Causal Control Chart Farrokh Alemi, Ph.D.

Weigh data so alternative explanations occur as often prior as after the intervention Remove Confounding

Method Based On:

Data Based On:

Goal: Same Rate of Backups Because of Alternative Explanations   Month Pre-Intervention Controls 1 2 3 4 5 6 7 8 9 10 11 12 13 Total Examined No Backup 17 27 21 15 18 29 Image Backup 16 26 24 Bed Availability Both Backup 14 Post-Intervention Cases 19 20 22 23 25 35

Step 1: Calculate Average of Controls   Month Pre-Intervention Controls 1 2 3 4 5 6 7 8 9 10 11 12 13 Average Total Examined No Backup 17 27 21 15 18 29 12.69 Image Backup 16 26 24 17.08 Bed Availability 5.00 Both Backup 14 12.92

Step 2: Calculate Weights   Alternative Explanations Post-Intervention Cases Average Controls 14 15 16 17 18 19 20 21 22 23 24 25 Total Examined No Backup 10 9 29 6 2 26 27 12 12.69 Image Backup 4 5 8 13 17.08 Bed Backup 35 5.00 Image & Bed Backup 12.92 Weights 0.79 0.71 1.81 2.28 1.89 0.47 1.97 0.16 2.05 2.13 0.95 0.23 0.29 0.76 0.00 0.35 1.35 1.05 0.88 1.11 0.82 0.12 1.20 3.00 0.40 3.40 2.60 4.20 1.80 4.80 7.00 0.70 1.93 0.77 1.32 1.39 1.70 2.09 1.47 1.24 1.16 Cases Control

Post-Intervention Cases Total Weighted Controls Step 3: Weigh Controls   Month Post-Intervention Cases Average Controls 14 15 16 17 18 19 20 21 22 23 24 25 Total Examined No Backup 10 9 29 6 2 26 27 12 12.69 Image Backup 4 5 8 13 17.08 Bed Backup 35 5.00 Both Backup 12.92 Weights 0.79 0.71 1.81 2.28 1.89 0.47 1.97 0.16 2.05 2.13 0.95 0.23 0.29 0.76 0.00 0.35 1.35 1.05 0.88 1.11 0.82 0.12 1.20 3.00 0.40 3.40 2.60 4.20 1.80 4.80 7.00 0.70 1.93 0.77 1.32 1.39 1.70 2.09 1.47 1.24 1.16 Total Weighted Controls 54 43 44 61 72 62 68 81 92 By design same as total of cases Total Weighted Control = SUMPRODUCT(Range of Avg Control, Range of weights)

Step 4: Weigh Excessive Boarding   Month Post-Intervention Cases Average Controls 14 15 16 17 18 19 20 21 22 23 24 25 Total Examined No Backup 10 9 29 6 2 26 27 12 12.69 Image Backup 4 5 8 13 17.08 Bed Backup 35 5.00 Both Backup 12.92 Weights 0.79 0.71 1.81 2.28 1.89 0.47 1.97 0.16 2.05 2.13 0.95 0.23 0.29 0.76 0.00 0.35 1.35 1.05 0.88 1.11 0.82 0.12 1.20 3.00 0.40 3.40 2.60 4.20 1.80 4.80 7.00 0.70 1.93 0.77 1.32 1.39 1.70 2.09 1.47 1.24 1.16 Weighted Controls Total 54 43 44 61 72 62 68 81 92 57.83 Excessive Boarding 31 28 45 41 47 31.42 Probability 0.52 0.65 0.42 0.41 0.61 0.51 0.60 0.45 0.66 0.57 0.54 Wt UCL 0.81 0.74 0.73 0.72 0.69 Wt LCL 0.26 0.33 0.31 0.34 0.36 0.37 0.38 Weighted Excessive Boarding = SUMPRODUCT (Range of Excessive Boarding in Avg Controls, Range of weights)

Step 5: Weighted Control Limits   Month Post-Intervention Cases Average Controls 14 15 16 17 18 19 20 21 22 23 24 25 Total Examined No Backup 10 9 29 6 2 26 27 12 12.69 Image Backup 4 5 8 13 17.08 Bed Backup 35 5.00 Both Backup 12.92 Weights 0.79 0.71 1.81 2.28 1.89 0.47 1.97 0.16 2.05 2.13 0.95 0.23 0.29 0.76 0.00 0.35 1.35 1.05 0.88 1.11 0.82 0.12 1.20 3.00 0.40 3.40 2.60 4.20 1.80 4.80 7.00 0.70 1.93 0.77 1.32 1.39 1.70 2.09 1.47 1.24 1.16 Weighted Controls Total 54 43 44 61 72 62 68 81 92 57.83 Excessive Boarding 31 28 45 41 47 31.42 Probability 0.52 0.65 0.42 0.41 0.61 0.51 0.60 0.45 0.66 0.57 0.54 Wt UCL 0.81 0.74 0.73 0.72 0.69 Wt LCL 0.26 0.33 0.31 0.34 0.36 0.37 0.38

Step 6: Plot Chart

Limits are based on same rate of image and bed backup Step 6: Plot Chart Limits are based on same rate of image and bed backup

Step 7: Interpret Chart Holding alternative causes of backup constant, new hire reduced excessive boarding