Statistics and Math Guidance Quiz

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Questions and Answers

What is indicated by a p-value less than 0.05?

The result is statistically significant. (correct)

The result is not statistically significant.

The study should consider a larger sample size.

There is no effect present.

What issue can arise from having too small a sample size?

Study results may take longer to obtain.

Precision may be improved.

Clinically important effects may be missed. (correct)

Research resources may be wasted.

What is the primary goal of power-based sample size calculations?

To estimate the population mean accurately.

To ensure ethical treatment of subjects.

To minimize costs in conducting the study.

To detect pre-specified effects as statistically significant. (correct)

Type I error occurs when which of the following happens?

Ho is rejected when it is true. Signup and view all the answers

What can excessive sample size lead to?

Unethical treatment of subjects. Signup and view all the answers

What is one consequence of lacking precision in a study?

The conclusion may be unreliable. Signup and view all the answers

Power in statistical testing refers to:

The ability to detect a true effect when it exists. Signup and view all the answers

What characterizes power-based sample size calculations in hypothesis testing?

They aim to find statistically significant effects. Signup and view all the answers

What does a 95% confidence interval indicate about the sampling process?

95% of confidence intervals will capture the true population parameter over many samples. Signup and view all the answers

What affects the width of a confidence interval?

Standard error and confidence level. Signup and view all the answers

What is the null hypothesis (H0) in hypothesis testing?

It asserts that there is no difference or relationship in the population. Signup and view all the answers

Which statement about confidence intervals is true?

A higher confidence level will result in a wider confidence interval. Signup and view all the answers

What should be done after stating the null hypothesis in hypothesis testing?

Use the results from the statistical test to decide whether to reject H0. Signup and view all the answers

If the standard error is large, how will that affect the confidence interval?

The confidence interval will be wider. Signup and view all the answers

In hypothesis testing, which hypothesis represents a claim of no effect?

Null hypothesis. Signup and view all the answers

Why is it essential to state competing hypotheses in research?

It distinguishes between different possible outcomes. Signup and view all the answers

What does a P-value of p = 0.024 indicate in hypothesis testing?

Reject the null hypothesis Signup and view all the answers

What is defined as a type II error in hypothesis testing?

Failing to reject the null hypothesis when it is false Signup and view all the answers

What is the probability of making a type I error typically set to?

0.05 Signup and view all the answers

What statistical outcome results from failing to reject the null hypothesis when it is true?

True negative Signup and view all the answers

Which of the following represents the power of a hypothesis test?

1 - 𝛽 Signup and view all the answers

What is indicated by a P-value of p = 0.587 in hypothesis testing?

Insufficient evidence to reject the null hypothesis Signup and view all the answers

What happens when the null hypothesis is rejected when it is false?

True positive Signup and view all the answers

Which statement is correct regarding type errors in hypothesis testing?

A type II error occurs when we accept a false null hypothesis. Signup and view all the answers

What is the purpose of studying a sample in research?

To learn about the entire population. Signup and view all the answers

What best describes inferential statistics?

Techniques to make conclusions about a wider population. Signup and view all the answers

What is a characteristic of descriptive statistics?

They summarize the data observed for the sample. Signup and view all the answers

Which statement about population and sample is true?

A sample is used to generalize results to the entire population. Signup and view all the answers

Why is the sample design important in research?

It affects how generalizable the results are. Signup and view all the answers

What is the main difference between descriptive and inferential statistics?

Descriptive statistics summarize observed data, while inferential statistics make predictions about unobserved data. Signup and view all the answers

Which of the following best describes a sample?

It is a subset selected to represent the larger population. Signup and view all the answers

What role does statistical analysis play in understanding research findings?

It helps understand patterns and make inferences from data. Signup and view all the answers

Which test is appropriate for assessing normality with a small dataset?

Shapiro-Wilk test Signup and view all the answers

What does a p-value indicate in hypothesis testing?

The strength of evidence against the null hypothesis Signup and view all the answers

What is the expected consequence of a Type I error?

Rejecting a true null hypothesis Signup and view all the answers

Which graphical method is most effective for assessing normality with larger datasets?

Q-Q plot Signup and view all the answers

What should be considered when groups are not independent in a categorical analysis?

