Intro to Public Health Unit 4 ReviewBiostatistics and Data Analysis for Public Health

Key Concepts and Definitions

• Population refers to the entire group of individuals, objects, or events that share a common characteristic of interest
• Sample is a subset of the population selected for study or analysis
• Parameter represents a characteristic or measure of the entire population, often estimated using sample statistics
• Statistic is a numerical value calculated from a sample used to estimate population parameters
• Variable is a characteristic or attribute that can take on different values across individuals or observations
  • Categorical variables have values that fall into distinct categories (gender, race, disease status)
  • Continuous variables can take on any value within a specified range (age, weight, blood pressure)
• Bias occurs when the sample does not accurately represent the population, leading to systematic errors in estimates or conclusions
• Confounding variables are extraneous factors that can distort the relationship between the variables of interest

Data Types in Public Health

• Nominal data consists of categories with no inherent order or ranking (blood types, zip codes)
• Ordinal data has categories with a natural order or ranking, but the differences between categories are not necessarily equal (socioeconomic status, pain severity)
• Interval data has ordered categories with equal intervals between them, but no true zero point (temperature in Celsius or Fahrenheit)
• Ratio data possesses all the properties of interval data, with the addition of a true zero point (height, weight, age)
• Discrete data can only take on specific, countable values (number of children in a family, number of hospital admissions)
• Continuous data can take on any value within a specified range (body mass index, cholesterol levels)
• Time-to-event data measures the time until a specific event occurs (survival time after a cancer diagnosis, time to relapse after treatment)

Descriptive Statistics

• Measures of central tendency summarize the center or typical value of a dataset
  • Mean is the arithmetic average of all values in a dataset, sensitive to extreme values or outliers
  • Median is the middle value when the data is arranged in order, robust to outliers
  • Mode is the most frequently occurring value in a dataset
• Measures of dispersion describe the spread or variability of a dataset
  • Range is the difference between the maximum and minimum values in a dataset
  • Variance measures the average squared deviation from the mean, expressed in squared units
  • Standard deviation is the square root of the variance, expressing dispersion in the same units as the original data
• Percentiles indicate the value below which a given percentage of the data falls (50th percentile is the median)
• Skewness measures the asymmetry of a distribution, with positive skew indicating a longer right tail and negative skew a longer left tail

Probability and Distributions

• Probability is a measure of the likelihood that an event will occur, expressed as a value between 0 and 1
• Random variables are variables whose values are determined by the outcome of a random event
• Probability distributions describe the likelihood of different outcomes for a random variable
  • Discrete probability distributions (binomial, Poisson) are used for discrete random variables
  • Continuous probability distributions (normal, exponential) are used for continuous random variables
• The normal distribution is a symmetric, bell-shaped curve characterized by its mean and standard deviation
  • Approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three
• The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, used for standardizing variables
• The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution

Hypothesis Testing

• Hypothesis testing is a statistical method for making decisions or inferences about a population based on sample data
• The null hypothesis ($H_0$) states that there is no significant difference or relationship between variables
• The alternative hypothesis ($H_a$ or $H_1$) states that there is a significant difference or relationship between variables
• Type I error (false positive) occurs when the null hypothesis is rejected when it is actually true, with the probability denoted by $\alpha$ (significance level)
• Type II error (false negative) occurs when the null hypothesis is not rejected when it is actually false, with the probability denoted by $\beta$
• Statistical power is the probability of correctly rejecting the null hypothesis when it is false, calculated as $1 - \beta$
• P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true
• Confidence intervals provide a range of plausible values for a population parameter based on sample data, with a specified level of confidence (95%, 99%)

Statistical Methods for Public Health

• t-tests compare means between two groups (independent samples) or for paired observations (dependent samples)
• Analysis of variance (ANOVA) compares means across three or more groups
• Chi-square tests assess the association between two categorical variables
• Correlation measures the strength and direction of the linear relationship between two continuous variables (Pearson correlation for normally distributed data, Spearman rank correlation for non-normal data)
• Linear regression models the relationship between a dependent variable and one or more independent variables
  • Simple linear regression involves one independent variable
  • Multiple linear regression involves two or more independent variables
• Logistic regression models the relationship between a binary dependent variable and one or more independent variables, estimating odds ratios
• Survival analysis examines the time until an event occurs, using methods such as Kaplan-Meier curves and Cox proportional hazards regression

Data Visualization Techniques

• Bar charts compare frequencies or proportions across categories, with bars representing the count or percentage for each category
• Histograms display the distribution of a continuous variable, with bars representing the frequency of observations within each bin or interval
• Pie charts show the proportion of each category relative to the whole, with slices representing the percentage of each category
• Line graphs display trends or changes over time, with data points connected by lines to emphasize patterns
• Scatterplots show the relationship between two continuous variables, with each point representing an individual observation
• Box plots summarize the distribution of a continuous variable, displaying the median, quartiles, and potential outliers
• Heat maps use color intensity to represent the magnitude of a variable across two dimensions (geographic maps, correlation matrices)
• Forest plots display the results of multiple studies or subgroup analyses, with point estimates and confidence intervals for each

Interpreting Results for Public Health Decision-Making

• Consider the practical significance of the results in addition to statistical significance, as small differences may be statistically significant but not meaningful in a public health context
• Assess the generalizability of the findings to the target population, considering the representativeness of the sample and any potential sources of bias
• Evaluate the strength of the evidence based on the study design, sample size, and control of confounding variables
• Interpret effect sizes (relative risk, odds ratios, mean differences) to understand the magnitude of the relationship or difference between variables
• Consider the precision of the estimates, as indicated by the width of confidence intervals, with narrower intervals suggesting more precise estimates
• Assess the consistency of the findings with previous research and established theories in the field
• Identify any limitations of the study that may impact the interpretation or application of the results (cross-sectional design, self-reported data, loss to follow-up)
• Translate the findings into actionable recommendations for public health practice, policy, or future research, considering the context and feasibility of implementation