Example 7.7

EXAMPLE 7.7 The Effect of Altering a Software Parameter

The MeasureMind® 3D MultiSensor metrology software is used by various companies to measure complex machine parts. As part of a technical review of the software, researchers at GE Healthcare discovered that unchecking one option reduced measurement time by 10%. This time reduction would help the company’s productivity provided the option has no impact on the measurement outcome. To investigate this, the researchers measured 76 parts using the software both with and without this option checked.³

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Table 7.5: TABLE 7.2 Parts measurements using optical software

Part	OptionOn	OptionOff	Diff	Part	OptionOn	OptionOff	Diff
1	118.63	119.01	0.38	11	119.03	118.66	−0.37
2	117.34	118.51	1.17	12	118.74	118.88	0.14
3	119.30	119.50	0.20	13	117.96	118.23	0.27
4	119.46	118.65	−0.81	14	118.40	118.96	0.56
5	118.12	118.06	−0.06	15	118.06	118.28	0.22
6	117.78	118.04	0.26	16	118.69	117.46	−1.23
7	119.29	119.25	−0.04	17	118.20	118.25	0.05
8	120.26	118.84	−1.42	18	119.54	120.26	0.72
9	118.42	117.78	−0.64	19	118.28	120.26	1.98
10	119.49	119.66	0.17	20	119.13	119.15	0.02

geparts

Table 7.2 gives the measurements (in microns) for the first 20 parts. For analysis, we subtract the measurement with the option on from the measurement with the option off. These differences form a single sample and appear in the “Diff” columns for each part.

To assess whether there is a difference between the measurements with and without this option, we test

Here is the mean difference for the entire population of parts. The null hypothesis says that there is no difference, and says that there is a difference, but does not specify a direction.

The 76 differences have

Figure 7.8 shows a histogram of the differences. It is reasonably symmetric with no outliers, so we can comfortably use the one-sample procedures. Remember to always check assumptions before proceeding with statistical inference.

Figure 7.8: FIGURE 7.8 Histogram of the differences in measurements (option off minus option on), Example 7.7.

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The one-sample statistic is

The -value is found from the distribution. Remember that the degrees of freedom are 1 less than the sample size.

Table D does not provide a row for 75 degrees of freedom, but for both and lies to the left of the first column entry. This means the -value is greater than . Software gives the exact value . There is little evidence to suggest this option has an impact on the measurements. When reporting results, it is usual to omit the details of routine statistical procedures; our test would be reported in the form: “The difference in measurements was not statistically significant .”