McNemar’s test Signup and view all the answers

Which of the following best describes a two-sided hypothesis?

Hypotheses that consider both sides of the distribution Signup and view all the answers

In statistical terms, what do alpha (𝜶) and beta (𝜷) represent?

The probability of Type I and Type II errors, respectively Signup and view all the answers

Which statistical test is commonly used to compare means across groups?

ANOVA Signup and view all the answers

Which measure is essential for calculating the power of a statistical test?

Effect size Signup and view all the answers

What type of plot is suitable for illustrating the relationship between two numeric variables?

Scatter plot Signup and view all the answers

Study Notes

Applied Statistics 1

Course code: VMS3012
Course instructors: Alice Batchelor, Liz Grant
Course offered by: Library and Learning Services, University of Surrey
Maths and Statistics Advice (MASA): A free service for all students at the University of Surrey, offering non-judgemental, impartial guidance on mathematics and statistics problems.
Maths and Statistics Hub located on Level 1 Library.
Drop-in sessions: Mondays 11:00-13:00, Wednesdays 15:00-17:00 (check SurreyLearn for updates)
Online resources accessible on the SurreyLearn module (interactive tools, demo videos).
Appointments available every weekday, in-person or online (via Teams), for all students with longer queries (e.g., statistics relating to a research project). Book through SurreyLearn.
Email: [email protected]

Learning Outcomes

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

Importance of Statistics in Veterinary Medicine

Evidence-based veterinary medicine relies critically on the scientific validity of research.
Statistical design and analysis is a critical component of research validity.
Even without conducting research, you need to read and interpret published research of others.
Broad aims of AS1 & AS2 lectures: Recognize, explain, and interpret common statistical measures and methods; understand and critique statistics in veterinary research papers (more in semester 2).

Quantitative Research Process

Identify/refine research questions/hypotheses.
Design study and choose variables/plan statistical analysis. (Includes: Choose variables, Sample size calculation, Sample design, Plan analysis)
Conduct study: Collect data from a sample.
Analyze data.
Present and interpret results.

Research Questions

Research studies often seek to determine whether two or more things are linked.
Examples include: vet salaries in urban vs. rural areas; student lecture attendance and exam results, and prevalence of particular diseases.

Overview of Selecting Appropriate Analysis Methods

The statistical approach depends on the research questions and the type of variables measured.
Researchers should choose variables that help to answer the research question.
Plan and think ahead to the analysis that could be performed on the chosen variables.

Recap: Types of Variables

Continuous: A measurement on a continuous numeric scale (e.g., weight or height).
Discrete: Takes a limited number of discrete numeric values (e.g., age in years, number of something). Can usually be treated as continuous if there are enough levels in the data.
Interval: Numbers can be positive/negative; no absolute zero.
Ratio: Negative numbers not possible; absolute zero.
Categorical:
- Nominal: Categories with no meaningful order (e.g., color, country).
- Ordinal: Categories that can be ordered or ranked (e.g., Likert-type item, finish positions in a race).

Model of the Data Analysis Process

Exploratory Data Analysis:
- Whether sets of measurements differ from each other.
- Whether there is an association/relationship/correlation between variables.
- Whether 2 categorical variables are associated.
- Whether 2 numeric variables are related to each other.

Descriptive vs. Inferential Statistics

Descriptive statistics: Summarize the data observed for a sample (i.e., describe the data).
Inferential statistics: Methods that use sample data to try to make conclusions about a wider population (i.e., draw conclusions).
Note: The selection of a sample is crucial for the generalizability of results from the sample to the population.

Descriptive Statistics: What Are They For?

Generate summaries to describe key features of a dataset.
Organize and present data in a meaningful way.
Reduce large amounts of data to a few relevant pieces of information.
Highlight potential relationships between variables.
Examples in a research study: Exploratory study, inferential studies, descriptive statistics used alongside statistical tests. Used for qualitative methods.

Types of Descriptive Statistics

Central tendency: Mean, median, mode (describes the "centre").
Variability: Standard deviation, interquartile range, range (describes data dispersion).
Distribution: Histogram, counts, percentages (deals with each value's frequency).
Usually presented as a combination of text, tables, and/or graphs.
Univariate descriptive statistics describe single variables only.

