Question

In a study of the effect of aluminum intake on the mental development of infants, a group of 92 infants who had been born prematurely were given a special aluminum-depleted intravenous-feeding solution. \({ }^{18}\) At age 18 months the neurologic development of the infants was measured using the Bayley Mental Development Index. (The Bayley Mental Development Index is similar to an IQ score, with 100 being the average in the general population.) A \(95 \%\) confidence interval for the mean is (93.8,102.1) (a) Interpret this interval. That is, what does the interval tell us about neurologic development in the population of prematurely born infants who receive intravenousfeeding solutions? (b) Does this interval indicate that the mean IQ of the sampled population is below the general population average of \(100 ?\)

Short answer

The 95% confidence interval (93.8, 102.1) suggests that it is likely the mean neurologic development score for the study population is within the general population's average range. The interval includes the general average (100), indicating no significant difference from the general population.

Step-by-step solution

Understanding the Confidence Interval

The given confidence interval (93.8, 102.1) implies that we can be 95% confident that the true mean of the neurologic development score for prematurely born infants who receive aluminum-depleted intravenous feeding solutions lies between 93.8 and 102.1 on the Bayley Mental Development Index.

Interpreting the Confidence Interval

The confidence interval indicates that the mean neurologic development index for the population of prematurely born infants receiving the special feeding solution does not show a marked deviation from the average (100) in the general population. The interval is close to 100, suggesting that their development may be within the normal range.

Comparing to the General Population Average

Because the confidence interval includes the value 100, which represents the general population average on the Bayley Mental Development Index, it does not provide evidence that the mean IQ of the sampled population of prematurely born infants is below the general population average.

Key concepts

Bayley Mental Development Index

The Bayley Mental Development Index (MDI) is a standard tool used in pediatric psychology to assess the early cognitive and motor skills of infants. Comparable to an IQ score for older individuals, an MDI score of 100 is designated as the average for the general infant population.

The MDI helps trace cognitive and motor development starting as young as one month old until the age of three and a half. The index covers multiple developmental domains, including language, social-emotional, and adaptive behavior. Evaluating an infant's score against the average enables healthcare professionals to detect potential developmental delays and guide early intervention strategies.

Neurologic Development in Infants

Neurologic development in infants is a critical aspect of their overall growth, comprising the maturation of the brain, spinal cord, and nerves. This process is foundational for the acquisition of motor skills, sensory processing, cognitive development, and emotional regulation.

Monitoring this development, particularly in premature infants who may face higher risks for developmental issues, is crucial. Prematurity can impact various stages of brain growth, and interventions like specialized nutritional support can have significant implications for neurologic health and development outcomes.

Statistical Significance

Statistical significance is a determination used in hypothesis testing to judge whether the observed effects or differences in a study are unlikely to have occurred by random chance. It is often represented by a p-value, where a p-value less than a commonly accepted threshold (e.g., 0.05) suggests that the results are unlikely due to chance alone.

The term is vital when interpreting study findings, ensuring that conclusions drawn are robust and not just due to random variability. In the context of the Bayley MDI, if a study were to find a statistically significant difference between groups, it would imply a genuine effect of the variable being studied, such as the impact of aluminum intake on neurologic development.

Inferential Statistics

Inferential statistics are a set of tools and techniques used to make generalizations about a population based on a sample. They enable researchers to draw conclusions and make predictions with a calculated level of certainty.

Confidence intervals are a product of inferential statistics and provide an estimated range believed to contain the true population parameter (e.g., the average Bayley MDI score), with a specified level of confidence. These intervals are essential for grasping the precision and reliability of the sample estimates, assisting stakeholders in making informed decisions based on the study's results.