Statistical Methods Key Points
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Questions and Answers

What does an odds ratio of 1 indicate about two groups being compared?

  • One group has a higher probability than the other.
  • One group is statistically insignificant compared to the other.
  • The groups have equal proportions. (correct)
  • The odds of an event happening are identical in both groups. (correct)

Which of the following best describes the significance of log odds in statistical analysis?

  • Log odds can range from 0 to 1.
  • Log odds are irrelevant to probability calculations.
  • Log odds are used to simplify calculations involving odds ratios. (correct)
  • Log odds are a direct reflection of probability without modification.

In the Vit C study, what odds was calculated for the placebo group?

  • 2.88
  • 1.53
  • 335/76 = 4.41 (correct)
  • 0.43

What condition is indicated by a log odds ratio estimate of 0?

<p>Odds of the event are equal in both groups. (B)</p> Signup and view all the answers

What does the standard error (se) formula approximate in the context of log odds analysis?

<p>The variance associated with the log odds ratio estimate. (D)</p> Signup and view all the answers

What is the primary characteristic of a Prospective Binomial sample?

<p>The number in each group is fixed at the start. (D)</p> Signup and view all the answers

Which sampling model is primarily used for case-control studies?

<p>Retrospective Binomial sample. (D)</p> Signup and view all the answers

What does the term 'odds' refer to in the context of Odds Ratios?

<p>The ratio of events to non-events. (A)</p> Signup and view all the answers

In which sampling model is the total number of subjects fixed?

<p>Multinomial sample. (A)</p> Signup and view all the answers

When using Odds Ratios to compare two proportions, what issue is avoided?

<p>Comparing proportions across different populations. (B)</p> Signup and view all the answers

What does the formula Odds = π/(1 − π) calculate?

<p>The likelihood of an event occurring versus not occurring. (B)</p> Signup and view all the answers

Which of the following statements about Retrospective Binomial sampling is accurate?

<p>It estimates P[group | event] but not P[event | group]. (D)</p> Signup and view all the answers

What is a potential disadvantage of using simple differences in proportions across populations?

<p>It may not reflect the actual effect size in diverse samples. (C)</p> Signup and view all the answers

What is the consequence of violating the assumption of independence in statistical analysis?

<p>Incorrect p-values and confidence intervals (B)</p> Signup and view all the answers

When is it suggested to use t-tests in the presence of data assumptions?

<p>If assumptions are not reasonably violated (B)</p> Signup and view all the answers

Which type of data would require the use of non-parametric tests?

<p>Data with skewed distributions or outliers (B)</p> Signup and view all the answers

What is the role of transforming responses in statistical methods?

<p>To enhance the validity of test assumptions (A)</p> Signup and view all the answers

What is indicated by the term 'Bernoulli data' in relation to statistical models?

<p>Data representing binary outcomes (Yes/No) (D)</p> Signup and view all the answers

Under what circumstances should a researcher consider using a randomization test?

<p>When the assumptions of t-tests are poorly violated (A)</p> Signup and view all the answers

In the context of equality of two proportions, which situation is described by the Vit C study example?

<p>Comparing treatment effects on binary outcomes (C)</p> Signup and view all the answers

What important aspect must be considered regarding sample sizes when checking for equality of variance?

<p>Unequal sample sizes may lead to wrong standard errors (B)</p> Signup and view all the answers

Flashcards

Odds

The ratio of the probability of an event occurring to the probability of it not occurring.

Log Odds

The natural logarithm of the odds, used for statistical analysis, usually for easier calculations.

Odds Ratio

A statistical measure used to compare the odds of an event in two different groups.

Log Odds Ratio Estimation

An estimate obtained by taking the difference of the log odds for the event in one group versus the log odds for the event in another group.

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Confidence Interval

A range of values that likely contains the true population parameter of interest in the context of the log odds ratio or odds ratio.

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Sampling Models

Different ways to gather data, like prospective binomial, retrospective binomial, and multinomial samples, determining what is fixed in the design.

