Descriptive statistics for cardiothoracic surgeons: part 2 — the foundation of data interpretation

Abstract

Descriptive statistics are essential for summarizing and interpreting clinical data in cardiothoracic surgery. Understanding measures of central tendency and dispersion, such as mean, median, range, variance, and standard deviation, provides insights into patient outcomes and surgical effectiveness. Confidence intervals offer a range for population parameters, enhancing decision-making precision. Data visualization tools like histograms, box plots, and scatter plots illustrate distributions and relationships. Interpreting tables and figures accurately, recognizing biases, and evaluating statistical validity are crucial for applying research findings to clinical practice. These statistical tools ultimately support evidence-based practice and ensure informed decision-making by clinicians.

Introduction

Descriptive statistics are crucial in clinical research as they provide a foundation for understanding and summarizing data. This helps us in identifying patterns and trends within datasets, making it easier to interpret and present complex information [1]. In the context of cardiothoracic surgery, descriptive statistics are essential for summarizing patient outcomes, treatment efficacy, and other critical variables, thus facilitating evidence-based practice [2].

Interpreting data accurately is fundamental to evidence-based practice. Descriptive statistics enable clinicians to make informed decisions by providing a clear summary of the data, highlighting central trends, variability, and distribution [3]. This not only aids in clinical decision-making but also enhances the quality of patient care by ensuring that conclusions drawn from research are based on robust and comprehensible data.

Scope of descriptive statistics

This article is the second part in the series on biostatistics in cardiothoracic surgery, aiming to further deepen the understanding of statistical concepts and their applications. We will cover key measures of central tendency, such as mean, median, and mode, as well as measures of dispersion, including range, variance, and standard deviation [4–6]. Additionally, we will delve into data visualization techniques like histograms, box plots, scatter plots, and more advanced visualizations such as violin plots, raincloud plots, and Bland–Altman plots [7]. The role of confidence intervals in clinical research will also be explored.

Understanding the difference between descriptive and inferential statistics is vital. While descriptive statistics focus on summarizing and presenting data, inferential statistics are used to make predictions or inferences about a population based on a sample. This distinction is important for clinicians to grasp, as it underpins the methodologies used in various research studies and their implications for clinical practice. The topics on inferential statistics will be dealt with in future papers of this series.

Measures of central tendency

Mean

The mean, or average, is calculated by summing all the values in a dataset and dividing by the total number of values. In clinical research, the mean provides a straightforward summary of central tendency, making it widely applicable.

Example: In a study assessing post-operative recovery times for patients undergoing coronary artery bypass grafting (CABG), the mean recovery time can be calculated by adding all the individual recovery times and dividing by the number of patients.

This measure offers a clear, single figure that represents the average experience of patients. However, the mean has limitations, particularly in datasets with outliers or skewed distributions (discussed later).

Example: If a few patients experience significantly longer recovery times due to complications, the mean recovery time might be higher than the typical patient experience.

Therefore, while the mean is useful for providing an overall snapshot, it should be interpreted with caution in the presence of extreme values [8].

Median

The median is the middle-most value in a dataset when the values are arranged in ascending order. If the dataset contains an even number of values, the median is the average of the two middle values. It is particularly advantageous in clinical research involving skewed data, as it is not affected by outliers.

Example: In a study examining the survival times of patients with advanced heart failure treated with left ventricular assist devices (LVADs), the median survival time can offer a more accurate reflection of typical patient outcomes compared to the mean [9].

If the dataset includes a few patients who survive for exceptionally long periods, the mean survival time could be misleadingly high. The median, by contrast, would provide the survival time of the patient at the 50th percentile, offering a better representation of what most patients might expect. This is particularly important in clinical settings where the distribution of outcomes is not symmetrical.

Mode

The mode is the value that appears most frequently in a dataset. It is especially useful for categorical data in clinical settings.

Example: In a study analyzing the most common complications following lung resection surgeries, the mode can identify the complication that occurs most frequently, such as postoperative pneumonia.

Knowing the mode helps clinicians focus on the most prevalent issues and develop targeted strategies to mitigate these complications.

Example: In a study of echocardiographic findings in patients with mitral valve prolapse, the mode might reveal the most common abnormal finding, such as mitral regurgitation.

This information can guide clinicians in prioritizing diagnostic and therapeutic approaches based on the most frequently encountered issues. However, mode is more often unused, particularly as using data in the form of counts and percentages allows for an easier interpretation of the data as a whole rather than the single most relevant factor.

