OpenIntro Statistics Fourth Edition Quiz

Questions and Answers

What do researchers aim to determine about the use of stents in stroke patients?

Does the use of stents reduce the risk of stroke?

How many patients were in the treatment group of the stent study?

451

227

224 (correct)

What was the outcome for patients in the treatment group who had strokes within 30 days?

33 patients (correct)

45 patients

0 patients

191 patients

The study indicated that stents reduced the risk of stroke in patients.

False Signup and view all the answers

What were the two time points measured for patient outcomes in the study?

30 days and 365 days after enrollment. Signup and view all the answers

What was the proportion of patients who had a stroke in the treatment group at the end of the first year?

20% Signup and view all the answers

What was the proportion of patients who had a stroke in the control group at the end of the first year?

12% Signup and view all the answers

The results of the study can be generalized to all patients and all types of stents.

False Signup and view all the answers

What does the variable 'loan amount' represent?

Amount of the loan received, in US dollars Signup and view all the answers

The interest rate variable is categorical.

False Signup and view all the answers

Population change is classified as a discrete numerical variable.

False Signup and view all the answers

What information does the 'homeownership' variable provide?

Indicates whether the person owns, owns but has a mortgage, or rents. Signup and view all the answers

What is the length of the loan typically measured in?

Months Signup and view all the answers

A variable that can take a wide range of numerical values is called a ______ variable.

continuous Signup and view all the answers

What are the levels of the 'state' variable?

Up to 51 values representing US states and Washington, DC. Signup and view all the answers

The variable 'median edu' represents education levels such as below hs, hs diploma, ______, and bachelors.

some college Signup and view all the answers

What is an observational study?

A data collection method that does not interfere with how the data arise. Signup and view all the answers

What is the response variable if median household income is the explanatory variable?

Population Signup and view all the answers

What is the main issue with selecting graduates based on personal interests?

It introduces bias into the sample. Signup and view all the answers

A simple random sample is equivalent to a raffle.

True Signup and view all the answers

What is non-response bias?

It occurs when a high percentage of those selected do not respond, making results unrepresentative. Signup and view all the answers

A convenience sample is where individuals who are easily ______ are more likely to be included.

accessible Signup and view all the answers

What kind of conclusions are generally difficult to draw from observational data?

Causal conclusions Signup and view all the answers

Sunscreen usage can be considered a confounding variable in studies about skin cancer risk.

False Signup and view all the answers

What is the purpose of prospective studies?

To identify individuals and collect information as events unfold. Signup and view all the answers

What are the two forms of observational studies?

Prospective and retrospective studies. Signup and view all the answers

Which sampling method utilizes random selection for subgroups?

Stratified sampling Signup and view all the answers

What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture?

10 / 43 = 0.23 or 23% Signup and view all the answers

What percent of patients in the control group were pain free 24 hours after receiving placebo acupuncture?

2 / 46 = 0.04 or 4% Signup and view all the answers

In which group did a higher percentage of patients become pain free 24 hours after receiving treatment?

Treatment Group Signup and view all the answers

What was the average age of patients in group A?

35.93 years Signup and view all the answers

What type of treatment did group B receive?

Placebo acupuncture Signup and view all the answers

The two groups in the sinusitis study consisted of group A, receiving _______ and group B, receiving a placebo.

antibiotics Signup and view all the answers

How many participants were enrolled in the migraine study?

94 females Signup and view all the answers

What was the maximum pressure exerted by the algometer in the migraine study?

250 g Signup and view all the answers

Acupuncture was determined to be ineffective in treating migraines according to the study.

False Signup and view all the answers

What is the data matrix used for in data analysis?

It organizes and describes data for analysis. Signup and view all the answers

What is the grade of the first loan in the loan50 data set?

not specified in provided content Signup and view all the answers

What is the home ownership status of the borrower for the first loan in the loan50 data set?

not specified in provided content Signup and view all the answers

What are observational studies?

Studies that provide evidence of naturally occurring associations between variables but do not show causation. Signup and view all the answers

Observational studies can conclude a causal connection between variables.

