Research Methods Quiz: Variables and Analysis

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Questions and Answers

What type of research question examines the connection between students' lecture attendance and their exam results?

This is an example of a correlational research question.

When planning a research study, why is it important to consider the type of variables being measured?

The type of variables dictates the appropriate statistical analysis methods to be used.

What distinguishes continuous variables from categorical variables?

Continuous variables can take any value within a range, while categorical variables represent distinct groups or categories.

Give an example of a discrete variable.

An example of a discrete variable is the number of students attending a lecture. Signup and view all the answers

What is a characteristic of ordinal variables?

Ordinal variables can be ranked or ordered but do not have a consistent difference between ranks. Signup and view all the answers

In the context of exploratory research, what might researchers focus on estimating?

Researchers might focus on estimating the prevalence of a particular condition or phenomenon. Signup and view all the answers

What is a nominal variable and how does it differ from an ordinal variable?

A nominal variable consists of categories with no meaningful order, unlike ordinal variables which can be ranked. Signup and view all the answers

What is the significance of identifying and refining research questions in a study design?

Identifying and refining research questions ensures clarity and direction for the research process. Signup and view all the answers

How can categorical variables be treated in data analysis?

Categorical variables can be treated as continuous if there are enough levels in the data. Signup and view all the answers

What is the key difference between interval and ratio data?

The key difference is that ratio data has an absolute zero, while interval data can have negative values. Signup and view all the answers

What is exploratory data analysis primarily concerned with?

Exploratory data analysis is concerned with understanding differences between sets of measurements and relationships between variables. Signup and view all the answers

What type of statistics helps make inferences about populations based on sample data?

Inferential statistics helps make inferences about populations based on sample data. Signup and view all the answers

In the context of research, what is typically collected for a study?

Typically, data is collected for a sample rather than the entire population. Signup and view all the answers

What common objective can be identified when examining two numeric variables?

The common objective is to determine if the two numeric variables are related to each other. Signup and view all the answers

What falls under the purpose of descriptive statistics?

Descriptive statistics summarize and describe the characteristics of a dataset. Signup and view all the answers

What defines the distance between possible values in interval data?

In interval data, the distance between each possible value is always the same. Signup and view all the answers

What are the types of data involved in the relationship between oxygen saturation and intestinal wall thickness?

Two continuous variables. Signup and view all the answers

What is the primary assumption of a chi-square test regarding the expected frequencies?

At least 80% of expected frequencies must be greater than or equal to 5, and none can be 0. Signup and view all the answers

What type of test would be appropriate to assess the association between two continuous variables?

Pearson's correlation or simple regression. Signup and view all the answers

What is the expected relationship between oxygen saturation and intestinal wall thickness?

Higher intestinal wall thickness is expected for lower oxygen saturation. Signup and view all the answers

When should Fisher’s exact test be used instead of the chi-square test?

Fisher's exact test is used when the assumptions about expected frequencies in the chi-square test are not met. Signup and view all the answers

What does Pearson’s correlation measure?

Pearson's correlation measures the strength and direction of a linear relationship between two continuous variables. Signup and view all the answers

In the context of the tests mentioned, how many variables are involved?

Two variables. Signup and view all the answers

What statistical test is mentioned for analyzing the association between two categorical variables?

Chi-squared test. Signup and view all the answers

How does simple linear regression differ from Pearson’s correlation?

Simple linear regression predicts the value of the dependent variable based on the independent variable, while Pearson’s correlation evaluates the strength of the relationship between them. Signup and view all the answers

If one variable is nominal and the other variable is ordinal, which statistical test could be used?

Fisher's exact test. Signup and view all the answers

What type of variables does Spearman’s correlation apply to?

Spearman’s correlation applies to ordinal variables or continuous variables that do not meet the assumptions for Pearson’s correlation. Signup and view all the answers

What should be assessed before performing a Pearson's correlation test?

Whether the test assumptions are satisfied. Signup and view all the answers

What must be true about the categories of variables in a chi-square test of association?

The categories must be mutually exclusive, meaning each subject fits into only one level. Signup and view all the answers

What does a correlation coefficient indicate in correlation analysis?

A correlation coefficient, ranging from -1 to 1, indicates the strength and direction of the relationship between two variables. Signup and view all the answers

Under what conditions might you use both ordinal and scale variables in an analysis?

When comparing the relationship between an ordinal variable and a continuous scale variable. Signup and view all the answers

Can correlation analysis definitively demonstrate causation between variables?

No, correlation analysis does not imply causation; it only indicates the strength and direction of a relationship. Signup and view all the answers

What is a confidence interval (CI) and why is it important in statistics?