In clinical research, measures of central tendency should be carefully chosen and interpreted based on the nature of the data and the specific context of the study. For instance, when presenting mean values, it is crucial to also discuss the standard deviation (discussed in the following section) to provide a sense of the data’s variability. In studies with skewed distributions, the median might be more appropriate, while the mode can highlight the most common occurrences in categorical datasets. By understanding and appropriately applying these measures, clinicians can derive meaningful insights from their data. Table 1 presents a sample dataset for pulmonary hypertension and its interpretation using measures of central tendency.

Table 1.

Presentation of central tendency measures in pulmonary hypertension

Measure	Description	Calculation	Example data (Days)	Result	Interpretation in clinical context
Mean	Sum of all values divided by the number of values	Mean = ∑X/N N = Total count	10, 12, 15, 20, 25, 30, 100	(10 + 12 + 15 + 20 + 25 + 30 + 100)/7 = 30.29	The mean post-operative recovery time for patients with pulmonary hypertension, including an outlier, suggests a longer average recovery period, potentially skewed by extreme values
Median	Middle value when data is ordered	Arrange data in ascending order and find middle value	10, 12, 15, 20, 25, 30, 100	20	The median recovery time indicates that half of the patients with pulmonary hypertension recover within 20 days, providing a more typical recovery period without the influence of the extreme outlier
Mode	Most frequently occurring value	Identify the most frequent value in the dataset	10, 12, 15, 20, 25, 30, 100	No mode (all values are unique)	No mode in this dataset indicates a diverse range of recovery times without any single recovery time being most common

Measures of dispersion

Range

The range is the simplest measure of dispersion, calculated as the difference between the highest and lowest values in a dataset [10].

Example: If we consider the ages of pediatric patients undergoing congenital heart defect surgery, with ages ranging from 1 month to 12 years, the range would be 12 years minus 1 month. This measure provides a quick snapshot of the spread of values.

However, the range is highly sensitive to outliers, which can distort the overall understanding of data variability.

Example: If one patient in the dataset is significantly older or younger than the others, the range may suggest greater variability than what is typical for the majority of patients.

Clinicians should use the range cautiously and consider additional measures of dispersion to gain a more accurate picture.

Variance

Variance measures the average of the squared differences from the mean. It is calculated by subtracting the mean from each data point, squaring the result, summing these squared differences, and then dividing by the number of observations minus one [11]. The squaring in the calculation of variance serves a crucial purpose: it ensures that differences above the mean do not cancel out those below the mean, which would otherwise lead to a variance of zero. Squaring the differences also emphasizes larger deviations from the mean, making variance sensitive to outliers.

Example: In a study of blood loss during different types of lung resections, variance helps to understand how much the blood loss varies from the average. High variance indicates that the blood loss amounts are spread out over a wider range of values, while low variance suggests they are more clustered around the mean.

This information is crucial in clinical settings to anticipate potential complications and prepare accordingly. However, because variance is expressed in squared units, it can be difficult to interpret directly, leading to the use of standard deviation.

Standard deviation

The standard deviation is the square root of the variance and provides a measure of the average distance of each data point from the mean. It is widely used in clinical research due to its intuitive interpretation [12].

Example: In a study of post-operative recovery times following mitral valve replacement surgery, a standard deviation can indicate how much individual recovery times typically deviate from the mean recovery time.

A small standard deviation suggests that recovery times are consistently close to the mean, indicating a predictable recovery process, whereas a large standard deviation indicates more variability. Standard deviation is typically mentioned in the form of mean ± standard deviation (SD) and not independently. When reporting standard deviation, it is helpful to use phrases such as:

"The mean recovery time was 15 days with a standard deviation of 3.2 days,"

to convey both the central tendency and the variability. Alternatively, other expressions can be used, like

"The mean recovery time with standard deviations as 15 (3.2) days"

or

"The mean recovery time was 15 (SD 3.2) days."

This is highly dependent on individual authors and personal preferences; however, the concept conveyed remains the same.

Coefficient of variation

The coefficient of variation (CV) is the ratio of the standard deviation to the mean, expressed as a percentage. It is particularly useful for comparing variability between datasets with different units or widely different means [13].

Example: Comparing the variability in surgical outcomes between adult and pediatric heart transplant patients can be challenging due to differences in baseline characteristics.

The CV standardizes these comparisons by expressing variability relative to the mean, allowing clinicians to understand which group has greater relative variability. A high CV indicates greater dispersion relative to the mean, while a low CV indicates less. It is also important that CV helps authors and readers understand the consistency of the data in relation to the parameter of interest.

