Basic Veterinary Statistics - Lectures 1 to 5

Vocabulary flashcards covering fundamental statistical concepts, sampling methods, descriptive measures, probability distributions, hypothesis testing, test selection, correlation, and regression for veterinary medicine.

Statistics

The science of collecting, presenting, analysing and interpreting data, applied in veterinary fields such as epidemiology, evidence-based veterinary medicine (EBVM), diagnostics, animal production, drug safety, and food safety.

Population

All members of the group of interest in a study (for example, all cattle on farms in a region).

Sample

A selected subset of the population used to estimate characteristics of the entire population (for example, $160$ trout tested from a pond of $8{,}000$).

Parameter

A numerical characteristic of an entire population, such as the population mean ($\mu$).

Statistic

A numerical characteristic calculated from a sample, such as the sample mean ($\bar{x}$), which estimates a population parameter.

Qualitative nominal variable

A categorical variable consisting of categories without any intrinsic order (examples include breed, coat colour, and blood group).

Qualitative ordinal variable

A categorical variable consisting of ordered categories (examples include body condition score and exam grade).

Quantitative discrete variable

A numerical variable that takes countable numerical values (such as the number of calves).

Quantitative continuous variable

A numerical variable that takes measured numerical values along a continuous scale (examples include body mass, height, and temperature).

Simple random sampling

A probability sampling method in which every individual member of the population has an equal chance of being selected.

Stratified sampling

A sampling method in which the population is divided into distinct subgroups (strata), and samples are taken from within every stratum (taking some individuals from every group).

Cluster sampling

A sampling method where entire groups or clusters are randomly selected from the population and all individual units within those selected groups are examined.

Multi-stage sampling

A sampling method in which clusters are selected first, and then individual units are sampled from within those selected clusters.

Systematic sampling

A sampling method that begins with a random start and then selects every $k\text{th}$ unit from a list or sequence (for example, every 10th animal).

Arithmetic mean

A measure of central tendency calculated as the sum of observations divided by the number of observations ($\bar{x} = \frac{\sum x}{n}$); it is best suited for symmetric quantitative data.

Geometric mean

A measure of central tendency for positive data calculated by multiplying all values together and taking the $n\text{th}$ root: $G = (x_1 \times \dots \times x_n)^{\frac{1}{n}}$.

Harmonic mean

A measure of central tendency useful for averaging rates, defined by the formula $H = \frac{n}{\sum \left(\frac{1}{x}\right)}$.

Median

The middle value in an ordered dataset (the 50th percentile); it is resistant to outliers and is more representative than the mean for skewed data or extreme values.

Mode

The most frequent value in a dataset; it is especially useful as the measure of central tendency for categorical nominal data.

Range

A measure of total spread calculated as $R = \text{maximum} - \text{minimum}$; it is sensitive to outliers.

Interquartile range (IQR)

A robust measure of spread covering the middle $50\%$ of observations, calculated as $IQR = Q_3 - Q_1$, where $Q_1$ is the 25th percentile and $Q_3$ is the 75th percentile.

Population variance ($\sigma^2$)

The average squared deviation of all observations in a population from the population mean, calculated as $\sigma^2 = \frac{\sum (x - \mu)^2}{N}$.

Sample variance ($s^2$)

A sample-based estimate of population variance calculated as $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$.

Standard deviation (SD)

A measure of the typical spread of observations expressed in original units, calculated as $SD = \sqrt{\text{variance}}$.

Coefficient of variation (CV)

A measure of relative variability used to compare variables with different measurement scales or units, calculated as $CV = \left(\frac{SD}{\text{mean}}\right) \times 100\%$.

Positive skewness

A distribution shape characterized by a longer or heavier tail extending toward the right (higher values).

Negative skewness

A distribution shape characterized by a longer or heavier tail extending toward the left (lower values).

Leptokurtic

A distribution shape that is more sharply peaked and has heavier tails than a normal distribution in standard comparisons.

Platykurtic

A distribution shape that is flatter with lighter tails than a normal distribution in standard comparisons.

Sampling distribution

The probability distribution formed by calculating a sample statistic (such as the sample mean) from repeated random samples drawn from the same population.

