Chapter 1. The Normal Curve, Standardization, and z Scores: Does a Head Injury Last a Lifetime?

1.1 The Normal Curve, Standardization, and z Scores: Does a Head Injury Last a Lifetime?

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Question 1.1

Traumatic brain injury (TBI)—a disruption to normal brain functioning caused by a blow to the head—has received a lot of media attention lately, largely because it is a problem for National Football League players. But traumatic brain injury is not new to the medical community, as it has always plagued members of the military. Although TBI has obvious short-term consequences, those symptoms typically disappear with time.

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1.2

Participants in this study were 169 veterans, age 50 or older, living in one of two veterans retirement homes in the United States. The researchers determined that 88 of the participants had a history of TBI at some point in their lifetime, while 81 had no history of TBI. The researchers reported, “Participants completed a comprehensive neuropsychology battery, an expanded version of the Alzheimer’s Disease Centers’ Uniform Data Set battery. . . . This battery was comprised of measures assessing cognitive functioning in five domains: (1) attention/working memory, (2) learning/memory, (3) language, (4) processing speed, and (5) executive functioning” (p. 58). Note that each of these five domains was assessed by multiple measures or tests of that domain. The researchers wanted to create a single score in each of the domains for each participant in the study.

1.3

The researchers went on to say, “[W]e converted each individual’s raw test score into age-corrected z scores, reflecting the extent to which an individual’s test performance diverges from that of healthy, age-matched peers [from existing large normative data sets] . . . [I]ndividuals’ z scores for individual tests within a cognitive domain were averaged to create five cognitive domain composite scores: attention/working memory, learning/memory, language, processing speed, and executive functioning composites” (p. 85).

1.4

Recall that the researchers indicated, “[W]e converted each individual’s raw test score into age-corrected z scores, reflecting the extent to which an individual’s test performance diverges from that of healthy, age-matched peers [from existing large normative data sets] . . . [I]ndividuals’ z scores for individual tests within a cognitive domain were averaged to create five cognitive domain composite scores: attention/working memory, learning/memory, language, processing speed, and executive functioning composites” (p. 85). Imagine a participant had an average z score of –1.00 in the domain of attention/working memory.

1.5

image description

The bar graph shows the average z score for five different measures (Attention/Working Memory), Learning/Memory, Processing Speed, Executive Functioning, and Language), with two conditions (TBI and No TBI). The horizontal x-axis is labeled “Cognitive Domain” and shows a pair of bars for each of the five different measures. Unlike most bar graphs, the vertical bars go below the x-axis which is at 0 and represents the norms for the healthy, age-matched groups. The vertical y-axis is labeled “Average z score” and the z scores range from -1.5 to 0.5 in intervals of 0.5. All of the z scores, in both conditions for each of the five measures, are negative z scores. For Attention/Working Memory, the score for the No TBI condition is about -0.5 and the score for the TBI condition is about -0.7. For Learning/Memory, both scores are about -0.5. For Processing Speed, the score for the No TBI condition is about -0.7 and for the TBI condition is about -1.2. For Executive Functioning, these scores are about -0.2 and -0.7, respectively, and for Language, they are about -0.1 and -0.2, respectively.

Question 1.5

This graph represents the results of the study.

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Correct! Because both groups’ average z scores were less than zero, we know that, on average, both groups scored below the mean of the healthy, age-matched normative group.

Actually, because both groups’ average z scores were less than zero, we know that, on average, both groups scored below the mean of the healthy, age-matched normative group.

1.6

Recall that the researchers were investigating whether veterans who have a history of TBI have different patterns of cognitive decline than veterans with no history of TBI. The graph representing the results of the study is again shown here.

image description

The bar graph shows the average z score for five different measures (Attention/Working Memory), Learning/Memory, Processing Speed, Executive Functioning, and Language), with two conditions (TBI and No TBI). The horizontal x-axis is labeled “Cognitive Domain” and shows a pair of bars for each of the five different measures. Unlike most bar graphs, the vertical bars go below the x-axis which is at 0 and represents the norms for the healthy, age-matched groups. The vertical y-axis is labeled “Average z score” and the z scores range from -1.5 to 0.5 in intervals of 0.5. All of the z scores, in both conditions for each of the five measures, are negative z scores. For Attention/Working Memory, the score for the No TBI condition is about -0.5 and the score for the TBI condition is about -0.7. For Learning/Memory, both scores are about -0.5. For Processing Speed, the score for the No TBI condition is about -0.7 and for the TBI condition is about -1.2. For Executive Functioning, these scores are about -0.2 and -0.7, respectively, and for Language, they are about -0.1 and -0.2, respectively.

Question 1.6

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Correct! On average, veterans with TBI had more extreme negative z scores than did those without a history of TBI for the domains of processing speed and executive functioning.

Actually, on average, veterans with TBI had more extreme negative z scores than did those without a history of TBI for the domains of processing speed and executive functioning.

1.7

image description

The bar graph shows the average z score for five different measures (Attention/Working Memory), Learning/Memory, Processing Speed, Executive Functioning, and Language), with two conditions (TBI and No TBI). The horizontal x-axis is labeled “Cognitive Domain” and shows a pair of bars for each of the five different measures. Unlike most bar graphs, the vertical bars go below the x-axis which is at 0 and represents the norms for the healthy, age-matched groups. The vertical y-axis is labeled “Average z score” and the z scores range from -1.5 to 0.5 in intervals of 0.5. All of the z scores, in both conditions for each of the five measures, are negative z scores. For Attention/Working Memory, the score for the No TBI condition is about -0.5 and the score for the TBI condition is about -0.7. For Learning/Memory, both scores are about -0.5. For Processing Speed, the score for the No TBI condition is about -0.7 and for the TBI condition is about -1.2. For Executive Functioning, these scores are about -0.2 and -0.7, respectively, and for Language, they are about -0.1 and -0.2, respectively.

Question 1.7

The graph representing the results of the study is again shown here. From the graph, we can see that the TBI group had an average z score of approximately –1.20 for the domain of processing speed.

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Correct! Assuming a normal distribution, 84% of the scores are greater than a z score of –1.00.

Actually, assuming a normal distribution, 84% of the scores are greater than a z score of –1.00.

1.8

image description

The bar graph shows the average z score for five different measures (Attention/Working Memory), Learning/Memory, Processing Speed, Executive Functioning, and Language), with two conditions (TBI and No TBI). The horizontal x-axis is labeled “Cognitive Domain” and shows a pair of bars for each of the five different measures. Unlike most bar graphs, the vertical bars go below the x-axis which is at 0 and represents the norms for the healthy, age-matched groups. The vertical y-axis is labeled “Average z score” and the z scores range from -1.5 to 0.5 in intervals of 0.5. All of the z scores, in both conditions for each of the five measures, are negative z scores. For Attention/Working Memory, the score for the No TBI condition is about -0.5 and the score for the TBI condition is about -0.7. For Learning/Memory, both scores are about -0.5. For Processing Speed, the score for the No TBI condition is about -0.7 and for the TBI condition is about -1.2. For Executive Functioning, these scores are about -0.2 and -0.7, respectively, and for Language, they are about -0.1 and -0.2, respectively.

Question 1.8

Clinical psychologists and neuropsychologists often use normative test batteries for determining whether an individual’s performance falls outside of the normal range, indicating some kind of impairment.

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Correct! When defining performance as abnormally impaired, we would want to include only the extreme negative tail of the distribution.

Actually, when defining performance as abnormally impaired, we would want to include only the extreme negative tail of the distribution.

1.9

Robert Willett/Raleigh News & Observer/MCT via Getty Images