THE OVERSIZED POWER OF SMALL DATA
Tis lack of statistical knowledge has important consequences. Without using statistical methods to plan an experiment, it is more likely to provide too much data (overly costly), to provide too little data (not enough data to answer questions accurately) or to have little hope of provid- ing data needed to answer the questions of interest. Te latter was what happened when the test was modified in the sensor example above. A thorough explanation of these points may be useful, but would also a bit much to cover in this article. Suffice it to say that if people plan an experiment by thinking of interesting things to do, with- out using statistical methods to create and evaluate the plan, it’s easy to unknowingly make a mistake. Using design of experi- ments helps us leverage our knowledge to avoid these mistakes.
Once data is collected from a well- designed experiment, we should use statistical methods such as regression anal- ysis to understand how the variables we controlled in our experiment (and some- times those we didn’t) affect the results we measured. Where our intuition often fails us, statistical analysis allows us to under- stand better whether changes in our data were caused by changes to the controlled variables or by randomness. Furthermore, we can understand the uncertainty in our conclusions. Understanding our uncer- tainty is crucial to making decisions that appropriately consider risk. Without considering the uncertainty, it would be difficult to make good decisions that rely on knowing how hard Bert and Ernie are pushing the box. Just knowing the aver- age values (the black dots) isn’t enough. We must consider the uncertainty because it is directly related to the risk of a wrong decision.
Without appropriate statistical methods, it's easy to plan an experiment, execute it,
UNFORCED ERROR
Say Bert and Ernie are working together to push a heavy box on a dolly across the floor. (See Figure 1.) You want to conduct an experiment to estimate, on average, how hard each of them pushes. The dolly moves easily in all directions. You will measure how far the box moves in five seconds to determine how hard each of them is pushing. Bert and Ernie represent the variables we control in any experiment. Since neither Bert nor Ernie will push exactly the same way each time, you will ask them to do this several times to avoid making your conclusion based on an unusual data point.
If Bert and Ernie push on the same side of the box (in the same direction at the same spot) as shown in the right side of Figure 1, there’s no way to know how hard each one is pushing. This is a worst-case scenario, and sometimes occurs when people don’t use statistical methods to design experiments. If this happens, you can know how hard they pushed together, but there is no way to understand their individual contributions. Their effects are confounded. This is what happened in our sensor test. Because of the way the test was changed, it was as if the error and some of the other variables that we controlled were pushing from nearly the same side of the box, and it kept us from understanding how each of vari- able affected the result.
The middle picture shows our goal when designing an experiment. Because Bert and Ernie are on adjacent sides of the box (pushing perpendicular to each other), it is easy to tell how hard each one is pushing.
When planning or modifying an experiment, our goal is to plan it so that the variables we are controlling mimic Bert and Ernie pushing on adjacent sides of the box. This allows us to understand—accurately—how each variable we control affects the result we measure.
When we plan a test by thinking of interesting things to try, but without using appropriate statistical methods, the results are often somewhere in between the best and worst case scenarios. The effect is that we don’t understand the effects of variables as well as we could. With several vari- ables, this can easily become a big problem.
WHAT’S THE DAMAGE?
The two mistakes in the sensor test have different consequences. First, by not knowing how much data was needed to determine whether the error improved the vehicle’s ability to avoid detection, it is possible that the test was modified unnecessarily. However, modifying the test incorrectly was the biggest mistake—it resulted in a less accurate under- standing of the effect each variable had on the ability of the vehicle to avoid the sensor.
88
Army AL&T Magazine
Summer 2021
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116 |
Page 117 |
Page 118 |
Page 119 |
Page 120 |
Page 121 |
Page 122 |
Page 123 |
Page 124