False Signup and view all the answers

What is the main goal of a randomized experiment?

To investigate the possibility of a causal connection between explanatory and response variables. Signup and view all the answers

What are the two types of variables typically involved in an experiment?

Explanatory variable and response variable. Signup and view all the answers

What does the Buteyko method aim to reduce?

Asthma symptoms. Signup and view all the answers

How many asthma patients were involved in the study of the Buteyko method?

600 Signup and view all the answers

In the experiment about cheaters, children were asked to toss a _____ in private.

coin Signup and view all the answers

How many variables were reported in the study of 160 children regarding honesty and age?

Three Signup and view all the answers

What social class comparison did the study involving 129 undergraduates examine?

Low or high social class. Signup and view all the answers

What was the response variable in the migraine and acupuncture study?

Pain-free status after treatment. Signup and view all the answers

What type of evidence may only represent extraordinary cases?

Anecdotal evidence. Signup and view all the answers

Match the following terms with their definitions:

Explanatory Variable = A variable that is manipulated in an experiment Response Variable = A variable that is observed in response to changes in explanatory variable Anecdotal Evidence = Data based on individual cases that may not represent a larger population Randomized Assignment = Method to reduce bias by randomly assigning subjects to groups Signup and view all the answers

What is the target population in the question about average mercury content in swordfish?

All swordfish in the Atlantic Ocean. Signup and view all the answers

How can biases be reduced in research sampling?

By randomly selecting samples from populations. Signup and view all the answers

A sample represents the entire population.

False Signup and view all the answers

Study Notes

OpenIntro Statistics Overview

OpenIntro Statistics is designed for undergraduate statistics courses but also serves high schools and graduate-level education.
The textbook emphasizes applied statistics, ensuring accessibility and clarity.
Available as a free PDF at openintro.org/os and distributed under a Creative Commons license.

Table of Contents Highlights

Introduction to Data: Covers case studies, data basics, sampling strategies, and experimental design.
Summarizing Data: Focus on graphical and statistical data summaries.
Probability: Discusses foundational principles, including conditional probability and random variables.
Distributions of Random Variables: Examines key distributions such as normal, binomial, and Poisson.
Foundations for Inference: Introduces statistical inference concepts, including point estimates and hypothesis testing.
Inference for Categorical and Numerical Data: Covers methodologies for analyzing categorical and numerical variable data.
Introduction to Linear Regression: Discusses regression analysis for one predictor variable.
Multiple and Logistic Regression: Explores regression with multiple predictors for both numerical and categorical outcomes.

Preface Insights

Readers should develop a robust statistical thinking foundation and understand the real-world application of statistics.
The approach acknowledges that data can be messy and tools are not perfect; understanding their strengths and weaknesses is crucial.

Case Study: Using Stents to Prevent Strokes

Researchers aimed to evaluate if stents effectively reduce the risk of strokes.
Conducted on 451 patients, with random assignment into treatment (n=224) and control (n=227) groups.
Treatment group received stents plus medical management; control group received only medical management.
Outcomes studied at two time points: 30 days and 365 days after enrollment.

Key Findings from the Stent Study

Summary statistics reveal:
- 20% of treatment patients had a stroke within a year (45 out of 224).
- 12% of control patients had a stroke within the same period (28 out of 227).
An unexpected result showed higher stroke rates in the treatment group than anticipated.
The statistical significance of the 8% difference raises questions about the effectiveness of stents.

Statistical Concepts Introduced

Summary Statistics: Single numbers summarizing larger datasets to highlight differences and trends.
Statistical Evidence: Evaluates if observed differences are likely due to chance or indicate a genuine effect.
Emphasizes caution in generalizing study results, noting that volunteers may not represent the broader population.

