Weekday summer afternoons will usually find me in my office, huddled under a blanket. I work on the fourth floor of Building S on the SAS campus, with most of the other JMP staff. It seems cold in my office in the afternoons, especially in summer. I’ve discovered I’m not the only one, and one theory is that the air conditioning gets cranked up during the hottest part of the day. However, other colleagues are cold in the mornings instead, leading to a second theory that office temperatures are affected by whether they get the morning or afternoon sunlight. A third theory is that the people in the offices are just warmer or colder by nature. Determining what factors influence office temperature is a problem JMP can help us solve.
JMP can help us design an observational study. First, we’ll brainstorm a list of possible factors that may affect office temperature. Next, we will use JMP’s design of experiments (DOE) platform to design a way that we can record the appropriate information.
Possible factors that affect office temperature are:
Office – There are 90 offices on this floor, and we want to sample all of them for each recording period.
Time of Day – Morning and afternoon. In our building, this seems as if it might affect the temperature in a number of offices.
Outside Conditions – Rainy, sunny, cloudy, etc. The weather and amount of direct sunlight could certainly affect the inside temperature.
Outside Temperature – Could extreme heat versus mild heat have an effect on what the temperature was indoors?
Type of Space – Interior offices versus exterior offices, larger offices versus smaller offices, common rooms versus private rooms. Any of these could have an effect on office temperature.
Thermometer – We have nine different thermometers available to take samples with. We want to control for variations among the thermometers.
East/West – Those with offices on the east side of the building might expect to have warmer temperatures in the morning with the sun shining into the windows.
Wing – Does the north wing of the building differ at all from the south wing?
Floor – Heat rises, so they say. Would offices on higher floors have a higher average temperature?
Volunteers – Sampling 90 offices multiple times is a large experiment, and we would need many volunteers. Different people may hold the thermometer differently, and some will be more patient than others.
When I first entered all of the factors in to JMP’s design of experiments platform, the number of runs required was more than 20,000. This was too many, and we had to sit back and consider the practical applications of this experiment. How could we take all factors into account and still have a manageable experiment? The number of offices (90) and potential large number of volunteers were greatly increasing the number of runs. To make the design manageable, we divided the floor into nine “sectors” of 10 offices each. A sector is completely arbitrary, but it makes the office chunks manageable for the purpose of giving assignments and taking measurements and reducing the number of runs. We chose nine sectors because we had nine thermometers.
Our final list of factors in DOE looked like this:
A few notes about the factors:
• The factors we cannot know in advance are specified as “Uncontrolled” factors. Outside temperature and outside conditions are beyond our control; we will make note of their values because we think they may have an effect. A third uncontrolled factor is volunteers, since we had no way of knowing who our volunteers would be each day or how many we would have.
• There are a few other factors not shown in this design, such as type of space and east or west. We will add these factors to the model later. Each office has a known value for these variable which will not change over the course of the experiment.
• One factor from the above list was left out completely: floor. It would be interesting to conduct an experiment that compared offices on various floors, but for this study our hands are full with a single floor.
We determined that three days would be long enough to get multiple observations per office, without being so long as to run out of volunteers or wear out our welcome. We wanted each office measured twice per day, or a total of six times. This translates to 54 “runs," where one run consists of one sector assignment of 10 offices. For design generation, we’ll group runs into three random blocks to represent the three days the study will last. That means the blocks are each of size 18.
This is manageable, although admittedly we might have cut a few corners in order to reduce the amount of work we need to do. Remember, this is intended to be an observational study to help determine what factors are most likely to affect office temperature; this is not a rigorous experiment. Here is a look at our finished design.
This post is the first in a series that will show how we conducted this observational study, from design to execution to analysis and visualization. In the next post, you'll see how we managed to sample 90 offices in an orderly fashion and how the data was assembled.
Can you think of any other factors that might affect office temperature? What might we have left out?
