Population: The entire set of individuals or objects with which a statistical investigation is concerned.
Sample: A subset of the population that is selected for study to gather information about the population.
Parameter: A numerical characteristic of a population, often represented by a symbol (e.g., mean, variance).
Statistic: A numerical characteristic of a sample, used to estimate parameters of the population.
Descriptive Statistics: Methods used to summarise and describe the characteristics of a dataset.
Inferential Statistics: Methods used to draw conclusions or make predictions about a population based on sample data.
Variable: Any characteristic or attribute that can be measured or categorised.
Categorical Variable: A variable that represents categories or groups (e.g., gender, color).
Numerical Variable: A variable that represents measurable quantities (e.g., height, weight).
Continuous Variable: A numerical variable that can take on an infinite number of values within a range.
Discrete Variable: A numerical variable that can only take on specific, distinct values.
Frequency: The number of times a particular value occurs in a dataset.
Frequency Distribution: A table or graph that shows the frequency of each value or category in a dataset.
Central Tendency: A measure that represents the center or middle of a dataset (e.g., mean, median, mode).
Mean: The average of a set of values, calculated by summing all values and dividing by the number of values.
Median: The middle value in a sorted list of values, or the average of the two middle values if the list has an even number of values.
Mode: The value that occurs most frequently in a dataset.
Dispersion: A measure of the spread or variability of a dataset (e.g., range, variance, standard deviation).
Range: The difference between the maximum and minimum values in a dataset.
Variance: A measure of how much the values in a dataset differ from the mean, calculated as the average of the squared differences from the mean.
Standard Deviation: A measure of the average deviation of values from the mean, calculated as the square root of the variance.
Coefficient of Variation: A standardised measure of dispersion, calculated as the standard deviation divided by the mean.
Skewness: A measure of the asymmetry of the distribution of values in a dataset.
Kurtosis: A measure of the “tailedness” of the distribution of values in a dataset.
Normal Distribution: A symmetric, bell-shaped distribution characterised by its mean and standard deviation.
Standard Normal Distribution: A normal distribution with a mean of 0 and a standard deviation of 1.
Z-Score: A standardised score representing the number of standard deviations a data point is from the mean of the distribution.
Sampling Distribution: The distribution of a statistic calculated from multiple samples of the same size taken from the same population.
Central Limit Theorem: A fundamental theorem in statistics stating that the sampling distribution of the mean of any independent and identically distributed random variables approaches a normal distribution as the sample size increases, regardless of the shape of the original distribution.
Confidence Interval: A range of values constructed from sample data that is likely to contain the true population parameter with a certain level of confidence.
Hypothesis Testing: A statistical method used to make inferences about population parameters based on sample data.
Null Hypothesis (H0): A statement that there is no significant difference or relationship between variables in a population.
Alternative Hypothesis (H1 or Ha): A statement that contradicts the null hypothesis and suggests there is a significant difference or relationship between variables in a population.
Type I Error: Rejecting the null hypothesis when it is actually true (false positive).
Type II Error: Failing to reject the null hypothesis when it is actually false (false negative).
Significance Level (α): The probability of committing a Type I error, typically set at 0.05 or 0.01.
P-Value: The probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true.
Degrees of Freedom: The number of independent observations or parameters in a statistical analysis.
T-Test: A statistical test used to determine if there is a significant difference between the means of two groups.
ANOVA (Analysis of Variance): A statistical method used to compare means across multiple groups to determine if there are any statistically significant differences.
Chi-Square Test: A statistical test used to determine if there is a significant association between two categorical variables.
Regression Analysis: A statistical method used to model the relationship between one or more independent variables and a dependent variable.
Linear Regression: A type of regression analysis where the relationship between the independent variables and the dependent variable is modelled as a linear equation.
Logistic Regression: A type of regression analysis used when the dependent variable is categorical, and the relationship between the independent variables and the probability of a particular outcome is modelled.
Correlation: A statistical measure that describes the strength and direction of a relationship between two variables.
