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Adding computerized medical images to a database promises to provide great resources for physicians. However, there are other methods of obtaining such information, so the issue of efficiency of access needs to be investigated. The article "The Comparative Effectiveness of Conventional and Digital Image Libraries" \((J\). of Audiovisual Media in Medicine, 2001: 8-15) reported on an experiment in which 13 computerproficient medical professionals were timed both while retrieving an image from a library of slides and while retrieving the same image from a computer database with a Web front end. \(\begin{array}{lrrrrrrr}\text { Subject } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\ \text { Slide } & 30 & 35 & 40 & 25 & 20 & 30 & 35 \\ \text { Digital } & 25 & 16 & 15 & 15 & 10 & 20 & 7 \\ \text { Difference } & 5 & 19 & 25 & 10 & 10 & 10 & 28 \\ \text { Subject } & 8 & 9 & 10 & 11 & 12 & 13 & \\ \text { Slide } & 62 & 40 & 51 & 25 & 42 & 33 & \\ \text { Digital } & 16 & 15 & 13 & 11 & 19 & 19 & \\ \text { Difference } & 46 & 25 & 38 & 14 & 23 & 14 & \end{array}\) a. Construct a comparative boxplot of times for the two types of retrieval, and comment on any interesting features. b. Estimate the difference between true average times for the two types of retrieval in a way that conveys information about precision and reliability. Be sure to check the plausibility of any assumptions needed in your analysis. Does it appear plausible that the true average times for the two types of retrieval are identical? Why or why not?

Step by step solution

01

Calculate Descriptive Statistics

First, calculate the key descriptive statistics for each retrieval method (Slides and Digital): minimum, Q1 (first quartile), median, Q3 (third quartile), and maximum. These statistics will help build the boxplots. For the 'Slide' retrieval times, calculate the median, quartiles, and any potential outliers. Do the same for the 'Digital' retrieval times. This will allow for comparison through boxplots.

02

Construct the Boxplot for Slide Times

Use the descriptive statistics from Step 1 to construct a boxplot for times using slides. Determine the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum for slide times. Draw a boxplot with these values. Look for any unusual features like outliers.

03

Construct the Boxplot for Digital Times

Using the descriptive statistics computed for digital retrieval times, construct a boxplot. Make sure to identify the five-number summary (min, Q1, median, Q3, max) and draw the boxplot. Identify and note any outliers or interesting features.

04

Analyze Boxplot Comparisons

Compare the boxplots from slides and digital retrieval times. Look at medians, the spread of the data (interquartile range), and any potential outliers. Note which retrieval method tends to be faster based on these boxplots and any interesting tendencies or variations.

05

Estimate Difference Between Averages

Calculate the difference in average retrieval times between slides and digital methods. This involves computing the mean difference of the times for each subject (slide time - digital time). Find the confidence interval to measure the precision and reliability of this difference.

06

Analyze Assumptions and Plausibility

To ensure accurate results, check assumptions such as normality of the differences and equal variances. Conduct a statistical test, like a paired t-test, on the difference in retrieval times. The hypothesis test will determine if the mean difference is statistically significant, indicating whether the average times are likely to be different.

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Key Concepts

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

Descriptive Statistics

Descriptive statistics serve as a foundation for analyzing the data from the slide and digital retrieval methods. It involves summarizing and interpreting data in a meaningful way using calculations like the mean, median, and quartiles. These statistics make it easier to understand the overall data trends and variability.
For the exercise, start by calculating the five-number summary for both methods: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This summary provides a snapshot of the data range and central tendency. For example, if the median retrieval time for slides is 35 seconds and for digital is 15 seconds, it suggests that digital is generally quicker. Descriptive statistics also help in identifying outliers, like unusually high retrieval times, which can skew interpretations.
Calculating these statistics is crucial for developing comparative data visuals like boxplots, adding clarity and context to the findings.

Comparative Analysis

Comparative analysis involves looking at the differences and similarities between the two retrieval methods. It allows us to visually and statistically assess which method is more efficient.
By constructing boxplots, we can compare the distribution of retrieval times for slides and digital systems. Boxplots are effective because:

• They provide a clear visual of the data distribution.
• They show how the medians (central tendency) of each method stack up against each other.
• They help identify outliers that may affect the efficiency.

For instance, if the boxplot depicts the slide retrieval times as wider or more spread out than the digital retrieval times, it suggests higher variability and perhaps lower efficiency. This comparative visual lays the groundwork for deeper statistical analysis, directing focus to actual mean differences and not just visual cues.

Confidence Interval

Estimating a confidence interval involves calculating a range of values which is likely to contain the true difference in average retrieval times between the two methods. It highlights how reliable your estimate of the difference between the means is and provides insight into the statistical significance of your findings.
To compute the confidence interval, follow these steps:

• Calculate the mean difference between the two methods for all subjects.
• Compute the standard deviation of these differences.
• Apply the formula to determine the confidence interval around this mean difference.

The confidence interval not only informs us about how precise our measurement is but also helps in comparing methods under study. If this interval does not contain zero, it suggests a significant difference between the two methods. Thus, it becomes a pivotal component in evaluating if the digital method is indeed faster in a reliable manner.

Paired t-test

A paired t-test is a statistical method used when comparing two related samples, like the digital and slide retrieval times, to determine if there is a significant difference between them. It is particularly useful when you have two observations on the same subject, as in this experiment.
To perform this test, remember these key steps:

• Calculate the mean difference for each subject.
• Assess the standard deviation of the differences.
• Use these values to compute the t-statistic.

The t-test checks if the mean difference is significantly different from zero, suggesting a real difference in retrieval times. If your resulting p-value is less than a chosen significance level (commonly 0.05), you reject the null hypothesis, indicating a meaningful difference between the two retrieval methods.
In this experiment, using a paired t-test is crucial because it helps validate the conclusion drawn from descriptive and comparative statistics, confirming the efficiency of the retrieval systems.