Descriptives for a Categorical Variable

Central tendency: Mode (most frequent category), median (middle category).
Variability: Range (difference between largest and smallest category values).
Distribution: Counts (number of occurrences in each category), percentages (proportions of each category).

Presenting Descriptives Graphically

Bar charts: Show counts/percentages; mode is often visually identifiable.
Frequency tables: Table presenting counts/percentages of each category.

Descriptive Statistics for Scale Variables

Distribution: Observing the shape (skewed or symmetrical) of data.
Histograms: Bar graphs with no gaps between bars, to show frequency distribution of a continuous variable.
Frequency (Y-axis) values: The height of each bar corresponds to the frequency of the data points falling within specific groups of interval values along the X axis.
Skewed vs. symmetrical data; knowing if the data is skewed or symmetrical helps inform which other descriptives are appropriate for presentation.

Descriptors for Scale Variables (continued)

Measures of Central Tendency (Typical center): Mean, median, mode.
Measures of Spread/Variability: Standard deviation, range, interquartile range (IQR).

Presenting Descriptive Statistics Graphically

Bar charts: Typically used to display means; error bars for standard deviation/standard error.
Box plots: Visual representation of data distribution (median, quartiles, min/max values). Show variability around the median; outliers are presented as dots or stars if present.

Bivariate Descriptive Statistics

Describing two variables together.
Examples:
- Whether groups of measurements differ from each other (e.g., means and SDs or medians and IQR by group).
- Whether categorical variables are associated (e.g., 2-way frequency tables).
- Whether numeric variables are related (e.g., scatter plots, correlation coefficient).

Inferential Statistics

Methods use sample data to draw conclusions about a wider population.
Often involves testing hypotheses.
Examples include confidence intervals, hypothesis tests, and regression analysis.

Choosing a Statistical Test

Identify research question (is there a difference or is there a relationship).
Consider the type of data (categorical or scale variables).
Test assumptions must be considered and satisfied.
Check for sample size requirements.

Tests of Difference

Used to determine if there is a difference between groups of measurements.
Example questions: are there differences in salaries of vets in urban vs. rural areas? Are there differences in student confidence before, during, and after a clinical placement?
Groups may be related or unrelated.

Choosing a Test of Difference

Decide if a difference is being investigated.
Identify the groups being compared.
Determine if the groups are independent or related.
Is the dependent variable (DV) categorical or continuous?

Parametric tests of difference:

Use of Continuous dependent variable
DV: approximately normally distributed in each group (and other appropriate assumptions are met
examples include independent/paired t-test, one-way ANOVA, one-way repeated measures ANOVA.

Non-parametric tests of difference:

Use of ordinal dependent variable or continuous dependant variable with violated assumptions.
Examples include Mann-Whitney U test, Wilcoxon Signed Ranks test, Kruskal-Wallis test, Friedman test.

Choosing a test of Association/Relationship

Exploring relationships between numeric/scale variables
Exploring relationships between categorical/ordinal variables

Tests of Association/Relationship

Parametric tests: Pearson's correlation or simple linear regression.
Non-parametric tests: Spearman's rank correlation.
Chi-square test and Fisher's exact test.

Sample Size Calculations

Power-based calculations use effect size, significance level, and desired power to determine the required sample size.
Precision-based calculations use margin of error (desired precision), variability in a sample, and confidence level.

One-sided vs Two-sided tests

One-tailed: alternative hypothesis specifies a specific direction. One-tailed tests have more power to detect a significant effect in that specific direction.
Two-tailed: alpha is split evenly among the two directions.
Use one-sided test only if there is a strong basis to expect an effect in a specific direction.

Learning outcomes

Explain and interpret a p-value and one sided and two sided hypotheses
Explain type 1 error, type 2 error and calculate a beta probability and power for a statistical study.
Compare and contrast descriptive and inferential statistics.
Identify appropriate statistics for different types of data.
Outline assumptions and how to choose a statistical test
Outline methods to calculate sample size/power

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Description

Test your knowledge on the guidance offered by Maths and Statistics Advice. This quiz covers essential concepts such as p-values, sample sizes, and confidence intervals, as well as practical questions about resources and appointments. Perfect for students looking to enhance their understanding of statistical principles.