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Learn how margin of error and CIs affect the interpretation of results.

From patient admission data to laboratory results, data is constantly collected in healthcare. Data analysis transforms this data into insights for cost reduction, risk identification, error reduction, technology development, and drug discovery.

Read on to understand basic statistics and their applications to healthcare analytics, and examine a fictional case study that assesses the effectiveness of a new mattress in preventing pressure ulcers.

Understand Averages: Mean, Median, and Mode

To describe what a group of numbers or data is like overall, we use measures of central tendency. Central tendency is a way to summarize data by showing what is typical or common in that data. The mean (often called an average), median, and mode are common measures of central tendency.

• Mean: The sum of all numbers divided by how many numbers there are
• Median: The middle number in a list of numbers arranged from lowest to highest
• Mode: The value that appears the most in a data set

Decipher the Difference Between Continuous and Discrete Data

Continuous data can have any value in a range. For example, temperature is continuous because it can have any value within a range: 98.6 degrees Fahrenheit, 100 degrees Fahrenheit, or 101.5 degrees Fahrenheit are all valid temperatures. In contrast, discrete data is limited to certain values, typically whole numbers. An example of discrete data is number of hospitalizations, which can be a whole number like 10, but not 10.25.

Get to Know Normal Distribution

A normal distribution, or 鈥渂ell curve,鈥� represents continuous data where values cluster around the average and taper off on either the higher or lower side. Ideally, normal distributions are symmetrical. Newborn weight is normally distributed, as most newborns weigh around the average, with fewer being very underweight or overweight. The statistical tests in this article should only be used with roughly symmetrical normal distributions. Otherwise, use tests that do not assume a specific distribution (non-parametric tests).

Know What Sampling Means

Samples are smaller subsets taken from a population used to draw conclusions about the whole. In health data analysis, a target population of interest is often sampled.

Example: Researchers want to study the impact of a new aerobic exercise program on the immune systems of people with lupus. Researchers randomly sampled 300 adult lupus patients (the target population) to reduce bias. Statistics performed on this sample can inform us about all adults with lupus.

Break Down Margin of Error and Confidence Intervals

Margin of error is the expected difference between the estimated values from the sample and real-world results. It is usually written as plus or minus (卤) a value, and can be a percentage (e.g., 卤 1 percent) or an absolute value (e.g., 卤 2 years of age). Larger samples decrease the margin of error.

A confidence interval (CI) is a range of values that provides a plausible estimate of the true value. CIs are calculated as the sample mean plus or minus the margin of error. A 95 percent CI is commonly used in statistics. This indicates that in repeated sampling the CIs are expected to contain the true mean 95 out of 100 times.

Example: A hospital studying 30-day readmission rates for heart failure (HF) finds the average rate is 27 percent with a 卤 3 percent margin of error. This is a 95 percent CI of 24 to 30 percent. The true average readmission rate is expected to fall between 24 percent and 30 percent in 95 out of 100 cases.

Examine This Fictional Case Study

A hospital wants to evaluate the effectiveness of a new mattress, known as the EquiCloud, in reducing hospital-acquired pressure ulcers (bedsores) in patients with hip fractures who are at increased risk due to limited mobility. These sores develop on the skin and underlying tissues from prolonged pressure.

Step 1: Form a Hypothesis

A hypothesis is a testable prediction, often about the relationship between two variables. There are two main types: the null hypothesis, which states there is no significant relationship between variables; and the alternative hypothesis, which indicates a significant relationship exists. Statistical hypothesis tests either reject the null hypothesis (supporting the alternative) or fail to reject it (indicating no significant effect).

In this case study, the variables are mean pressure ulcer stage and mattress type. The hypotheses are:

• Null hypothesis (H₀): No significant difference exists in the mean pressure ulcer stage between patients with hip fractures using the EquiCloud mattress and those using the standard mattress.
• Alternative hypothesis (H_a or H₁): Hip fracture patients using the EquiCloud mattress will have a lower mean pressure ulcer stage.

Step 2: Collect Data

Patients with hip fractures were separated into two groups: those who received the EquiCloud mattress and those using a standard hospital mattress. Researchers collected data from the electronic health records (EHRs) of 1,000 patients over six months. Pressure ulcer stage (1-4) was recorded.

Step 3: Data Analysis

Once researchers collected the data, they calculated the mean pressure ulcer stage with a 95 percent CI.

• Group 1 (EquiCloud mattress): Mean pressure ulcer stage: 1.5 卤 0.25 (1.25 to 1.75)
• Group 2 (Standard mattress): Mean pressure ulcer stage: 3 卤 0.5 (2.5 to 3.5)

What Was Statistically Significant?

We need a statistical test to know whether the difference in mean pressure ulcer stage is statistically significant. A t-test compares the means of two groups, allowing us to see if there is a difference in mean pressure ulcer stage with and without the EquiCloud. We use a two-sample t-test since the two groups are independent; Group 1鈥檚 results do not affect Group 2鈥檚. Analysts use t-tests for continuous data with an assumed normal distribution. Although pressure ulcer stage is discrete data (1-4), the calculated mean of the stages is continuous.

One of the statistics you can calculate from a t-test is the p-value, which shows the likelihood of the observed results if the null hypothesis is true. The p-value is compared to a significance level (usually 0.05) to assess statistical significance. A p-value below or equal to 0.05 indicates the null hypothesis is rejected, since those results are unlikely if it were true. If the p-value is above 0.05, the results are within the 95 percent CI and the null is not rejected. Let鈥檚 say our t-test in this study gives a p-value of 0.03.

Since a p-value of 0.03 is less than 0.05, we reject our null hypothesis that the EquiCloud mattress has no significant effect on the mean pressure ulcer stage in patients with hip fractures. A p-value of 0.03 suggests only a 3 percent chance of obtaining the same results if bed type had no effect on pressure ulcer stage, which is unlikely.

Step 4: Decision-Making

In this fictional case study, our analysis showed a statistically significant reduction in mean pressure ulcer stage for patients with hip fractures using EquiCloud mattresses. The results were also clinically significant, as the difference was enough to improve patient quality of life. Based on these findings, the hospital implements the EquiCloud mattresses for all patients at risk for developing pressure ulcers.

Look to Future Analysis

To further evaluate the impact of the new mattresses, the hospital might study the incidences of hospital-acquired pressure ulcers. Researchers could perform a comparative analysis to evaluate the current pressure ulcer incidence rates with historical data from when standard mattresses were used.

The EquiCloud mattress case study shows how data analysis can help turn raw data into evidence-based decisions. As healthcare data collection grows, being able to analyze this data is crucial for improving patient care and outcomes.

Angela Halasey, BS, CPC, CCS, Contributing Writer