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# Break All the Rules - Answers to Part Two

The answers to Part 2 of our QC basic interpretation series. Now we see what happens when we have 2 controls, and need to interpret across materials, across levels, and across runs.

## Break All the Rules! (Answers to Part Two)

#### Sten Westgard, MSNovember 2015

We're continuing in our effort to break all the "Westgard Rules." As we'll soon see, Part One was easy - just one control to worry about. Now that we've got two controls, we're going to have to start looking in many directions to detect the errors.

### The data - converted to z-scores

Recall that low control has a mean of 47 and an SD of 3 and a high control has a mean of 71 and an SD of 8. Rather than deal in the "raw" numbers, we're going to convert those values into z-scores, which tell you how many standard deviations each point is from the mean. It's easier to pick up the rule violations this way.

Value 2

Z-value 2

#### Rule Broken

1  51.5  1.5  82.2  1.4
2  38.9  -2.7  51  -2.5 2:2s on both
3 47.6  0.2 74.2  0.4
4 46.0  -0.33 91.8  2.6
5 50.9  1.3 74.2  0.4
6 53.9  2.3  69.0  -0.25
7 52.7  1.9  58.2  -1.6
8 49.1  0.7  95.5  3.06  1:3s on 2
9 48.5  0.5  65.4  -0.7
10 37.0  -3.33  90.0  2.375 1:3s on 1 and
R:4s on both
11 47.0  0  63.0  -1
12 54.0  2.33  82.2  1.4
13 53.3  2.1  65.4  -0.7  2:2s on 1
14 40.0  -2.33  86.2  1.9  R:4s by calc
15 55.4  2.8  70.2  -0.1
16 49.4  0.8  88.6  2.2
17 46.7 -0.1  87.8  2.1 2:2s on 2
18 45.8  -0.4  85.0  1.75
19 52.7  1.9 76.6  0.7
20 51.1  1.4  65.4  -0.7
21 54.0  2.33  86.2  1.9
22 53.0  2  71.0  0  4:1s on 1 and
2:2s on 1
23 49.7  0.9  81.4  1.3
24 48.2  0.4 90.2  2.4
25 46.4  -0.2  80.6  1.2
26 54.2  2.4  54.0  -2.12  R:4s
27 51.2  1.4  53  -2.25
28 53.9  2.3  76.6  0.7
29 44.3  -0.9  72.6  0.2
30 48.5  0.5  84.6  1.7

To make it a little easier to see the errors, we've marked them on a Levey-Jennings chart with z-scores for these first 30 values:

Value 2

Z-value 2

#### Rule Broken

31 48.5 0.5 85.4 1.8
32 48.8 0.6 86.2 1.9
33 46.7 -0.1 80.0  1.12
34 46.1  -0.3 79.9  1.11 4:1s on 2
35 46.0 -0.33 83.8 1.6
36 53.9 2.3 68.0 -0.37
37 43.0  -1.33 64.6  -0.8
38 42.0  -1.67 71.0  0
39 40.0  -2.33 83.0  1.5
40 42.5  -1.5 67.0  -0.5  4:1s on 1
41 50.3  1.1 74.2  0.4
42 44.3  -0.9 46.0 -3.12 1:3s on 2
43 51.8  1.6 71.8  0.1
44 41.9  -1.7 59.8  -1.4
45 40.0  -2.33 57.0 -1.75 4:1s on both
46 48.8  0.6 86.2  -2
47 53.0  2 55.0 -0.12
48 52.4 1.8 70.0 1
49 38.0  -3 79.0 -0.12 1:3s on 1
50 49.1  0.7 70.0  -0.25
51 44.0  -1 69.0  -0.25
52 48.8  0.6 75.0  0.5
53 50.6  1.2 76.6  0.7
54 43.7  -1.1 72.6  0.2
55 47.6 0.2 80.0  1.12
56 45.5  -0.5 79.0  1
57 44.3  -0.9 74.0  0.37
58 52.4  1.8 82.0  1.37
59 53.9  2.3 72.0  0.12 8:x on 2

Here is the second set of Levey-Jennings charts for values 31 through 59:

Value 2

Z-value 2

#### Rule Broken

60 45.8 -0.4 74.2 0.4
61 50.6  1.2 64.6  -0.8
62 48.0  0.33 71.0  0
63 49.0  0.67 83.0  1.5
64 51.0  1.33 67.0  -0.5
65 53.0  2 74.2  0.4
66 48.0  0.33 80.6  1.2
67 49.0  0.67 71.8  0.1
68 50.0  1 69.4  -0.2  8:x on 1
69 47.8  0.26 81.4  1.3
70 45.5 -0.5 65.4  -0.7
71 46.0  -0.33 70.0  -0.12
72 45.0  -0.67 69.0  -0.25
73 46.0  -0.33 66.0  -0.62 8:x on both
74 47.9 0.3 68.6  -0.3
75 48.5  0.5 86.2  1.9
76 50.9  1.3 59.8  -1.4
77 46.7  -0.1 67.8  -0.4
78 47.8  0.26 86.2  1.9
79 50.3  1.1 72.6  0.2
80 52.0  1.67 81.4  1.3
81 52.0  1.67 74.2  0.4  8:x on both
82 48.5 0.5 80.6  1.2
83 44.3  -0.9 79.8  1.1
84 49.4  0.8 75.0  0.5
85 46.7  -0.1 76.6  0.7
86 52.7  1.9 72.6  0.2
87 45.2  -0.6 55.8  -1.9
88 48.8 0.6 79.0  1
89 46.4  -0.2 70.2  -0.1
90 49.7  0.9 82.2  1.4

Finally, here is the third set of Levey-Jennings charts for the values 60 through 90:

Remember the caveats:

• We are running TWO controls per run; assume each pair of values represents one run
• We're NOT going to look for 2s violations. Let's break that habit right now. In any case, I didn't generate these data points randomly, so we should not expect to see a certain number "natural false rejections" in the form of 2s outliers
• We ARE going to try to find outliers of the following "Westgard Rules": 1:3s/2:2s/R:4s/4:1s/8:x
• We're NOT going to sink into the swamp that is the repeating of controls. So don't assume anything you see is a repeated control - just stick with "in" or "out"

So, at the end of this, can you answer the following questions?

• How many rule violations were there? 17 violations
• Which rules were violated and how many times?
• 1:3s (2 times)
• 2:2s (4 times)
• R:4s (3 times)
• 4:1s (4 times)
• 8:x violations (4 times)
• What would be different if I told you that only the "Westgard Rules" 1:3s/2:2s/R:4s were necessary?
• Ignore the 4:1s and 8:x violations because they aren't significant errors
• What would be different if I told you that only the 1:3s control rule was necessary?
• Only 3-4 violations
• What's the extra little error that exists in these charts and data points?

[Did you miss something? Do you still feel like you're missing something? Please don't feel afraid to ask for more explanations.]

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