Percentile and interquartile range

Percentiles indicate the value below which a given percentage of observations fall. For instance, the 25th percentile (Q1) and 75th percentile (Q3) divide the dataset into quartiles, with the interquartile range (IQR) being the difference between Q3 and Q1 [10]. It is always advisable to mention IQR in parenthesis with median when used and should not be mentioned independently.

Example: In a study of survival times after mediastinal tumor resection, the IQR can provide insight into the middle 50% of survival times, offering a robust measure of dispersion that is less sensitive to outliers.

Reporting percentiles can help clinicians understand the distribution of outcomes and identify patients at higher or lower ends of the spectrum.

Example: “The IQR for survival time was 5 to 15 months, indicating that 50% of patients survived within this range.”

Figure 1 shows a graph visualizing the standard deviation and IQR.

Fig. 1.

Graphical representation of standard deviation and interquartile range

Pooled variance

Pooled variance combines variances from different groups to estimate a common variance. This is particularly useful in meta-analyses where data from multiple studies are combined [14].

Example: Pooling variance in studies comparing the efficacy of different vascular graft materials helps to assess the overall variability across studies, providing a more comprehensive understanding of the performance of each material.

Calculating pooled variance involves weighting the variance of each group by their degrees of freedom and averaging them. This approach provides a more accurate estimate of variability when combining datasets.

Skewness and kurtosis

Skewness measures the asymmetry of the data distribution. Positive skewness indicates a longer right tail, while negative skewness indicates a longer left tail (Fig. 2).

Example: The distribution of patient ages in a study on Ravitch procedure might be positively skewed if most patients are infants and a few are older children.

Fig. 2.

Graphical representation of positive and negative skewness

Kurtosis measures the “tailedness” of the distribution. High kurtosis indicates more outliers, while low kurtosis indicates fewer (Fig. 3). In clinical studies, understanding skewness and kurtosis helps to anticipate and adjust for non-normal data distributions, ensuring more accurate statistical analyses [15]. This is particularly helpful when deciding between mean and median for data representation in a study. In simpler terms, it provides details on the peakness or flatness of the distribution compared to the normal distribution.

Fig. 3.

Graphical representation of kurtosis

Sum of squares

The sum of squares is a foundational concept in variance and standard deviation calculations, representing the total squared deviation from the mean. In clinical research, it helps quantify the total variability within a dataset [16].

Example: In a study comparing surgical outcomes, the sum of squares helps to identify the overall variability in patient recovery times.

Understanding this concept is crucial for performing further statistical analyses, such as analysis of variance (ANOVA) (discussed in later papers), which partitions the total sum of squares into components attributable to different sources of variation.

Frequency distribution

Frequency distribution is a summary of how often each value occurs in a dataset. Constructing a frequency distribution involves counting the occurrences of each value and presenting them in a table or graph (discussed later) [17].

Example: A frequency distribution of complications following aortic arch surgery might show the most common complications, helping clinicians prioritize preventive measures.

Frequency distributions provide a straightforward way to visualize and interpret categorical data, which can be clearly seen in Table 2, with an explanatory footnote.

Table 2.

Sample frequency distribution table

Complication	Number of patients	Percentage (%)
Stroke	15	10.0
Spinal cord injury	5	3.3
Heart failure	8	5.3
Pneumonia	12	8.0
Others	20	13.3

This table presents the frequency distribution of various complications observed in a patient cohort. The frequency columns are as follows: Number of patients, which shows the absolute number of patients who experienced each type of complication; and Percentage (%), which displays the proportion of the total patient cohort that experienced each complication, expressed as a percentage. Stroke was observed in 15 patients, accounting for 10% of the total complications. This means that out of every 100 patients, 10 experienced a stroke, with similar inference for the other rows as well. The Others category could include various other complications experienced by 20 patients, accounting for 13.3% of the total. This category likely includes less common or miscellaneous complications not specifically listed. The percentages provide a clear understanding of the relative frequency of each complication. The sum of the percentages may sometimes (though not in this case), exceed 100% because each patient might experience more than one complication

These measures of dispersion complement measures of central tendency by providing a more complete picture of the data. While central tendency measures like the mean and median offer a central value, measures of dispersion such as standard deviation and IQR describe how spread out the values are around this central point. Quite often, researchers ignore the standard deviation and IQR values associated with the mean and median values and focus on measures of central tendency instead. The data represented by the measures of dispersion often take a secondary role in the eyes of researchers but are equally important in interpreting data and uncovering certain facts hidden by the measures of central tendency. Understanding both aspects is crucial for accurate data interpretation in clinical research.

