Biostatistics Lectures 1-4 Summary

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Questions and Answers

What is the range of values a proportion can take?

  • From -1 to 1
  • From 0 to 1 (correct)
  • From -100% to 100%
  • From 1 to 10

What does the parameter 'p' represent in the binomial distribution?

  • Number of successes out of n trials
  • Probability of success in each trial (correct)
  • Total number of trials
  • Average number of successes

Which of the following statements about the binomial distribution is true?

  • It can be analyzed using the normal distribution.
  • It is a discrete probability distribution. (correct)
  • It is a continuous distribution.
  • It assumes trials are dependent.

If the prevalence of type 2 diabetes (T2DM) is 11.3%, how many individuals would you expect to find with T2DM in a sample of 50 Americans?

<p>11 individuals (A)</p> Signup and view all the answers

In the context of a binomial distribution, what can be said about the frequency representation of diseases?

<p>They are represented as proportions. (C)</p> Signup and view all the answers

What does a p-value of less than 0.05 in the Shapiro-Wilk test indicate?

<p>There is a deviation from normality. (C)</p> Signup and view all the answers

What is the significance of the central limit theorem?

<p>It establishes that the means of repeated random samples will follow a normal distribution. (C)</p> Signup and view all the answers

What is represented by the standard error (SE)?

<p>The standard deviation of the sampling distribution of the sample mean. (A)</p> Signup and view all the answers

In a Q-Q plot, what does it indicate if the points lie along the line y = x?

<p>The data is normally distributed. (D)</p> Signup and view all the answers

Which of the following best describes the distribution of a variable in the sample?

<p>It provides the estimated mean and standard deviation. (B)</p> Signup and view all the answers

What is the main purpose of biostatistics?

<p>To generate medical knowledge through data analysis (B)</p> Signup and view all the answers

Which of the following describes a characteristic of a sample in biostatistics?

<p>It is used to infer about the population (B)</p> Signup and view all the answers

What type of research must be randomized to ensure unbiased results?

<p>Clinical Research (C)</p> Signup and view all the answers

What is the consequence of using a small and biased sample in research?

<p>Higher chance of random error (B)</p> Signup and view all the answers

What distinguishes continuous numeric variables from discrete ones?

<p>Continuous variables can be converted to other units of measurement (B)</p> Signup and view all the answers

Which type of variable has inherent ordering?

<p>Ordinal Variable (C)</p> Signup and view all the answers

What is a key difference between sample quantities and population quantities in biostatistics?

<p>Sample quantities are known and being measured, while population quantities are unknown and being estimated (D)</p> Signup and view all the answers

What is a dichotomous variable?

<p>A variable that takes only two possible values (D)</p> Signup and view all the answers

What is the purpose of the sample mean and sample variance in relation to a population?

<p>To estimate the population mean and population variance (C)</p> Signup and view all the answers

Which measures are more appropriate for analyzing skewed or non-normal data?

<p>Median and quantiles (B)</p> Signup and view all the answers

In a probability distribution, what characterizes a random variable?

<p>Its values depend on outcomes of a random phenomenon (B)</p> Signup and view all the answers

What is the shape of a standard normal distribution?

<p>Symmetrical and unimodal (D)</p> Signup and view all the answers

To standardize a normally-distributed variable, which formula is used?

<p>$Z = \frac{X - \mu}{\sigma}$ (D)</p> Signup and view all the answers

What percentage of the probability lies within ±1 standard deviation from the mean in a normal distribution?

<p>68% (D)</p> Signup and view all the answers

Which of the following pairs are the parameters that define a normal distribution?

<p>Mean and standard deviation (C)</p> Signup and view all the answers

What does a cumulative probability in a probability distribution represent?

<p>The probability of a value being less than or equal to a given value (A)</p> Signup and view all the answers

What does the null hypothesis (H0) signify in the context of comparing two population means?

<p>Any difference in sample means is due to random error. (D)</p> Signup and view all the answers

What is a key characteristic of the Wilcoxon-Mann-Whitney test?

<p>It assesses whether two samples come from the same distribution. (A)</p> Signup and view all the answers

What does a p-value less than 0.05 typically indicate in hypothesis testing?

<p>There is a statistically significant difference between population means. (B)</p> Signup and view all the answers

What would be the appropriate interpretation if the confidence interval (CI) includes the null value of zero?

