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Nighttime bladder control is an important developmental milestone, with failure dependent on age. Continence is usually achieved between 4 and 6 years of age, but an important minority of children experience delays in success. A longitudinal study was conducted in Britain in which nighttime bedwetting was assessed at ages \(4,6,8,9,11,\) and 15 years among 3272 children in the Medical Research Council's 1946 National Survey of Health [21]. The following data were presented. There were 1362 boys and 1313 girls who reported no bedwetting at any of the six ages just listed. Consider this as the control group. There were 6 boys and 2 girls who reported no bedwetting at ages \(4,6,\) and 8 but reported some bedwetting at both ages 9 and \(11 .\) Consider this as the case group. Ignore children with any other pattern of bedwetting over the six ages. What test can be used to assess whether the percentage of cases among boys is significantly different from the percentage of cases among girls?

Step by step solution

01

Define the Problem

We need to determine if the proportion of boys who experienced bedwetting at ages 9 and 11 is significantly different from the proportion of girls who experienced the same issue. This involves comparing proportions between two independent groups.

02

Gather the Required Data

From the study, we have 1362 boys with no bedwetting and 6 boys with bedwetting at ages 9 and 11. Similarly, we have 1313 girls with no bedwetting and 2 girls with bedwetting at ages 9 and 11.

03

Calculate the Proportions

Calculate the proportion of bedwetting in each gender. For boys, the proportion is calculated as \( \frac{6}{1362 + 6} \). For girls, it is \( \frac{2}{1313 + 2} \).

04

Choose the Appropriate Test

The situation involves two independent groups with categorical data and we want to test if there is a significant difference between their proportions. The appropriate statistical test to use is the Chi-Squared Test for Independence or Fisher's Exact Test, depending on sample sizes.

05

Consider the Sample Sizes

As the number of subjects with bedwetting issues is quite small (6 boys and 2 girls), Fisher's Exact Test is more suitable than the Chi-Square Test since it handles small sample sizes more effectively.

06

Execute the Selected Test

Perform Fisher's Exact Test on a 2x2 contingency table created from the case/control data for boys and girls to assess statistical significance of differences in proportions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bedwetting in Children

Bedwetting, or nocturnal enuresis, is a common childhood issue where a child unintentionally urinates during sleep after the age when nighttime bladder control is typically achieved. Most children master this control between the ages of 4 and 6. However, some continue to struggle with bedwetting beyond this age range. This can occur for various reasons, including delayed development of bladder control, a family history of the issue, or even psychological factors.
In the context of the study mentioned, children were assessed at several developmental stages to monitor changes in bedwetting. A group of children, defined as cases, reported no bedwetting at earlier ages but experienced it at ages 9 and 11. Understanding these patterns helps in identifying children who might benefit from interventions.

Developmental Milestones

Developmental milestones are specific skills or behaviors most children can do by a certain age, helping gauge overall child development. They encompass various domains such as:

• Motor skills
• Cognitive abilities
• Social interactions
• Emotional maturity

Bedwetting control is one such milestone signaling the development of bladder control during the night. Longitudinal studies, like the one referenced, help track developmental milestones over time. They provide essential data about when and how children typically achieve these, informing both normal and delayed development cases.

Statistical Tests for Proportions

Statistical tests for proportions are crucial tools in comparing the success rates or occurrences of an event between two groups. In this case, boys and girls are assessed for bedwetting incidences at certain ages.
Such tests help determine whether observed differences are statistically significant or might have occurred by chance. They are essential for researchers looking to make informed conclusions about their data. Comparing proportions involves categorical data and typically uses tests like the Chi-Squared Test or Fisher's Exact Test when sample sizes are smaller as they offer precise results.

Fisher's Exact Test

Fisher's Exact Test is a statistical significance test used when sample sizes are small. Unlike the Chi-Squared Test, which approximates probabilities, Fisher's Exact Test calculates the exact probability of observing the data if the null hypothesis is true.
This characteristic makes it particularly suitable for analyzing small datasets, providing an accurate assessment of whether differences between two groups are statistically significant. In the context of determining whether there is a difference in bedwetting proportions among boys and girls, Fisher's Exact Test serves as the better choice due to the small number of cases: 6 boys and 2 girls.