Confidence intervals

Confidence intervals are a statistical tool used to estimate the range within which a population parameter is likely to fall based on sample data. They provide a measure of uncertainty around the estimate, reflecting the degree of confidence that the interval contains the true parameter value. A 95% confidence interval means that if we were to take multiple samples from the same population and calculate a confidence interval for each sample, approximately 95% of these intervals would be expected to contain the true population parameter. This concept is crucial in clinical research as it helps in understanding the reliability and precision of the estimated values [18, 19]. Figure 4 provides a graphical representation of the same.

Fig. 4.

Graphical representation of 95% confidence interval

The calculation of a confidence interval involves several steps. First, the mean of the sample data is calculated. Then, the standard error of the mean is determined, which is the standard deviation divided by the square root of the sample size. The confidence interval is then constructed by adding and subtracting a margin of error from the sample mean. The margin of error is calculated as the product of the standard error and a critical value from the t-distribution or z-distribution, depending on the sample size and whether the population standard deviation is known.

Example: If the mean recovery time after Diaphragmatic Hernia Repair is 15 days with a standard deviation of 3 days and the sample size is 30, the standard error would be 0.55 days. For a 95% confidence interval, the critical value from the t-distribution is approximately 2.045. Thus, the margin of error would be 1.12 days, and the confidence interval would be 13.88 to 16.12 days.

Interpreting confidence intervals in clinical research involves understanding the range of values provided and their implications for clinical practice.

Example: If a study reports a 95% confidence interval for the mean recovery time following the Ness procedure as 12 to 18 days, this interval suggests that the true mean recovery time for the population is likely between 12 and 18 days.

This information can be crucial for clinicians in planning post-operative care and setting patient expectations. A narrow confidence interval indicates high precision and reliability of the estimate, while a wide interval suggests greater uncertainty and variability [20].

In cardiothoracic surgery studies, confidence intervals are particularly valuable for comparing the effectiveness of different surgical techniques.

Example: If one study reports a 95% confidence interval for the success rate of mitral valve replacement as 85% to 95% and another study reports a confidence interval of 78% to 88% for mitral valve repair, clinicians can infer that the mitral valve replacement likely has a higher success rate.

Additionally, overlapping confidence intervals might indicate that the differences between the surgeries are not statistically significant, guiding clinicians to consider other factors such as patient suitability and surgical expertise. However, depending on the context, it is possible to take 90% or even 99% confidence interval levels to ensure higher accuracy or increased data variation as needed for the relevant studies. A graphical representation showing the differences of these intervals can be found in Fig. 5.

Fig. 5.

Comparative representation of 90%, 95%, and 99% confidence intervals

Confidence intervals also aid in decision-making by providing a range within which the true effect size is expected to lie, helping to balance clinical judgments with statistical evidence.

Example: In assessing the effectiveness of leukocyte depletion of transfused blood on postoperative complications, a confidence interval around the reduction rate can help determine whether the observed effect is likely to be clinically meaningful. If the confidence interval is entirely above a clinically relevant threshold, it supports the transfusions efficacy. Conversely, if the interval includes values below the threshold, further investigation may be needed.

However, it is important to note that while confidence intervals are extremely useful tools for both descriptive and inferential analysis, the phrase “less is more” applies well here. Using this metric for the parameter of interest is far more effective than applying it arbitrarily to simpler variables like age, height, or weight, especially when these are not the primary focus of investigation. Additionally, the interpretation of confidence intervals is specific to patients, diseases, and the medical procedures or medications involved. While certain small variations may be insignificant in some contexts, these same differences can be far more significant in others. This understanding is crucial when evaluating the clinical and statistical significance of confidence intervals.

Statistical Significance: Suppose a study measures the effectiveness of thymus transplants in enhancing immune function, quantified by the number of new T-cell generations post-transplant. A 95% confidence interval for the average increase in T-cell count might range from 200 to 400 cells per microliter of blood. This interval does not include 0, indicating that the transplant statistically significantly increases T-cell counts.

Clinical Significance: While the increase is statistically significant, its clinical significance depends on whether the change in T-cell count translates into meaningful improvements in patient outcomes. For example, if the threshold for a clinically meaningful improvement (based on historical data) is a 500-cell increase per microliter, the observed increase (200 to 400 cells) might not be considered clinically significant, despite being statistically significant. In contrast, if patient survival or quality of life significantly improves even with smaller increases in T-cell counts, then the clinical significance is affirmed.

Data visualization

Histograms

Histograms are bar graphs representing the frequency distribution of a dataset by dividing the data into intervals (bins) and counting the number of observations in each bin [21].