<p>There may be no statistically significant difference in population means. (D)</p> Signup and view all the answers

In the formula for the difference between two population means, $d = μ1 - μ2$, what does $d = 0$ signify?

<p>There is no difference between the population means. (D)</p> Signup and view all the answers

What does the standard error (SE) of the sample mean represent?

<p>The population standard deviation divided by the square root of sample size (A), The variability of the sample mean from the population mean (C)</p> Signup and view all the answers

In the formula for a 95% confidence interval, what does Z represent?

<p>The z-value corresponding to the confidence level (C)</p> Signup and view all the answers

What additional distribution is used for calculating confidence intervals for smaller sample sizes?

<p>t-distribution (B)</p> Signup and view all the answers

Which assumption is NOT required for performing a one-sample t-test?

<p>The samples must have equal sizes (A)</p> Signup and view all the answers

What is the primary purpose of calculating a confidence interval?

<p>To estimate the range in which a population parameter lies (C)</p> Signup and view all the answers

If the assumptions for a t-test are violated, which method might you need to use?

<p>Bootstrap methods (A)</p> Signup and view all the answers

What does a 95% confidence level imply about the confidence interval?

<p>It suggests the interval will contain the population mean in 95 out of 100 cases when sampled multiple times (A)</p> Signup and view all the answers

What is indicated by a confidence interval that is wide?

<p>Greater variability in the sample data (C)</p> Signup and view all the answers

Flashcards

Biostatistics

The application of statistical methods to biomedical research to collect, classify, analyze, and interpret data.

Empirical Science

Knowledge based on observation and experience, using natural or experimental observations, and inductive reasoning to reach generalizations.

Clinical Research

Research aiming to understand and improve human health, often involving human subjects.

Randomized Clinical Trials

Clinical research methods that impartially assign subjects to different treatment groups to minimize bias and increase reliability.

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Sample

A subset of a population selected for study, used to infer about the characteristics of the larger population.

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Population

The entire group of individuals or objects that are of interest.

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Categorical Variables

Variables that represent categories or groups, like blood type or gender.

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Numeric Variables

Variables measured numerically, further divided into continuous and discrete types, involving quantities.

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Proportion

A fraction representing the number of individuals with a specific characteristic divided by the total number of individuals.

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Binomial Distribution

A probability distribution showing the chances of getting a specific number of successes in a set number of independent trials.

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Prevalence

The proportion of a population that has a particular disease or condition at a specific time.

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Probability Distribution

A function showing the probability of different outcomes of a random variable.

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Binomial Distribution Parameters

The Binomial Distribution is determined by 'n' (number of trials) and 'p' (probability of success).

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Population mean (µ)

The average value of a variable in the entire population.

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Population variance (σ²)

A measure of the spread or variability of a variable in the entire population.

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Sample mean (X)

The average value of a variable in a sample taken from a population.

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Sample variance (S²)

A measure of the spread or variability of a variable in a sample taken from a population.

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Normal distribution

A probability distribution that is symmetric and bell-shaped; characterized by its mean (µ) and standard deviation (σ).

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Z-score

A value representing how many standard deviations a data point is from the mean of a normal distribution.

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Probability distribution

A function that describes the possible outcomes of a random variable and their associated probabilities.

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Random variable

A variable whose value is a numerical outcome of a random phenomenon or experiment.

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Normal Distribution

A common probability distribution where data tends to cluster around a central value, often bell-shaped.

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Shapiro-Wilk Test

A statistical test used to determine if a dataset follows a normal distribution.

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Q-Q Plot

A plot used to visually assess if a dataset follows a normal distribution.

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Central Limit Theorem

The means of repeated samples from any distribution will be approximately normally distributed, even if the original data isn't.

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Standard Error (SE)

The standard deviation of the distribution of sample means. A measure of how much sample means differ from the population mean.

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Mann-Whitney test

A non-parametric test used to compare two samples, assessing if they come from the same distribution.

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Null hypothesis (H0)

The hypothesis that there is no difference between two population means.

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Alternative hypothesis (H1)

The hypothesis that there is a difference between two population means.

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P-value

Probability of observing results as extreme or more extreme if the null hypothesis is true.

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Proportion

Ratio of the number of items with a specific characteristic to the total number of items

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95% Confidence Interval

A range estimated to contain the true population mean with a 95% probability.

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Confidence Interval Equation (Large Samples)

CI = X ± Z * SE, where X is the sample mean, Z is the Z-value for the desired confidence level (e.g., 1.96 for 95%), and SE is the standard error.

