Lecture Notes: Summarizing Data in Health Data (Vocabulary Flashcards)

Purpose of summarizing data in health science

• The chapter focuses on how to summarize data and how those summaries help address health questions (e.g., patient recovery times, patterns of a spreading virus, treatment outcomes).

• Goal: turn raw health data into clear, actionable insights and numerical visualizations that reveal centers of tendency and spread, describe relationships, and support decision-making in health care.

• Emphasizes integrating data summarization with health research questions: Is there an effective drug? What is the pattern of recovery? How do we detect biases or gaps in medical data?

• Connections to real-world health work: epidemiology, clinical trials, pandemic response, vaccine allocation, and monitoring of treatment outcomes.

Case study from last week: Chronic Fatigue Syndrome (CFS) trial (1997)

• Study aim: evaluate cognitive behavioral therapy (CBT) for CFS and compare with a control condition.

• Recruitment and eligibility:

  • About 142 patients recruited from a hospital/clinic.

  • Only about 60 were eligible/ready for the trial; others did not meet criteria, had health issues, or refused participation.

• Randomization and groups:

  • Participants randomly assigned to CBT vs. relaxation (control) conditions.

  • Approximately 30 participants were placed in the relaxation (control) arm; the remainder were allocated to CBT.

• Follow-up and outcomes (6 months):

  • Follow-up data show about 19–27 participants in the CBT/treatment arm remained engaged.

  • Outcome rates: about 70% in the treatment group achieved the desired outcome vs about 19% in the control group.

• Takeaway question: Why is random assignment valuable?

  • Random assignment helps uncover information and insights by reducing bias, and it improves fairness across groups.

  • It supports more convincing, interpretable conclusions about treatment effectiveness.

Why summarize data in health science?

• Raw health data (clinical trials, health records, global health databases) are chaotic; summarization makes patterns, trends, and meaningful summaries clearer.

• Enables actionable accountability and decision-making (e.g., vaccine supply planning, resource allocation).

• Provides a basis for visualizations that communicate findings to clinicians, policymakers, and the public.

Numerical data in health science: variables and data types

• Numerical data fall into two main forms:

  • Continuous data (e.g., blood pressure, recovery time, life expectancy)

  • Discrete data (e.g., number of hospital visits, event counts)

• In health data, numerical variables help reveal trends (e.g., rising obesity rates, recovery times).

• Analogies to daily life: variables like steps counted by a wearable.

• Historical context: even early health data (e.g., 1918–1910 influenza data) used numerical summaries of death rates to identify vulnerable groups.

• Types of plots emphasize relationships between numerical variables (e.g., scatter plots, dot plots, histograms).

Visualizing numerical data: scatter plots and more

• Scatter plots display the relationship between two numerical variables and help assess association, linearity, and potential trends.

• Example discussions discussed in class:

  • Life expectancy vs total fertility rate (from Gapminder data): initial association appears negative (as fertility rises, life expectancy tends to be lower historically), with changes over time as health systems improve.

  • Across countries and regions (Africa, Europe, the Americas, Asia): scatter plots can illustrate regional patterns and inform policy (e.g., family planning as a policy lever to improve health outcomes).

  • Practical health examples: HIV viral load over time, COVID-19 cases and vaccination status.

• The scatter plot discussion emphasizes: are variables associated or independent? is the relationship linear or non-linear? How does the association evolve over time?

• The class planned a practical SPSS session to generate plots and analyze data from health datasets.

Other numerical visualizations

• Dot plots:

  • Show distribution of a single numerical variable (e.g., GPA distribution from 2.5 to 4.0).

  • The mean is often indicated with a marker (e.g., a red triangle) to show the center.

  • Interpretation considerations: skewness can mislead if only the mean is viewed without the distribution shape.

• Stack dot plots:

  • A stacked arrangement helps reveal density and clustering without overlap, giving a clearer sense of the distribution around the center.

• Histogram:

  • Bars show the density of values across bins (e.g., hours spent on activities, weekly performance).

  • Choice of bin width affects how spikes and tails are represented; too wide or too narrow bins can obscure important patterns.

  • Discussed how histogram shape and bin choices can mask or reveal spikes, e.g., in epidemiology (age-specific case counts) or activity measurements.

• Shape and modality of distributions:

  • Unimodal: one peak

  • Bimodal: two peaks

  • Multimodal: many peaks

  • Uniform: flat distribution

  • Symmetric: bell-shaped, mean ≈ median

• Skewness and outliers:

  • Right-skewed: long right tail; mean tends to be greater than the median

  • Left-skewed: long left tail; mean tends to be less than the median

  • Symmetric distributions have mean ≈ median

  • Outliers: isolated bars or gaps; can be data-entry errors or rare events; outliers impact the mean and standard deviation more than the median and IQR; need to scrutinize for data quality and potential insights.

• Practical examples discussed:

  • Ebola outbreak: a spike in Liberia illustrating how outliers can indicate areas with unique transmission dynamics.

  • COVID-19 and vaccination, and historical HIV data: distributions can reveal spikes and tails relevant to public health decisions.

• Transformations to handle skewness:

  • Log transformation (Y = log(X)) can normalize highly skewed data (e.g., viral loads, attendance counts, skewed health metrics).

  • Pros: reduces skewness, improves modeling and interpretation for statistical analyses.

  • Cons: interpretation after transformation can be harder; back-transformation and reporting original scale may be nontrivial.

  • Example discussion: log-transforming basketball game attendance to illustrate normalization; viral loads often exhibit right-skewness that becomes more symmetric after log-transform.

• Density and spatial patterns:

  • Intensity maps/heat maps illustrate how density or change varies across geography (e.g., opioid crisis density by county).