Example: A histogram showing the distribution of patient ages undergoing different types of cardiothoracic surgery can help identify demographic patterns (Fig. 6). If most patients undergoing CABG are between 50 and 60 years old, while those having lung resections are younger, this information can guide resource allocation and preoperative planning.

Fig. 6.

Sample histogram

Box plots

Box plots, or box-and-whisker plots, display the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box represents the IQR, and the line inside the box marks the median. Whiskers extend to the minimum (lower-fence) and maximum (upper-fence) values within 1.5 times the IQR from Q1 and Q3, with outliers plotted individually [22]. The parts of a box plot can be found in Fig. 7.

Example: A box plot of hospital costs for different types of cardiothoracic surgeries (e.g., CABG, valve replacement, lung resection) can reveal median costs, variability, and potential outliers (Fig. 8). This visualization can help hospital administrators identify cost drivers and areas for potential savings or efficiency improvements.

Fig. 7.

Parts of a sample box plot

Fig. 8.

Comparative sample box plot

An additional advantage of box plots is that they help detect outliers, particularly in situations where outliers could be problematic, and help overcome disadvantages with the mean (“Mean” section).

Scatter plots

Scatter plots display the relationship between two continuous variables by plotting data points on a Cartesian plane [23].

Example: A scatter plot comparing the pre-operative echocardiographic left ventricular ejection fraction (LVEF) with post-operative LVEF in heart transplant patients can reveal correlations (Fig. 9).

Fig. 9.

Sample scatter plot

The lines crossing the plot diagonally indicate the regression line. The regression line in a scatter plot represents the relationship between two quantitative variables. It is a straight line that best fits the data points, minimizing the distance between the line and each data point. The regression line indicates the average change in the dependent variable (y-axis) for a one-unit change in the independent variable (x-axis). Such a plot could indicate whether higher pre-operative LVEF predicts better post-operative heart function, helping clinicians refine patient selection criteria and post-operative care plans.

Violin plots

Violin plots combine box plots and kernel density plots to show data distribution and density [24]. A sample violin plot with detailed labeling can be seen in Fig. 10.

Example: Comparing resident wellness scores across different surgical rotations (e.g., cardiothoracic surgery, general surgery, orthopedics) using violin plots can illustrate the median and interquartile range of wellness scores while highlighting distribution shapes (Fig. 11). This helps residency program directors identify rotations that may need changes to improve resident well-being.

Fig. 10.

Parts of a sample violin plot

Fig. 11.

Comparative sample violin plot

In this case, we observe three distinct violin plots representing wellness scores across different surgical specialties. The plot for cardiothoracic surgery shows scores that are tightly clustered, primarily centered around 70, with the widest part of the violin plot around the middle, indicating a concentration of data points in this range. Conversely, the plot for orthopedics displays a more uneven distribution, with residents reporting both very high and very low wellness scores, suggesting significant variability. General surgery presents a mixed distribution, similar to cardiothoracic surgery, with most scores grouped around the middle but also including a few residents with very high scores.

Although it would be premature to draw conclusions about which department is better from a single diagram, this visualization offers more detailed data than a simple mean and standard deviation. It allows for a deeper interpretation of the data distribution. The inclusion of data points to the left of the plot is optional and varies according to individual preferences. In cases with many data points, adding them to the plot could be counterproductive as it may clutter the visualization and obscure key trends.

Raincloud plots

Raincloud plots merge box plots, density plots, and raw data points to provide a comprehensive view of the data. Similar to violin plots, raincloud plots too have a box plot in them to show the data distribution.

Example: Pre-operative and post-operative hemoglobin levels in relation to different cardiac procedures can combine summary statistics with the actual distribution and individual data points, offering a detailed picture of hemoglobin variability (Fig. 12). This can aid in understanding individual surgical risk factors and transfusion liability.

Fig. 12.

Comparative sample raincloud plot

Quantile–quantile plots (QQ-plots) and normal probability plots

QQ-plots and normal probability plots assess whether data follows a normal distribution by plotting observed data quantiles against theoretical quantiles of a normal distribution [25].

Example: Testing the normality of intraoperative blood loss measurements during different types of pediatric cardiac surgeries helps determine if parametric tests are appropriate for analyzing the data.

Figure 13 shows various QQ-plots and normal probability plots with both normal and deviated ranges. Deviations from the diagonal line in these plots indicate departures from normality, guiding appropriate statistical analyses [26, 27]. Table 3 explains the various deviations of the plots and what the interpretation means in each instance.

Fig. 13.

A QQ-plot showing normal distribution; B QQ-plot showing skewed distribution; C Normal probability plot showing a normal distribution; and D Normal probability plot showing a skewed distribution

Table 3.