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Standard Error (SE)

A measure of the variability of sample means around the population mean, calculated as standard deviation divided by the square root of the sample size.

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t-distribution

Used to calculate confidence intervals for smaller sample sizes when the population standard deviation is unknown.

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Degrees of Freedom (t-test)

A parameter in the t-distribution calculation, equal to sample size minus 1 (n-1).

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Assumptions of t-test

Normality of data, independence of data points, and equal variances assumptions to perform t-test effectively.

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Sample Mean (X)

Average of values obtained from a given set of samples.

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Sample Variability

The spread of values in a dataset, indicative of how much individuals in dataset differ from one another

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Study Notes

Biostatistics Lectures 1-4 Summary

  • Biostatistics involves collecting, classifying, analyzing, and interpreting data from biomedical research to generate medical knowledge.
  • Science is empirical, based on observations and experiences, using inductive reasoning to generalize from observations.
  • Basic and clinical research are interconnected. Clinical research must be randomized to ensure unbiased results.
  • In biostatistics, samples are subsets of a population, but the sample itself is not the primary focus.
  • Samples are studied to draw inferences about a population of interest.
  • Larger samples increase the likelihood of accurate results. Small or biased samples may lead to random errors. Random error is the difference between sample and population means due to sampling.
  • Sample quantities are known and measured, while population quantities are unknown and estimated.
  • Clinical research involves a study design, data collection, data analysis, and data processing. Software like R facilitates reproducible research.
  • Reproducible research involves using code throughout the entire research process and presents a direct link between analysis and final results.
  • Rectangular data, typically in tabular format, includes a patient ID, age, sex, vaccination status, and COVID-19 status, among other variables.
  • Units of observation are patients or other similar entities described by the data.
  • Observations (records) are rows in the table, and variables (or fields) are columns in the table, representing characteristics of the observation unit or entity.
  • Variables are classified as categorical or numeric. Numeric variables include continuous and discrete types. Categorical variables include nominal, ordinal, and dichotomous.
  • Frequency tables present the number and percentage of participants in each category, useful for categorical and grouped numeric variables.
  • Frequency tables may also be cumulative.
  • Contingency tables (cross-tabulations) examine the relationship between two categorical variables, examining marginal totals and category-specific proportions.
  • Plotting categorical variables involves pie charts and bar plots, illustrating relative frequencies (up to 100%) with appropriate colors/ordering choices.
  • Histograms and box-and-whisker plots illustrate numerical (continuous or discrete) variables; for histograms, bins have the same width with no space between; for box-and-whisker plots, features include median, hinges, whiskers, and outliers.
  • Measures of location include mean (average), median, quantiles, and mode.
  • Measures of spread include variance, standard deviation, range, and interquartile range (IQR).
  • Distributions describe the pattern of values in sample or population data and can be generalized to probability distributions for an individual.
  • A normal distribution (Ν(μ,σ)) is described by its mean (μ) and standard deviation (σ), is bell-shaped, and is symmetric with mean =median =mode = 0.
  • The characteristics of this distribution for a given range of values, and from −∞ to ∞: P(x) = 1. (with specific ranges representing specific probabilities).
  • Determining (testing) if data follows a normal distribution involves contextual knowledge and statistical tests (e.g., Shapiro-Wilk test) or Q-Q plots.
  • The central limit theorem shows that the means of repeated random samples from any distribution follow a normal distribution, even when the underlying variables aren't normally distributed.
  • There are three distributions to consider (population, sample, sample mean of the variable) and their associated statistics (mean, standard deviation, standard error).
  • Confidence intervals and the difference between two proportions give a range of values within which the mean and proportion are likely to lie.
  • Confidence intervals are estimated and calculated using critical values.
  • Statistical tests like the t-tests and non-parametric tests (Mann-Whitney) are useful for comparing sub-sample means, using probability values (p-values) for decision-making; the null hypothesis is that the means are the same, and the alternative hypothesis proposes otherwise. p-values represent probabilities of observing particular results (or more extreme values), thereby affecting decision-making on rejecting or not rejecting the null hypothesis.
  • Proportions are calculated by comparing A/(A+B). The analysis of proportions does not use the normal/t-distributions but other special methods (exact method; Clopper-Pearson).
  • The binomial distribution provides probabilities for discrete outcomes in binary trials.

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