Asthma symptoms. A study is proposed in which children will...

asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms. How many subjects should be recruited in each group (same number per group) to have a $90 \%$ chance of detecting a significant difference using a two-sided test with $\alpha=.05 ?$

asthma symptoms. A study is proposed in which children will be randomized to either an active intervention where a community health worker comes to the home and educates the children and parents as to approaches to reduce the risk of asthma symptoms or a control intervention where households will receive the same information in print but no home visits will be performed. It is expected that $30 \%$ of the children in the active group vs. $10 \%$ of the children in the control group will have an improvement in asthma symptoms.
How many subjects should be recruited in each group (same number per group) to have a $90 \%$ chance of detecting a significant difference using a two-sided test with $\alpha=.05 ?$

Key Concepts

Significance Level

The significance level, often denoted as alpha (?), is the threshold for rejecting the null hypothesis. In many studies, this is set at 0.05, meaning there is a 5% risk of concluding that an effect exists when it does not (type I error). It guides the criteria for determining statistical significance.

Statistical Power

Statistical power is the probability that a study will detect an effect when there is an effect to be detected. It is typically set at a desired level (such as 90% power) to minimize the risk of false negatives. High power ensures that the study is sensitive enough to identify a true intervention effect.

Effect Size

Effect size is a quantitative measure of the magnitude of the experimental effect. It is a critical component in sample size calculations as larger effect sizes require smaller sample sizes to detect, whereas smaller effect sizes may necessitate larger sample sizes. This helps in planning the study and assessing its potential clinical impact.

Randomized Controlled Trial

A randomized controlled trial (RCT) is a study design that randomly assigns participants into an experimental group or a control group, to ensure that any differences observed between groups are due to the intervention being tested and not other factors. This design is considered the gold standard for evaluating the efficacy of interventions as it minimizes bias.

Sample Size Calculation

Sample size calculation involves determining the number of participants needed in a study to detect a statistically significant difference between groups, if one exists. This calculation is critical to ensure that a study is adequately powered to investigate the research hypothesis and helps avoid type II errors (failing to detect a difference when one actually exists).

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