Interpretation of QQ-plots and normal probability plots

Plot characteristic	Interpretation	Example (blood loss)	Action required
Straight line	Data follows the theoretical distribution closely	If blood loss measurements are normally distributed, the points will lie on a straight line	No action required; the data can be used for parametric tests assuming normality
Upward curvature	Heavy tails; more extreme values than expected	If the plot curves upward, it indicates more patients have higher blood loss than expected under normal distribution	Consider using robust statistics or transforming the data
Downward curvature	Light tails; fewer extreme values than expected	If the plot curves downward, it indicates fewer patients have extreme blood loss than expected	Investigate potential data truncation or consider using a distribution with lighter tails
S-shaped curve	Skewness in the data	If the plot forms an S-shape, it suggests skewed distribution of blood loss, possibly more patients with lower or higher blood loss than the mean	Apply a transformation (e.g., log) to normalize the data or use non-parametric tests
Steep initial slope	Data is more spread out than the theoretical distribution	If the initial points are steep, indicating rapid increase in blood loss values, the variability in blood loss is higher than expected	Assess the cause of variability and consider data transformations or robust analysis methods
Flatter initial slope	Data is less spread out than the theoretical distribution	If the initial points are flatter, indicating slower increase in blood loss values, the variability in blood loss is lower than expected	Ensure data collection methods are accurate and consistent; might need less complex statistical models
Clusters of points	Presence of subpopulations or outliers	If points form clusters, it suggests distinct subgroups within the blood loss data (e.g., different surgery types or patient conditions)	Perform subgroup analysis or stratify data to handle heterogeneity
Points far from line	Outliers or unusual data points	If some points are far from the line, indicating extreme values of blood loss, these are potential outliers	Investigate and possibly exclude outliers, or use robust statistical methods to minimize their impact

Line charts

Line charts display data points connected by lines, illustrating trends over time.

Example: Tracking patient blood pressure (systolic and diastolic) during the first 48 hours post-surgery using line charts (Fig. 14) can reveal trends and fluctuations, helping clinicians monitor patient stability and respond promptly to any concerning changes.

Fig. 14.

Sample line chart

These can be used for individual patients or even for groups of patients.

Heatmaps

Heatmaps use color gradients to represent data values in a matrix format [28].

Example: A heatmap of gene expression levels in different tissue samples from patients with various stages of cardiomyopathy (Fig. 15) can provide a visual summary of complex data, helping researchers identify patterns or clusters that might indicate specific biological processes or disease states.

Fig. 15.

Sample heatmap

Bland–Altman plots

Bland–Altman plots assess agreement between two measurement methods by plotting the differences against the averages of the methods [29].

Example: Comparing traditional echocardiography and advanced magnetic resonance imaging techniques for measuring heart valve function (Fig. 16), Bland-Altman plots can highlight any systematic biases or discrepancies.

Fig. 16.

Sample Bland–Altman plot

This ensures that new diagnostic methods align well with established ones, enhancing clinical decision-making accuracy. Moreover, numerical data is required, and the plot has markings for standard deviation and confidence intervals.

In a Bland–Altman plot, if the dots are clustered closely around the center line (which represents the mean difference), it indicates good agreement between the two methods. The closer the points to this line, the more consistent one measurement is with the other. Conversely, if the dots are scattered far from the center line or show a pattern (e.g., increasing or decreasing trends across the range of averages), it suggests a lack of agreement or a systematic error that varies at different levels of measurement. The lesser the scatter and the closer the points to the mean difference line, the better the correlation and reliability between the two methods being compared.

Radar charts

Radar charts, or spider charts, compare multiple variables on a two-dimensional plane [30].

Example: Comparing various risk factors for different surgical techniques (e.g., CABG vs. minimally invasive valve repair) such as diabetes, hypertension, age, etc. (Fig. 17) can be visualized in a radar chart.

Fig. 17.

Sample radar chart

This thorough comparison helps surgeons and patients make informed choices about treatment options.

Frequency polygons

Frequency polygons are line graphs showing frequency distributions, similar to histograms but using points connected by lines.

Example: A frequency polygon of the number of days patients spend in the intensive care unit (ICU) after different cardiothoracic procedures (e.g., heart transplant, lung resection, aortic aneurysm repair) provides a continuous view of the distribution (Fig. 18).

Fig. 18.

Sample frequency polygon

This visualization helps clinicians understand recovery patterns and allocate ICU resources more effectively. It is often possible to confuse oneself between line charts and frequency polygons. Table 4 helps differentiate the two.

