Our recent look at preparation times for Dalgona coffee produced data that lent itself to 2ᵏ analysis. However, a closer look at the collected data indicated that with a single extra trial we could compare the variation explained by instant coffee type and beater type.
Procedure:
- Perform an experiment that produces most of the required data.
- Time Dalgona preparation with instant espresso and silicone beaters in a small bowl.
- Repeat analysis with instant coffee type and beater type as factors.
Data:
The additional trial with instant espresso using silicone coated beaters in a small bowl took 94 seconds. This sample, combined with the previously collected data, is shown in the table below. All times are in seconds.
| Beater Type (B) | ||
| Coffee Type (A) | Bare Metal | Silicone Coated |
| Coffee | 63 | 90 |
| Espresso | 45 | 94 |
Analysis:
The data, when put into the sign table for a two factor experiment, is shown below.
| I | A | B | AB | y |
| 1 | -1 | -1 | 1 | 63 |
| 1 | 1 | -1 | -1 | 45 |
| 1 | -1 | 1 | -1 | 90 |
| 1 | 1 | 1 | 1 | 94 |
| 292 | -14 | 76 | 22 | Total |
| 73.00 | -3.50 | 19.00 | 5.50 | Total/2ᵏ |
The resulting SST is 1614, and the percent of variation explained by the each factor is 3.04%, 89.47%, and 7.50% for factors A (coffee type), B (beater type), and AB (the interaction between A and B) respectively. Thus the beater type explains most of the variation in preparation time, but coffee type, in some way, does contribute quite a bit. Unfortunately we do not have enough data to determine if the variation explained by the coffee type is statistically significant.
Conclusion:
By reusing data collected in a previous experiment and adding one additional sample, the relative variation of beater type and instant coffee type was examined. The beater type alone accounted for approximately 90% of the variation, with an additional 7.5% explained by the interaction between type of coffee and the beater type.
Doing Science To Stuff 