Standard error of the mean (SEM)

A measure describing the uncertainty and variability of sample means, calculated as $SEM = \frac{SD}{\sqrt{n}}$; it decreases as sample size ($n$) increases.

Standard normal score ($z\text{-score}$)

A standardized value indicating how many standard deviations an observation lies above or below the population mean, calculated as $z = \frac{x - \mu}{\sigma}$.

Null hypothesis ($H_0$)

The hypothesis stating that there is no population difference or no treatment effect between groups (for example, mean milk yield is equal in both groups).

Alternative hypothesis ($H_a$)

The hypothesis stating that there is a real difference or treatment effect present in the population (for example, mean milk yield differs between groups).

p-value

The probability, assuming the null hypothesis ($H_0$) is true, of obtaining a test result at least as extreme as the observed data.

Type I error

The error committed when a true null hypothesis ($H_0$) is rejected (a false positive).

Type II error

The error committed when the test fails to reject a false null hypothesis ($H_0$) (a false negative).

Independent samples

Study designs where observations in each group come from completely different, unrelated animals or subjects (e.g., piglets on standard feed vs piglets on vitamin feed).

Dependent (paired) samples

Study designs where measurements are taken repeatedly on the same animals across different times or conditions (e.g., horse heart rate before vs after training).

Independent-samples t-test

A parametric statistical test used to compare the means of $2$ independent groups.

Mann-Whitney U test

A non-parametric statistical test used to compare $2$ independent groups when parametric assumptions are violated or data is ordinal.

Paired t-test

A parametric test used to compare the means of $2$ dependent (paired) measurements taken on the same subjects.

Wilcoxon signed-rank test

A non-parametric test used to compare $2$ paired or dependent measurements taken on the same subjects.

One-way ANOVA

A parametric test used to evaluate whether differences exist among the means of $3$ or more independent groups.

Kruskal-Wallis test

A non-parametric test used to evaluate differences among $3$ or more independent groups.

Repeated-measures ANOVA

A parametric test used to assess differences across $3$ or more repeated measurements obtained from the same subjects.

Friedman test

A non-parametric test used to evaluate differences across $3$ or more repeated (dependent) measurements obtained from the same subjects.

Post-hoc test

A pairwise statistical comparison performed after a statistically significant ANOVA to identify exactly which group pairs differ while adjusting for multiple testing.

Pearson correlation coefficient ($r$)

A statistic ranging from $-1$ to $+1$ that quantifies the direction and strength of a linear association between two numerical variables.

Coefficient of determination ($r^2$)

The square of the Pearson correlation coefficient ($r$), representing the proportion of total variation in outcome variable $Y$ that is explained by its linear relationship with predictor $X$.

Simple linear regression

A statistical modeling method that describes the mathematical relationship between an independent predictor variable ($X$) and a dependent outcome variable ($Y$) using the equation $Y = a + bX$.

Statistics

The science of collecting, presenting, analysing and interpreting data.

Population

All members of the group of interest (e.g., all cattle on farms in a region).

Sample

A selected subset of the population (e.g., $160$ trout tested from a pond of $8{,}000$).

Parameter

A numerical characteristic of a population, such as the population mean ($\mu$).

Statistic

A numerical characteristic of a sample, such as the sample mean ($\bar{x}$).

Qualitative Nominal Variable

A categorical variable consisting of categories without any inherent order (e.g., breed, coat colour, blood group).

Qualitative Ordinal Variable

A categorical variable consisting of ordered categories (e.g., body condition score, exam grade).

Quantitative Discrete Variable

A numerical variable that takes countable numerical values (e.g., number of calves).

Quantitative Continuous Variable

A numerical variable that takes measured numerical values (e.g., body mass, height, temperature).

Simple Random Sampling

A sampling method in which every member of the population has an equal selection chance.

Stratified Sampling

A sampling method that divides the population into strata and samples units within every stratum.

Cluster Sampling

A sampling method where groups are randomly selected and all units within those selected groups are examined.

Multi-stage Sampling

A sampling method where clusters are selected first, and then individual units are sampled within those clusters.