Table 4.

Frequency polygon vs. line chart

Aspect	Frequency polygon	Line chart
Purpose	Shows the distribution of a dataset	Shows trends over time or changes in continuous data
Data type	Continuous data grouped into bins or intervals	Continuous data changing over time or another continuous variable
Construction	Plots the frequency of data points within intervals, connects points by lines, often starts and ends at the x-axis	Plots data points based on their values, connects points by lines to show trends, usually does not form a closed shape
X-axis	Represents the intervals or bins of the data	Represents time or another continuous variable
Y-axis	Represents the frequency (count) of data points within each interval	Represents the variable being measured

Multi-Vari chart

Multi-Vari charts display the variation within subgroups and between subgroups over time, making them useful for identifying patterns and trends in clinical data.

Example: A Multi-Vari chart can be used to examine the variation in post-operative recovery times across different surgical techniques (e.g., traditional open surgery, minimally invasive surgery, robotic-assisted surgery) and patient demographics (e.g., age groups, comorbid conditions) in cardiothoracic surgery (Fig. 19).

Fig. 19.

Sample Multi-Vari chart

By plotting recovery times for different subgroups, clinicians can identify which factors contribute most to variability in recovery outcomes. This insight can help in optimizing surgical techniques and patient management protocols.

Bubble plot

Bubble plots extend scatter plots by adding a third dimension through the size of the data points, which represents an additional variable. This makes them particularly useful for multi-variable data analysis in clinical settings.

Example: A bubble plot can visualize the relationship between pre-operative risk scores, post-operative complication rates, and hospital costs in thymectomy (Fig. 20).

Fig. 20.

Sample bubble plot

Each bubble represents a patient or a group of patients, with the position on the x-axis and y-axis showing the relationship between two variables and the bubble size indicating a third variable.

Sankey diagrams

Sankey diagrams are flow diagrams that visually represent quantitative data as flows or connections between nodes. The width of the lines or arrows in the diagram is proportional to the quantity of the flow, making it easy to see relative differences in flow volumes at a glance. This type of visualization is particularly useful for displaying complex systems, such as patient pathways or the allocation of resources in healthcare settings.

Example: A Sankey diagram can illustrate the patient journey through various stages of cardiothoracic care, from initial diagnosis to various treatment options (e.g., medication, surgical intervention, rehabilitation), and subsequent outcomes (Fig. 21).

Fig. 21.

Sample Sankey diagram

Such a diagram could provide valuable insights into common treatment paths, bottlenecks in patient care, and potential areas for process improvement. These visualizations enhance the interpretation of clinical data by highlighting patterns, trends, and anomalies across various aspects of cardiothoracic surgery, including clinical findings, costs, and wellness. This comprehensive approach supports informed decision-making and improves patient outcomes.

Pie chart

Pie charts are reliable and simple tools that effectively represent frequencies in a graphical format. However, their use as standalone tools in research papers is limited due to the increased space required by an image compared to a frequency table. When dealing with a large number of interrelated frequencies, composite diagrams with multiple pie charts may be used to effectively represent the data as a group. However, it is more common to see pie charts used in conference presentations, either as part of oral or poster presentations, as they can be visually appealing.

Example: A composite pie chart figure can effectively illustrate the distribution of common complications across various lung tumor surgeries. In this case, six specific surgical procedures (e.g., Wedge Resection, Lobectomy, Pneumonectomy, etc.) and their related complications (e.g., postoperative infection, air leak, atelectasis, etc.) are represented, showcasing the frequency of each complication in a visually appealing and easy-to-interpret format (Fig. 22).

Fig. 22.

Sample pie chart

Interpreting descriptive statistics

Reading and understanding tables

Interpreting tables and figures in clinical research papers is a critical skill for clinicians. These visual tools condense complex data into accessible formats, allowing for quick insights into study results. To effectively interpret these elements, it is important to understand the layout and meaning of the data presented. Tables typically summarize descriptive statistics such as means, medians, ranges, standard deviations, and percentiles.

Example: A table in a study on post-operative recovery times for different cardiothoracic surgeries might include columns for the type of surgery, mean recovery time, standard deviation, and the range of recovery times.

Understanding these values helps clinicians compare outcomes across different surgical techniques. Table 5 summarizes the baseline characteristics of patients undergoing different types of cardiothoracic surgeries. It includes variables such as age, gender, body mass index (BMI), and the prevalence of hypertension and diabetes. This information is crucial for understanding the study population and ensuring that the groups are comparable.

Example: Higher age and BMI might indicate increased surgical risks, which should be considered in the analysis and interpretation of outcomes.

