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Medical errors are common in hospitals throughout the world. One possible causal factor is the long work hours of hospital personnel. In a pilot study investigating this issue, medical residents were encouraged to sleep \(6-8\) hours per night for a 3 -week period instead of their usual irregular sleep schedule. The researchers expected, given previous data, that there would be one medical error per resident per day on their usual irregular sleep schedule. Suppose two residents participate in the program (each for 3 weeks), and chart review finds a total of 20 medical errors made by the two residents combined. What test can be used to test the hypothesis that an increase in amount of sleep will change the number of medical errors per day?

Step by step solution

01

Define the Hypothesis

The null hypothesis (H0) states that the change in sleep does not affect the number of medical errors, so the error rate remains one per day per resident. The alternative hypothesis (H1) suggests that the increase in sleep will decrease the number of medical errors per day.

02

Calculate the Expected Errors

Calculate the expected number of errors under the null hypothesis over the 3-week period. Each resident works 21 days in 3 weeks, and with an error rate of one per day, this gives an expected 42 errors for the two residents combined (21 days per resident * 2 residents * 1 error per day).

03

Choose the Statistical Test

Since we are comparing observed errors (20) with expected errors (42) and data may not be normally distributed, a Poisson test, suitable for count data, is appropriate to test if the number of errors significantly deviates from what's expected based on the null hypothesis.

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Key Concepts

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

Hypothesis Testing

Hypothesis testing is a statistical procedure used to make decisions about a population parameter based on sample data. In our medical error study, we're trying to determine if a change in sleep patterns affects the error rate. Here's how we set this up:

• **Null Hypothesis (H0)**: The null hypothesis posits that there is no effect or difference. In this case, it states that increasing sleep does not alter the frequency of medical errors.
• **Alternative Hypothesis (H1)**: The alternative hypothesis suggests that there is an effect or difference. Here, it proposes that more sleep leads to fewer errors.

Once these hypotheses are defined, data is collected, and statistical tests are used to interpret the results. If data significantly supports the alternative hypothesis, we might reject the null hypothesis.

Poisson Distribution

The Poisson distribution is a probability distribution that describes the number of events happening within a fixed interval of time or space. It's particularly useful for modeling count data or rare events. In the context of the medical error study, here's how it applies:

• **Count Data**: The medical errors are count data since they're being tallied over a period.
• **Assumptions**: Poisson assumes these events happen independently and within a given time frame, suitable since each day is an independent unit for the study.
• **Poisson Test**: This statistical test measures if the observed count (20 errors) is significantly different from the expected count (42 errors) under the null hypothesis.

The analysis involves calculating probabilities and comparing them to expected outcomes to see if the deviation from expectations could be due to random chance.

Error Rate Analysis

Error rate analysis helps in understanding and quantifying the frequency and impact of errors within a given system. It is crucial for quality control and improvement measures in various fields, including healthcare. Here's how it fits into our discussion:

• **Baseline Error Rate**: In the study, a baseline or expected rate of 1 error per day per resident was established under existing conditions.
• **Observed Error Rate**: After intervention, 20 errors were observed over the study period, which is lower than expected based on the baseline rate (42 errors).
• **Statistical Testing**: By using statistical tools like a Poisson test, we determine if this reduction in error rate is statistically significant or not.

Being aware of such error rates and analyses helps draw insights into process improvements, potentially leading to reduced errors and enhanced outcomes in the healthcare setting.