  • Colors convey density or rate of change, guiding resource allocation and policy decisions.

Describing distributions with summary statistics

• Mean (average):

  • Symbol:

  • Population mean: $\\bar{x}\$ is the sample mean;$\mu$is the population mean.</p></li><li><p>Sample mean formula:$\bar{x} = \frac{1}{n} \sum{i=1}^{n} xi$</p></li><li><p>Population mean:$\mu = \frac{1}{N} \sum{i=1}^{N} xi$</p></li><li><p>In health trials, means are common but can be distorted by outliers; sometimes medians or transformed scales are preferred.</p></li></ul></li><li><p>Variance and standard deviation:</p><ul><li><p>Population variance: if we have the population, the definition mirrors the sample version; for a sample:</p></li><li><p>$s^2 = \frac{1}{n-1} \sum{i=1}^{n} (xi - \bar{x})^2$</p></li><li><p>Standard deviation:$s = \sqrt{s^2}$</p></li><li><p>Variance measures the average squared deviation from the mean; standard deviation preserves the same units as the data, aiding interpretation.</p></li><li><p>In health contexts, variance quantifies variability in responses (e.g., blood sugar responses, hormone levels) and helps assess consistency of treatment effects.</p></li></ul></li><li><p>Median and robustness to outliers:</p><ul><li><p>Median: middle value after ordering the data; for odd n, the middle value; for even n, the average of the two middle values.</p></li><li><p>Median is robust to outliers and extreme values (unlike the mean), making it a preferred center measure for skewed data.</p></li></ul></li><li><p>Quartiles and IQR:</p><ul><li><p>Q1 = 25th percentile; Q3 = 75th percentile; IQR = Q3 − Q1.</p></li><li><p>IQR describes the middle 50$p \le 0.05$$ to declare statistical significance.

• Example: gender bias in promotions (classroom study):

  • Sample: 48 supervisors; 24 male, 24 female; promotions observed.

  • Outcome example: 35 promotions overall; breakdown by gender showed higher promotion rate among males (e.g., 21/24 = 87.5%) vs females (e.g., 14/24 = 58.3%), a difference of about 29.2%.

  • Interpretation requires a statistical test to assess whether the observed gap could occur by chance under H0 (no bias).

• Randomization and bias reduction:

  • Random assignments (e.g., in clinical trials or experiments) help ensure comparability between groups and minimize biases from confounding factors.

  • In health experiments, randomization supports fair comparisons of treatments and reduces systematic differences between groups.

• Simulation and hypothesis testing in practice:

  • Card-shuffling and random allocation simulations illustrate how outcomes could arise under the null hypothesis.

  • The data inform whether to reject H0 or fail to reject, guiding conclusions about treatment effects or biases.

• Practical advice regarding hypothesis testing:

  • Always consider whether the observed effect size is practically meaningful, not just statistically significant.

  • Ensure study design minimizes confounding and bias; use randomization where possible.

  • Be mindful of data quality and whether assumptions (e.g., normality, independence) hold for the chosen test.

Practical takeaways and connections to real-world health research

• Data summarization is essential for transforming chaotic health data into actionable insights that can guide clinical and public health decisions.

• Visualizations (scatter plots, dot plots, histograms, box plots, mosaic plots, bar charts, pie charts) communicate complex data patterns to diverse audiences.

• Descriptive statistics (mean, median, IQR, variance, standard deviation) describe central tendency and variability, with careful choice depending on distribution shape and presence of outliers.

• Transformations (e.g., log) can normalize skewed data and improve modeling, but require careful interpretation and potential back-transformation for reporting.

• Categorical data and contingency tables enable exploration of associations between variables (e.g., treatment type and outcome; Titanic-era survivorship by age category) and underpin hypothesis testing.

• Hypothesis testing and randomization are core to evaluating treatment effects and identifying biases; the burden of proof lies with the alternative hypothesis, and p-values guide decisions to reject or not reject the null.

• Real-world relevance: these methods support epidemiological surveillance (e.g., post-COVID trends), clinical trials, vaccine and treatment assessments, and resource allocation in health systems.

Quick practice prompts (conceptual prompts you can try)

• Sketch or imagine the expected distribution for the following variables and state whether you anticipate unimodal, bimodal, skewness, or symmetry:

  • Number of glasses of coffee consumed daily

  • Hours spent on social media per day by students during exam week

  • ICU length of stay for a viral pneumonia cohort

• Given a small dataset with an obvious outlier, discuss how the mean, standard deviation, median, and IQR would likely differ with and without the outlier.

• Design a simple contingency table for a hypothetical vaccine trial, showing recovery status (recovered/not recovered) by vaccine type (A/B/Placebo). Explain how you would use a chi-square test to assess association.

• Describe a scenario in which a log transformation would help you analyze a health variable, and explain potential interpretation challenges after transformation.

• Outline the null and alternative hypotheses for a hypothetical study on whether a new drug improves recovery time, and describe what a p-value would tell you in this context.

Note on tools and upcoming work

• In the next sessions, we will practice with SPSS (or equivalent software) to generate scatter plots, histograms, box plots, contingency tables, mosaic plots, and bar plots from real health datasets.

• Projects will involve analyzing data from health records and clinical trials, with emphasis on summarization, visualization, and hypothesis testing.

Final recap

• Summarizing health data turns raw information into meaningful, decision-relevant insights.

• A toolkit of visualizations and statistics helps describe patterns, assess relationships, and determine whether observed effects are likely due to chance or to real factors.

• Always consider distribution shape, outliers, and robustness of summary statistics when interpreting health data.

• Use randomization and formal hypothesis testing to guard against bias and to support evidence-based conclusions in health research.