spent more than a minute per question, on average (there were 50 questions total). Thus, Figure 1 includes the averages for 12 students who virtually all worked at a noticeably quicker pace than they had previously.  Recall that the first few students finished in about 10 minutes, the last few students finished in about 40 minutes. 

My initial instinct to separate the earliest from the latest finishers changed with added perspective.  Instead, as I look at Figure 1 I am more tempted to compare these results to those from the first exam.  The main thing I notice is that the average was actually lower on the second exam (66.5) than on the first exam (70).  This comes despite the speed and seeming confidence with which students approached the second exam.

Of course, how do you really interpret such a result?  Perhaps the additional 3.5 points on average would not be worth the same as the time saved for an average student.  In a case like this, it may be that speed doesn’t kill.  Instead, speed is just speed.

I know the dynamics of my surprise – first at the speed, then at the confidence, then at the results – which are so-called because I can’t discern any real correlation.  In fact, Figure 1 depicts scores on exams submitted within a half-hour window and shows no clear relationship between exam score and order (time, by proxy) of completion. What I would have expected, going in, would be an upside-down bell curve spanning a larger window of time (at least an hour between first and last submissions).  My prediction at 20 minutes into the exam would have been much the same, only with a narrowed range between the high and low scores (the confidence was not exclusive to star students).

I’m not left with much to conclude, though my main goal was less to diagnose anything and more to share my striking observations.  There may be some classroom psychology phenomenon at work - I'd be interested to know if that's the case.  All I really know is that it was an interesting and quick day in class, and a lot of things (obviously) grabbed my attention.  My guess is that any or all of the following factors were at play, in no particular order of importance:

                - Confidence as test-takers

                                - Especially among those who have already performed at a high level

                                - Cushion from previous performances allows for a few small mistakes

                - Overconfidence as test-takers

                                - Especially among those who have less experience/success in the sciences

                                - Recognizing/choosing related but incorrect answers without careful reading

                - Freedom to go home after the exam and impatience at doing so

                                - Consideration of weather, which was inclement and worsening

                                - Weariness at this later stage in the semester

                                - Less incentive to hurry on first exam, as a lecture was scheduled to follow

                - Perceived pressure to rush at seeing others complete the exam so quickly

                                - Perceived correlation between exam success and speed of completion

                - My wording/selection of questions

                                - Subjects more numerous/difficult than first exam

                                - Questions themselves perhaps less specific/difficult than first exam

                               

My Electric Bills in Journal Article Format (Of Course)

Introduction
     It has been more than 8 months since I moved into my own apartment for the first time.  I hate getting superfluous postal mail, so I signed up for electronic billing through Indianapolis Power and Light (IPL) at the first opportunity when I moved back into Indianapolis from nearby Greenwood, IN.  I was on a mission with my energy consumption which was fueled by a few of my character traits:  the incredibly cheap and practical aspect that makes me seek to consolidate and reduce whenever possible, the scientist in me who likes to run "experiments" then collect and analyze "data," my major professional passion for ecology and environmentalism, and my side interest in energy efficiency.
     In this exercise I've managed to touch on all of these aspects of my personality.  I've provided some descriptive graphs to let you into my world a little bit, and from them you'll see both my tendencies to penny-pinch and to lean toward less environmentally-exhausting lifestyle changes (particularly practical/inexpensive/easy ones).  Even if we're able to incorporate less harmful energy sources - e.g. renewable wind energy rather than the vast majority of electricity generated by burning coal in Indiana - I think it's a no-brainer that we should seek to reduce our energy consumption drastically as well.
     Among my major goals were to reduce my energy consumption (both compared to my previous living arrangements and on a month by month basis moving forward) and in turn reduce my energy bill.  I wanted to take at least some baby steps toward a cleaner energy source, and enrolling in the Green Power Option (a whole $0.00100/kWh = it costs me a quarter a month, give or take) was a very affordable step on the dream path that ends with off-the-grid solar/wind energy in my home.

Methods
     The pdf files of all of my bills were accessible online via my IPL account (they keep something like your last 12 or 13 bills on file there), and I collected the following values each month: bill date, bill amount ($), kWh of energy used, number of days in billing cycle, and cost of my 100% opt-in for renewable energy preference.
     A straightforward calculation was done to normalize the data, as it became skewed by variations in the number of days per billing cycle, which ranged from 27 to 34 days: 

Daily Energy Use (in kWh/day) = (Total consumption in billing cycle)/(Number of days in billing cycle)

     By dividing the amount of energy consumed (in kWh) over a billing cycle by the number of days counted in that billing cycle, I could compare my energy consumption month by month in terms of energy consumption per day.