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Prospective Binomial Sample

A sampling method where you start with groups and observe the occurrence of an event in each group, potentially estimating the probability of the event in each group.

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Retrospective Binomial Sample

Samples 'events' and 'non-events' and observes groups, potentially estimating the probability of a group given an event, but not the reverse.

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Multinomial Sample

Observes multiple groups (defined by rows and columns). Used for multiple categories/outcomes, investigating independence of classifications.

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Odds Ratio

A measure of association between two proportions, useful across different base rates (probability of the event occurring in a relevant population).

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Odds

Probability of an event divided by the probability of the event not occurring.

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Chi-square test

Statistical test used for large sample sizes when comparing multiple binomial samples (including prospective, retrospective, and multinomial samples).

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Difference in proportions

A measure of the difference between two probabilities. It can be problematic when comparing across widely varying base rates.

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Assumption Violations

Violating assumptions in statistical analysis can lead to incorrect p-values and confidence intervals.

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Independence Assumption

In statistical analysis, each observation is independent of all others, meaning that no observation affects any other.

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Equal Variance Assumption

In statistical analysis, the variances in different groups are assumed to be equal. Sample sizes matter in this assumption.

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Normality Assumption

Data in a given analysis need to be normally distributed. Outliers are a major concern here.

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Choosing a Statistical Method

Selecting the most suitable statistical method depends on the research question, design, and data properties.

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Statistical Analysis Steps

The analysis process starts by determining the question, then the design (experimental vs. observational), followed by examining the data, and then deciding on the method.

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Bernoulli Data

Data consisting of binary outcomes (Yes/No).

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Discrete Response Data

Categorical data that consists of counts, like 0, 1, 2, etc., or Yes/No outcomes.

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Study Notes

Statistical Methods Key Points

  • Assumptions are crucial: Understanding assumptions of statistical tests and the consequences of violating them (e.g., independence, equal variance, normality) is vital. Incorrect assumptions lead to inaccurate p-values and confidence intervals.
  • Method Selection: No single best method exists; the optimal approach depends on the research question, study design, and data characteristics.
  • Question-Driven Approach: Start with the research question, then determine appropriate study design, collect data, and choose an appropriate analysis.
  • Independence: Data points should be independent of each other—crucial to avoid bias and inaccurate results.
  • Data Types: Distinguish between experimental and observational studies (causal conclusions depend on the design).
  • Paired or Independent Data: Paired data relate observations within groups; unpaired data involves independent observations.
  • Assumptions Evaluation: Assess whether data meet assumptions (reasonable or not seriously violated) before choosing a test.

Hypothesis Testing and Model Comparison

  • Model Comparison (T-tests): Model I assumes a shared mean, while Model II assumes different means. Use the model with the better fit to test the hypotheses.
  • Chi-Square Test: Employed when comparing proportions across groups (e.g., treatment and control).
  • Expected/Observed counts: compare the expected counts to observed values.

Bernoulli and Binomial Distributions

  • Bernoulli Data: Discrete data where a single event has two possible outcomes (i.e., success or failure).
  • Binomial Data: Represents the number of successes out of a given number of trials (using the Bernoulli distribution).

Sampling Models

  • Prospective Binomial: Observations are collected before the outcome is known.
  • Retrospective Binomial: Data are collected after the outcome is known. Often used in case-control studies when outcomes are uncommon.
  • Multinomial: Data involve observations categorized into multiple groups.

Odds Ratios

  • Odds Ratio Calculation: Used to compare the odds of an event between different groups (e.g., Vit C and Placebo).
  • Log Odds Ratio: Useful for analyzing differences in odds of proportions across several populations with diverse rates.

Inference for Log Odds Ratios

  • Log Odds Ratio Estimate: The log odds ratio is calculated to quantify the relationship between outcomes in the two groups. This is then used to estimate a confidence interval for the ratio.

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Description

This quiz covers essential key points regarding statistical methods and their assumptions. Understanding how to select the appropriate method based on the research question and data characteristics is crucial for accurate analysis. Key concepts like independence, data types, and the impact of assumptions are discussed.

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