Systematic Sampling

A sampling method that begins with a random start and selects every $k\text{th}$ unit thereafter.

Arithmetic Mean

A measure of central tendency calculated as the sum of observations divided by the number of observations ($\bar{x} = \frac{\sum x}{n}$).

Geometric Mean

A measure of central tendency calculated by multiplying values and taking the $n\text{th}$ root: $G = (x_1 \times \dots \times x_n)^{1/n}$; used for positive data.

Harmonic Mean

A measure of central tendency calculated as $H = \frac{n}{\sum (1/x)}$; useful for averaging rates.

Median

The middle value of a dataset after sorting ($50\text{th}$ percentile), which is resistant to outliers.

Mode

The most frequent value in a dataset; particularly useful for categorical nominal data.

Range

A measure of total spread calculated as $R = \text{maximum} - \text{minimum}$; sensitive to outliers.

Interquartile Range (IQR)

A robust measure of dispersion representing the spread of the middle $50\%$ of data, calculated as $\text{IQR} = Q_3 - Q_1$.

Population Variance ($\sigma^2$)

The average squared deviation from the population mean, calculated as $\sigma^2 = \frac{\sum (x - \mu)^2}{N}$.

Sample Variance ($s^2$)

A sample-based estimate of variance calculated as $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$.

Standard Deviation (SD)

A measure of the typical spread of measurements expressed in the original units, calculated as $\text{SD} = \sqrt{\text{variance}}$.

Coefficient of Variation (CV)

A measure of relative variability used to compare scales, calculated as $\text{CV} = \left(\frac{\text{SD}}{\text{mean}}\right) \times 100\%$.

Positive Skewness

A distribution asymmetry characterized by a longer tail extending to the right toward high values.

Negative Skewness

A distribution asymmetry characterized by a longer tail extending to the left toward low values.

Leptokurtic

A distribution shape that is more sharply peaked and has heavier tails than a normal distribution in standard comparisons.

Platykurtic

A distribution shape that is flatter than a normal distribution in standard comparisons.

Sampling Distribution

The distribution produced by sample statistics (such as sample means) derived from different random samples of the same population.

Standard Error of the Mean (SEM)

A statistic describing the uncertainty and variation of sample means, calculated as $\text{SEM} = \frac{\text{SD}}{\sqrt{n}}$.

Binomial Distribution

A discrete probability distribution modeling the number of successes across a fixed number of independent trials.

Poisson Distribution

A discrete probability distribution modeling counts of events occurring within a specified interval.

Normal (Gaussian) Distribution

A continuous, symmetric bell-shaped probability distribution defined by its mean and standard deviation.

Student t Distribution

A continuous probability distribution resembling the normal curve but with heavier tails, used for inference about means when the standard deviation is estimated.

Standard Normal Score ($z$-score)

A standardized value calculated as $z = \frac{x - \mu}{\sigma}$, indicating the number of standard deviations an observation lies from the mean.

Null Hypothesis ($H_0$)

The statement of no population difference or no treatment effect between groups.

Alternative Hypothesis ($H_a$)

The statement that there is a real population difference or treatment effect.

p-value

The probability, assuming $H_0$ is true, of obtaining a test statistic at least as extreme as the observed result.

Type I Error

The error committed by rejecting the null hypothesis when it is actually true (a false positive).

Type II Error

The error committed by failing to reject the null hypothesis when it is actually false (a false negative).

Independent-Samples t-test

A parametric test used to compare the means of two independent groups.

Paired t-test

A parametric test used to compare two paired or repeated measurements obtained from the same subjects.

One-Way ANOVA

A parametric test used to evaluate differences among the means of three or more independent groups.

Repeated-Measures ANOVA

A parametric test used to evaluate differences across three or more repeated measurements on the same subjects.

Mann-Whitney U Test

A non-parametric test used to compare two independent groups when parametric assumptions are violated.

Wilcoxon Signed-Rank Test

A non-parametric test used to compare two paired measurements from the same subjects.

Kruskal-Wallis Test

A non-parametric test used to compare three or more independent groups.

Friedman Test

A non-parametric test used to compare three or more dependent or repeated measurements.