Results

Figure 1 - Summary of data obtained from my last 8 energy bills.

Left: The y-axis (vertical) is multi-purpose here, representing the cost of my monthly bills (red squares and line) in US dollars, the cost of the IPL Green power pro-rate on those bills (green triangles and line) in US dollars, and the amount of energy consumption metered for my apartment (blue diamonds and line) in kilowatt-hours per day.  I've met my goal of generally trending downward in consumption and cost, but the amount of money going toward green energy is difficult to determine here, except that it shows that it's a small fraction of the cost and it amounts to just pennies a month.

Right:  Because the green energy pro-rate is hardly detectable in the figure at left, I made another just to show how much is actually going toward it.  Here the y-axis is US dollars, and therefore it is clear that since my first payment into the Green Energy Initiative (27 cents in July 2011), my cost here has declined right along with the consumption and monthly balances.

Discussion
     There are a couple of things I'd like to draw out of the above results.  First, recall that among my goals were reducing both my energy use and the amount I pay.  Despite a slight increase in my most recent statement, the general trend is certainly downward with respect to my daily energy usage (blue diamonds in the Figure).  I paid a four-month high for my energy last month, but this was due to an unusually long billing cycle.  Otherwise, my downward trend is satisfactory.  And believe me, people tend to be inspired (or at least jealous) when you say that your energy bill is consistently under $30. 
     We're nearing February - the month during which almost all the bad storms I recall from the last 5 years have occurred - but so far my furnace hasn't run all winter.  It has been unseasonably warm at times, but even the cold temperatures have been manageable with a sweatshirt or extra blanket.  Not surprisingly, my high months were July and August - air conditioner season - but note that I paid only a little more those months and not double and triple like some folks do to stay comfortable.  Believe me, if you'll re-evaluate your comfortable temperature (think of it particularly in relation to how much it will cost you) you may agree that using the A/C sparingly (and for only an hour at a time) is enough supplement to box fans and basketball shorts for the reward of a reasonable and predictable energy bill at the end of the month.  Now that it's late January, I don't long for any of the cooling energy I didn't use last summer.
     The other thing on my mind, and it may be clear from the Figure (especially at left), is the fraction-of-a-fraction of my bill that I'm charged extra to be enrolled in the Green Power Option.  On one hand, this is great for me because it's both a predictable and affordable surcharge.  On the other hand, I can afford more (albeit not a lot more) than a quarter a month for something I care about as a consumer, yet I have maximized my possible level of enrollment in the program.  I know that IPL takes pride in having such a low cost to participate, but I wonder if there are ways to better include the people who want to do more.  I'm certain that, particularly if IPL were to provide a clear and itemized sales pitch to interested customers, they could convince many of us to opt-in for more than the 100% maximum.  I say keep the rate the same in order to generate new interest, but if the company takes further steps toward showing a commitment to renewable energy then customers should be happy to go beyond 100% participation.  In fact, let someone like me pay 400% if I choose, since my bill is already low.  This way I would still pay less than $1/month extra yet the process might be sped along as my involvement essentially "sponsors" 1-3 additional consumers.  Plus, any more research and presentation IPL does to expand the opportunities provided by their Green Power Option, the more likely they'll be to find new participants as well.

Conclusion

     I hope any interested reader takes from this snapshot of my energy consumption that cost and energy-saving steps do pay off: less A/C and heat, fans and blankets as necessary, unplugging appliances when not in use.  I didn't install a programmable thermostat in my apartment, but investments in devices like this or in power strips to consolidate and shut off energy drawn from outlets can have great returns without the level of diligence necessary to monitor everything like I have had to do. 

     To any IPL customers who happen to stumble upon this, I hope you'll be interested in the Green Power Option, enroll with me and follow its development.  I'd love to discuss the possibilities for the program to go further as well as alternative ways to support renewable energy.  If you live in Indiana, remember that almost all of our electricity is derived from coal burning, so it is going to take some bottom-up efforts from the public to help push renewable energy in Indiana toward viability and then competitiveness.  I find inspiration when I drive by the mountain of coal to be burned at the power plant on South Harding Street here in Indianapolis, or when I see a monthly bill that was a half-dollar less than the one before.  I hope our city as a whole is inspired to lay down a cleaner energy grid for the future, but if we're not inspired we should at least choose to be responsible.

Suggested Reading

Green Power Option through IPL

Living Like Ed by Ed Begley, Jr. - Ed's a Hollywood actor who has long been on the cutting edge of environmental activism and "green" living, and this book really hit the spot when I first developed my interests in energy efficiency.  He is incredibly clear, helpful, and practical and this book is suitable for folks of all income and interest levels.