Additional Learning Resources

Supplementary materials are available, including exercises, examples, and online data sets through openintro.org.
A companion R package enhances the accessibility of data and learning resources.### Migraine Treatment and Acupuncture Study
Effective treatment points showed rapid pain relief within 1 minute, while others took 2 to 5 minutes for an antalgic response.
Semi-permanent needle insertion allowed for sustained migraine pain control, initiated within 30 minutes and lasting up to 24 hours.
The most effective site for managing migraine pain was the antero-internal part of the antitragus.
Comparison was conducted between appropriate (M) and inappropriate (S) acupuncture areas regarding their therapeutic effects on migraines.

Study Groups and Outcomes

94 female participants with diagnosed migraines were randomly assigned to two groups; Group A (46 patients) and Group B (48 patients).
Pain intensity was measured using the Visual Analog Scale (VAS) before treatment (T0) and at different intervals up to 24 hours (T5).
Acupuncture resulted in significant improvements in pain relief, with 89 out of 94 patients showing symptom improvement.

Antibacterial Treatment for Acute Sinusitis

Study involved 166 adults with acute sinusitis, comparing the effects of a 10-day amoxicillin course versus placebo.
Statistical analysis was conducted using ANOVA for variance and t-tests for unpaired data to evaluate symptom improvement.
Self-reported improvements were collected using symptom diaries throughout the study to track patient experiences.

Data Basics and Organization

Data organization is crucial in analyses, utilizing a data matrix where rows represent individual cases and columns represent variables.
Example highlighting a loan dataset showcasing variables like loan amount, interest rate, term, state, and income.
Importance of clarity in variable definitions and units of measurement for effective data management and analysis.

General Research Methodology

Emphasized the significance of structured datasets for analysis and the ability to add new data easily.
Suggested strategies for organizing data in education and county level statistics, illustrating the versatility of a data matrix format.### County Data Overview
Counties listed with various demographic statistics in Alabama and Wyoming.
Key variables include population, population change, poverty rate, homeownership, unemployment rate, and median household income.

Variables Description

Name: County name
State: State of the county
Population (pop): Total number of residents.
Population Change: Percentage change from 2010 to 2017.
Poverty: Percentage of population living in poverty.
Homeownership: Percentage of population that owns their home.
Multi-Unit Structures: Percentage of housing units in multi-unit buildings.
Unemployment Rate (unemp rate): Percentage of the labor force that is unemployed.
Metro: Indicates if the county is part of a metropolitan area.
Median Education: Highest education level attained in the county.
Median Household Income: Total income of households, averaged across the county.

Types of Variables

Numerical Variables:
- Continuous: Can take any value within a range (e.g., unemployment rate).
- Discrete: Countable numbers, e.g., population size.
Categorical Variables:
- Nominal: Categories without a specific order e.g., state names.
- Ordinal: Categories with a natural order, e.g., education levels.

Relationships Between Variables

Investigates associations such as:
- Homeownership rates and the percentage of multi-unit structures.
- Population growth and median household income levels.
- Median education as a predictor for household income.

Associations and Causal Relationships

Associated Variables: Show a relationship, can be dependent or independent.
Explanatory and Response Variables: Identifying which variable may be influencing the other in a relationship (e.g., household income as explanatory and population change as response).

Data Collection Methods

Observational Studies: Collecting data without intervening (e.g., surveys).
Experiments: Managing conditions to establish a cause-effect relationship, requiring random assignments to groups.

Examples and Applications

Real-world examples include studies on air pollution's impact on preterm births and the effectiveness of the Buteyko method for asthma treatment.
Observes how various factors like air quality and treatment methods affect health outcomes.

Statistical Analysis Tools

Use graphs, particularly scatterplots, to visualize and analyze relationships between numerical variables effectively.
Scatterplots can demonstrate trends, such as the relationship between median household income and population change.

Conclusion on Data Relationships

Recognizes that association does not imply causation; causal relationships require rigorous experimental studies.
Emphasizes the structured analysis to identify dynamics within demographic data and areas for further study.

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Description

Test your knowledge of the key concepts from the OpenIntro Statistics Fourth Edition textbook. This quiz covers important topics and contributions from authors David Diez, Mine Çetinkaya-Rundel, and Christopher D Barr. Perfect for students aiming to assess their understanding of statistics.