Table 5.

Sample demographic data

Variable	CABG (n = 50)	Valve replacement (n = 40)	Lung resection (n = 30)
Age (years)	67 ± 10	60 ± 12	55 ± 8
Male (%)	70%	65%	55%
BMI (kg/m2)	28 ± 5	26 ± 4	24 ± 3
Hypertension (%)	80%	75%	65%
Diabetes (%)	50%	40%	30%

Table 6 presents the recovery times for patients after different surgeries, including mean, median, range, and IQR. It helps to visualize the central tendency and dispersion of recovery times.

Example: The mean recovery time for CABG is 15 days with a standard deviation of 5 days, suggesting moderate variability.

Table 6.

Sample post-operative recovery times

Surgery type	Mean recovery time (days) ± SD	Median recovery time (days)	Range (days)	IQR (days)
CABG	15 ± 5	14	10–30	12–18
Valve replacement	12 ± 4	11	8–25	10–14
Lung resection	10 ± 3	10	7–20	8–12

The IQR provides additional insight into the middle 50% of the data, indicating typical recovery experiences.

Table 7 presents the incidence rates of common post-operative complications following Ivor Lewis esophagectomy, along with their standard deviations and 95% confidence intervals. The confidence intervals provide a range within which the true incidence rates are likely to fall, giving a measure of the estimate’s precision.

Example: The 95% confidence interval for anastomotic leaks is 6.4% to 9.6%, indicating that the true incidence rate is likely within this range.

Table 7.

Sample post-operative complication rates in Ivor Lewis surgery

Complication	Incidence rate (%) ± SD	95% Confidence interval (%)
Anastomotic leak	8 ± 2	6.4–9.6
Pneumonia	15 ± 3	13.2–16.8
Arrhythmia	12 ± 2	10.8–13.2
Pleural effusion	10 ± 3	8.1–11.9
Wound infection	5 ± 1	4.4–5.6

Clinicians can use this information to better understand the risks associated with Ivor Lewis surgery and to inform patients about potential complications.

Common pitfalls in interpreting tables and figures include misreading scales, overlooking outliers, and failing to consider the context of the data.

Example: A histogram with an uneven bin width might give a misleading impression of data distribution.

To avoid these pitfalls, clinicians should carefully examine the methodology sections of papers to understand how data were collected and processed. Practical tips for quick and accurate interpretation include cross-referencing tables and figures with the text of the paper, looking for consistency in reported values, and being mindful of the study’s objectives and hypotheses.

Example: If a paper reports a significant difference in recovery times between two surgical techniques, the supporting tables and figures should reflect this finding clearly.

Critical evaluation

Assessing the validity and reliability of statistical findings is essential for drawing accurate conclusions from research papers. Validity refers to the extent to which the study measures what it intends to measure, while reliability refers to the consistency of the measurements [31]. One way to assess validity is by examining the study design and methodology.

Example: In a paper reporting recovery times after maze procedure and mitral valve surgery in atrial functional mitral regurgitation, check if the sample size is adequate, if the patient selection criteria are clear, and if the follow-up period is appropriate.

Inadequate sample sizes or poorly defined selection criteria can undermine the validity of the study findings [32].

Reliability can be evaluated by looking at the consistency of the results [33].

Example: If a study reports mean recovery times with narrow confidence intervals and low standard deviations, it suggests that the findings are consistent and reliable.

Repetition of similar results in multiple studies further strengthens the reliability. Recognizing biases and limitations in presented data is another critical aspect of evaluation. Common biases include selection bias, where the study sample is not representative of the broader population, and measurement bias, where the data collection methods introduce systematic errors.

Example: If a study on post-operative complications relies solely on patient self-reports without clinical verification, it may be subject to recall bias.

Clinicians should also consider the limitations acknowledged by the authors, such as potential confounding factors, and whether the statistical methods used are appropriate for the data and research questions.

Example: If a study uses parametric tests on non-normally distributed data without appropriate transformations or justifications, the findings may be questionable.

Conclusion

Descriptive statistics play a fundamental role in clinical research by providing a clear and concise summary of data, which aids in identifying patterns, trends, and potential outliers. These statistics are crucial for interpreting study results, guiding clinical decision-making, and improving patient care. As healthcare continues to evolve, it is essential for clinicians to remain proficient in statistical methods to accurately analyze and apply research findings. Ongoing education and engagement with the latest statistical techniques will ensure that clinicians can effectively contribute to evidence-based practice.

Funding

None.

Declarations

Ethics approval and consent to participate

Not applicable.

Conflict of interest

None.