A confidence interval is a range of values that estimates a population parameter. It is important because it provides an indication of the precision of the estimate and the uncertainty associated with it. Signup and view all the answers

What does a P-value of p = 0.024 indicate about the null hypothesis?

It indicates that we reject the null hypothesis and conclude there is a statistically significant difference. Signup and view all the answers

How does the standard error affect the width of a confidence interval?

A larger standard error leads to a wider confidence interval. This reflects greater uncertainty about the estimate. Signup and view all the answers

What does a 95% confidence interval signify in statistical terms?

A 95% confidence interval means that if we were to sample multiple times, 95% of those intervals would contain the true population value. Signup and view all the answers

What is the definition of a Type I error in hypothesis testing?

A Type I error occurs when we reject the null hypothesis when it is actually true. Signup and view all the answers

If the P-value is p = 0.587, what should the conclusion regarding the null hypothesis be?

We do not reject the null hypothesis, concluding there is no statistically significant difference. Signup and view all the answers

In hypothesis testing, what are the null hypothesis (H0) and alternative hypothesis (H1)?

The null hypothesis (H0) states there is no effect or relationship, while the alternative hypothesis (H1) claims there is an effect or relationship in the population. Signup and view all the answers

What does β (beta) represent in hypothesis testing?

β represents the probability of making a Type II error or a false negative. Signup and view all the answers

What is the purpose of conducting a statistical test in hypothesis testing?

The statistical test assesses whether there is enough evidence to reject the null hypothesis. It tests the assumption that H0 is true. Signup and view all the answers

Define the significance level (α) in hypothesis tests.

The significance level (α) is the probability of making a Type I error, usually set at 0.05. Signup and view all the answers

Why might a researcher choose a higher confidence level than 95% when constructing a CI?

A higher confidence level increases the assurance that the interval contains the true population parameter, albeit at the cost of a wider interval. Signup and view all the answers

What is meant by 'power' in hypothesis testing?

Power is defined as 1 - β, representing the probability of correctly rejecting the null hypothesis when it is false. Signup and view all the answers

What factors can lead to a larger confidence interval?

Larger standard error and higher confidence levels both contribute to wider confidence intervals. Signup and view all the answers

What outcome occurs when we do not reject the null hypothesis when it is true?

This outcome is known as a true negative. Signup and view all the answers

How can we assess the strength of evidence against the null hypothesis?

The strength of evidence against the null hypothesis can be assessed by examining the results of the statistical test and the p-value derived from it. Signup and view all the answers

Why is it important to set α and β levels before conducting a hypothesis test?

Setting α and β levels ensures clear criteria for decision-making, reducing bias and enhancing the validity of the results. Signup and view all the answers

Study Notes

Applied Statistics 1

This is a course on applied statistics.
The course is offered by the University of Surrey's Library & Learning Services.
Course instructors are Alice Batchelor and Liz Grant.
Course code is VMS3012.

Maths and Statistics Advice (MASA)

A free service for all University of Surrey students.
Offers non-judgmental and impartial guidance on mathematics and statistics problems.
Located in the Maths and Statistics Hub, Level 1 Library.
Drop-in sessions on Mondays (11:00-13:00) and Wednesdays (15:00-17:00).
Accessible via SurreyLearn for up-to-date information.
Online resources, interactive tools, demo videos.
Appointments are available in-person or online via Teams.

Learning Outcomes

Explain type I error, type II error, alpha and beta probabilities, and the power of a study.
Explain and interpret p-values and one-sided and two-sided hypotheses.
Compare and contrast descriptive and inferential statistics.
Select an appropriate statistical analytical method (regression and correlation, parametric and non-parametric).
Estimate sample size and power.
This information is a review of VMS2008 statistics material.

Importance of Veterinary Statistics

Evidence-based veterinary medicine relies critically on the scientific validity of research.
The statistical design and subsequent analysis of data collected in the study are crucial to the validity of research.
Students need to be able to read and interpret published research.

Quantitative Research Process (Simplified)

Identify/refine research question(s)/hypotheses.
Design study and choose variables/plan statistical analysis (including variable selection, sample size calculation, and sample design).
Conduct study: collect data from a sample.
Analyze the data using descriptive/inferential statistics.
Present and interpret the results.

Research Questions

Examples of research questions involve determining if there is a link between variables, such as relationship between job location and salary for vets or examining the relationship between attendance in lectures and exam results.
More generally, estimating measures like prevalence of a disease.

Overview of Selecting Appropriate Analysis Methods

The statistical approach depends on the research question and the type of variables being measured.
A researcher needs to choose appropriate variables for the research question.

