Quantitative Methods & Hypothesis Testing

Flashcards covering quantitative methods, descriptive vs. inferential statistics, variable types, hypothesis testing, p-values, and common statistical tests used in veterinary epidemiology.

What are the two types of biological variation discussed in the lecture?

Inter-individual variation (between animals, e.g., genetics, breed) and intra-individual variation (within the same animal, e.g., weight changes, activity).

Distinguish between a 'Population' and a 'Sample'.

A population is the entire group you want information about (e.g., all UK dairy cows), while a sample is a smaller group selected from that population to be studied.

What is the difference between a 'Statistic' and a 'Parameter'?

A statistic is a value calculated from a sample (e.g., sample prevalence), whereas a parameter is a true value in the population, which is usually unknown.

What is the primary difference between Descriptive and Inferential Statistics?

Descriptive statistics describe the sample (e.g., mean, graphs), while inferential statistics make conclusions about the population (e.g., hypothesis testing, confidence intervals).

Define 'Nominal' and 'Ordinal' categorical variables.

Nominal variables are categories with no order (e.g., breed, species), while Ordinal variables are categories with a specific order or ranking (e.g., mild, moderate, severe disease).

Define 'Discrete' and 'Continuous' numerical variables.

Discrete variables are counts involving whole numbers only (e.g., number of calves), while Continuous variables can take any value (e.g., body temperature, weight).

When should you use the Mean versus the Median to describe numerical data?

Use the Mean for data that are normally distributed; use the Median when data are skewed or contain outliers.

Which measures of spread should be paired with the Mean and the Median respectively?

The Mean is paired with Standard Deviation (SD), and the Median is paired with the Interquartile Range (IQR).

What does a 95% Confidence Interval (CI) represent?

A range of values likely to contain the true population value; it means we are 95% confident the true value lies within that range.

How do sample size and variability affect the width of a Confidence Interval (CI)?

A larger sample size creates a narrower CI (more precise), while greater variability creates a wider CI (less precise).

Distinguish between the Null Hypothesis ($H_0$) and the Alternative Hypothesis ($H_1$).

The Null Hypothesis ($H_0$) assumes no difference or association, while the Alternative Hypothesis ($H_1$) assumes a difference or association exists.

What are Type I and Type II errors?

A Type I error is a false positive (concluding there is a difference when there isn't), while a Type II error is a false negative (failing to detect a real difference).

What is 'Statistical Power' and how is it calculated?

Power is the ability to detect a true effect, calculated as $Power = 1 - \beta$. It is usually set at $80\%$.

Define 'p-value'.

The probability of obtaining the observed result (or more extreme) assuming the Null Hypothesis ($H_0$) is true.

How are p-values interpreted regarding statistical significance?

If $p < 0.05$, reject $H_0$ (statistically significant); if $p \geq 0.05$, do not reject $H_0$ (not statistically significant).

What does it mean for significance if a Confidence Interval (CI) for a difference includes 0?

If the CI includes 0, the result is not statistically significant; if it excludes 0, it is statistically significant.

What does it mean for significance if a Confidence Interval (CI) for an Odds Ratio (OR) or Risk Ratio (RR) includes 1?

If the CI includes 1, there is no statistically significant association; if it excludes 1, the association is significant.

How is a Risk Ratio (RR) of $2$ interpreted compared to a Risk Ratio of $0.5$?

An $RR = 2$ means the risk is doubled; an $RR = 0.5$ means the risk is halved.

When should a Chi-Square Test be used?

When comparing two categorical variables (e.g., Breed vs. Disease status).

Contrast the use of an Independent t-Test and a Mann-Whitney U Test.

An Independent t-test compares means between two groups with normal data, while a Mann-Whitney U test is the non-parametric alternative for skewed data.

When is ANOVA (Analysis of Variance) used?

To compare means across $3+$ groups.

What is the difference between Statistical Significance and Clinical Significance?

Statistical significance ($p < 0.05$) means a difference was detected, while Clinical significance refers to whether that difference actually matters in practical medical terms.