Error scores

Consider the following scenario

A person is tasked with learning to project a slider down a fixed track to a specified goal distance of 100 cm using their non-dominant hand. The person performs 5 trials of this task. On each trial, you record the distance the slider traveled from the start point (wooden barrier).

Consider the following scenario

The result for each trial is shown below:

Constant error (CE) is a measures of bias

We can calculate using: \(Mean \,CE = \sum(x_{i} - T)/n\)

# Calculate CE for each trial then get the mean
((93 - 100) + (103 - 100) + (99 - 100) + 
 (105 - 100) + (96 - 100)) / 5

[1] -0.8

Constant error (CE) is a measures of bias

# Calculate CE
((99 - 100) + (99 - 100) + (100 - 100) + 
 (99 - 100) + (99 - 100)) / 5

[1] -0.8

Mean CE = -0.8 cm

Variable error (VE) is a measure of consistency

We can calculate using: \(Mean \,VE = \sqrt{\sum(x_{i} - M)^2/n}\)

# Step 1: Calculate M for the set of trials
mean(c(93, 103, 99, 105, 96))

[1] 99.2

# Step 2: Calculate squared difference then get mean
sqrt(((93 - 99.2)^2 + (103 - 99.2)^2 + (99 - 99.2)^2 + 
      (105 - 99.2)^2 + (96 - 99.2)^2) / 5)

[1] 4.4

Variable error (VE) is a measure of consistency

# Step 1: Calculate M for VE
mean(c(rep(99, 4), 100))

[1] 99.2

# Step 2: Calculate squared difference then get mean
sqrt(((99 - 99.2)^2 + (99 - 99.2)^2 + (99 - 99.2)^2 + 
      (99 - 99.2)^2 + (100 - 99.2)^2) / 5)

[1] 0.4

Mean VE = 0.4 cm

What is the mean CE for this set of trials?

# Calculate CE
((98 - 100) + (96 - 100) + (104 - 100) + 
 (102 - 100) + (100 - 100)) / 5

[1] 0

Absolute error (AE) is a measure of overall accuracy

We can calculate using: \(Mean \,AE = \sum|x_{i} - T|/n\)

# Calculate absolute difference for each trial then get mean
(abs(93 - 100) + abs(103 - 100) + abs(99 - 100) + 
 abs(105 - 100) + abs(96 - 100)) / 5

[1] 4

Mean AE = 4 cm \(\longrightarrow\) How do we interpret this?

Absolute error (AE) is a measure of overall accuracy

# Calculate CE
((98 - 100) + (96 - 100) + (104 - 100) + (102 - 100) + 
 (100 - 100)) / 5

[1] 0

# Calculate AE
(abs(98 - 100) + abs(96 - 100) + abs(104 - 100) + 
 abs(102 - 100) + abs(100 - 100)) / 5

[1] 2.4

What is the relationship among CE, VE, and AE?

If we calculated mean CE, mean VE, and mean AE for each person…

We can transform CE into absolute constant error (|CE| or ACE)

We can calculate using by taking the absolute value of our calculated CE:

# Calculate mean CE as before but afterwards take the absolute
abs(((93 - 100) + (103 - 100) + (99 - 100) + 
    (105 - 100) + (96 - 100)) / 5)

[1] 0.8

Mean |CE| = 0.8 cm \(\longrightarrow\) How do we interpret this?

Total variability (E) is a measure of “total error”

We can calculate using: \(Mean \,E = \sqrt{\sum(x_{i} - T)^2/n}\)

# Calculate squared difference then get mean
sqrt(((93 - 100)^2 + (103 - 100)^2 + (99 - 100)^2 + 
      (105 - 100)^2 + (96 - 100)^2) / 5)

[1] 4.472136

Mean E = 4.47 \(\longrightarrow\) How do we interpret this?