Recap: Types of Variables

Continuous: A measurement on a continuous numerical scale. (e.g., weight or height).
Discrete: Takes a limited number of discrete numerical values. (e.g., number of children).
Ordinal: Categories that can be ordered or ranked. (e.g., Likert-type items, finish positions in a race).
Nominal: Categories with no meaningful order. (e.g., colors, countries).

Model of the Data Analysis Process

Exploratory data analysis.
Determine whether sets of measurements differ from each other.
Determine whether there is an association/relationship/correlation between variables.
Determine whether two categorical variables are associated.
Determine whether two numeric variables are related to each other.

Descriptive vs. Inferential Statistics

Descriptive data summarizes observations in a sample.
Inferential data uses a sample to reach conclusions about a broader population (drawing inferences).

Descriptive Statistics

Generate summaries to describe key dataset features.
Organize and present data meaningfully, and reduce large amounts of data to manageable summaries.
Highlight potential relationships between variables.

Types of Descriptive Statistics

Central tendency involves finding averages or typical values (mean, median, mode).
Variability concerns how dispersed or spread out values are (standard deviation, interquartile range, range).
Distribution examines the frequency of each value or category (histogram, counts, percentages).

Descriptive Statistics for Categorical Variables

Central tendency is often expressed as the mode (most frequent category) and median (middle category).
Variability is often measured by the range (difference between maximum and minimum values).
Distribution is expressed as counts or percentages of each category.

Presenting Descriptive Statistics Graphically

Bar charts visually display counts or percentages of each category.
Frequency tables present each category's counts or percentages.
When appropriate, these two methods are effective for showing the data.

Descriptive Statistics for Scale Variables

Distribution shape is frequently examined as skewed or symmetrical.
Measurements of central tendency are common and useful for scale variables (e.g., mean, median, mode).
Measurements of spread / variability are also important (e.g., standard deviation, range, interquartile range).
Visual representations of data distributions using histograms and box plots.

Presenting Descriptive Statistics Graphically for Scale Variables

Typically, bar charts display mean values with error bars for standard deviation (SD) or standard error (SE).
Box plots present the median, quartiles, and outliers.

Bivariate Descriptive Statistics

Descriptive analysis for two variables simultaneously.
Determining whether the groups differ from each other or whether categorical variables are associated and whether two numerical variables are related.
Methods include grouped box plots, scatter plots, bar charts, and frequency tables.

Inferential Statistics

Making conclusions or inferences about a larger population based on a sample of data.
Common examples involving confidence intervals, hypothesis tests, and regression analysis.

Choosing a Statistical Test (Tests of Difference)

Identify the nature of the test (difference vs. association).
Determine type(s) of data (variables: categorical or numerical).
Check if assumptions of the tests are satisfied.

Choosing a Statistical Test (Tests of Association/Relationship)

Determine whether categories of variables are mutually exclusive.
Determine if observed frequencies are significantly different from those expected if there is no association between variables.
Measure the strength and direction of the relationship using a correlation coefficient.

Parametric vs. Non-parametric

Parametric tests make assumptions about the distribution (e.g., normal distribution).
Non-parametric tests do not assume a particular distribution.
Choose which test applies based on the distribution of the data.

Normality

Describes a bell-shaped distribution and used to assess data distribution.
Methods of assessing normality: Shapiro-Wilk test, Kolmogorov-Smirnov test, QQ-plots, histograms.

Sample Size Calculations

Crucial in study design, impacting precision and generalizability.
Two approaches:
- Power-based sample size - based on hypothesis testing considerations.
- Precision-based sample size - focused on desired precision estimates.
- Power - The probability of correctly rejecting the null hypothesis.
- Significance level - The probability of incorrectly rejecting the null hypothesis.
- Effect size - The minimum effect of the research question.

One-sided vs Two-sided Tests

Differences between one-tailed and two-tailed tests.
Appropriate application based on whether the research specifies a particular direction of the effect or not.

Key Concepts in Inferential Statistics

Understand concepts of hypothesis testing (null and alternative hypotheses), test statistics, p-values, significance, error types, power, sample sizes, confidence intervals, and appropriate application to different statistical tests.

Learning Outcomes (repeated for emphasis)

Explain type I error, type II error, alpha and beta probabilities, and the power of a study.
Explain and interpret p-values and one-sided and two-sided hypotheses.
Compare and contrast descriptive and inferential statistics.
Select an appropriate statistical analytical method (regression and correlation, parametric and non-parametric).
Estimate sample size and power.

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Description

Test your understanding of research methods with this quiz focused on variables, their characteristics, and data analysis techniques. Learn how research questions shape study design and how different types of data are treated in statistical analyses. Perfect for students studying research methodology.