Pearson Correlation Coefficient (r): A measure of the linear relationship between two continuous variables, ranging from -1 to 1.
Spearman Rank Correlation Coefficient: A non-parametric measure of correlation that assesses how well the relationship between two variables can be described using a monotonic function.
Covariance: A measure of how much two random variables change together, calculated as the expected product of their deviations from their respective means.
Scatterplot: A graphical representation of the relationship between two variables, with one variable on the x-axis and the other on the y-axis.
Interquartile Range (IQR): A measure of statistical dispersion, calculated as the difference between the upper (75th percentile) and lower (25th percentile) quartiles.
Quartile: Any of the three points that divide an ordered dataset into four equal parts.
Percentile: A measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.
Outlier: An observation that lies an abnormal distance from other values in a dataset.
Robust Statistics: Statistical methods that are insensitive to the presence of outliers.
Residual: The difference between the observed value and the predicted value in regression analysis.
Goodness of Fit: A measure of how well a statistical model fits a set of observations.
R-Squared (Coefficient of Determination): A measure of the proportion of the variance in the dependent variable that is predictable from the independent variables.
Adjusted R-Squared: An adjustment of R-squared that penalises the addition of unnecessary independent variables to a regression model.
Multicollinearity: The phenomenon where independent variables in a regression model are highly correlated with each other.
Confounding Variable: A variable that influences both the dependent variable and the independent variable, leading to a spurious correlation.
Causality: The relationship between cause and effect, often inferred from statistical analysis but requiring additional evidence to establish.
Random Variable: A variable whose possible values are outcomes of a random phenomenon.
Probability Distribution: A function that describes the likelihood of obtaining different possible outcomes from a random experiment.
Probability Density Function (PDF): A function that describes the likelihood of a continuous random variable falling within a particular range of values.
Cumulative Distribution Function (CDF): A function that describes the probability that a random variable takes on a value less than or equal to a given value.
Binomial Distribution: A discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.
Normal Distribution: A continuous probability distribution that is symmetric and bell-shaped, characterised by its mean and standard deviation.
Poisson Distribution: A discrete probability distribution that describes the number of events occurring in a fixed interval of time or space.
Exponential Distribution: A continuous probability distribution that describes the time between events in a Poisson process.
Uniform Distribution: A continuous probability distribution where all outcomes are equally likely.
Hypothesis: A statement or claim about a population parameter that is subject to statistical testing.
Parameter Estimation: The process of using sample data to estimate the value of a population parameter.
Point Estimate: A single value used to estimate a population parameter.
Interval Estimate: A range of values used to estimate a population parameter, typically expressed with a confidence level.
Sampling Bias: A bias introduced in a sampling process that leads to a non-representative sample of the population.
Nonparametric Statistics: Statistical methods that do not require the assumption of a specific probability distribution for the data.
Parametric Statistics: Statistical methods that assume a specific probability distribution for the data.
Robust Statistics: Statistical methods that are insensitive to violations of assumptions such as normality or homoscedasticity.
Power: The probability of correctly rejecting the null hypothesis when it is actually false.
Effect Size: A measure of the strength of the relationship between two variables in a statistical population.
Statistical Significance: The likelihood that a result or relationship is not due to chance, typically assessed using a significance test.
Degrees of Freedom: The number of independent pieces of information available to estimate a statistic.
Cramer’s V: A measure of association between two categorical variables, similar to Pearson’s correlation coefficient for continuous variables.
Bayesian Statistics: A statistical approach that uses Bayes’ theorem to update the probability of a hypothesis as new evidence becomes available.
Monte Carlo Simulation: A computational technique that uses random sampling to estimate the probability distribution of an outcome.
Bootstrapping: A resampling technique used to estimate the distribution of a statistic by repeatedly sampling with replacement from the original dataset.
Jackknife: A resampling technique used to estimate the bias and variance of a statistic by systematically omitting one observation at a time from the dataset.
Permutation Test: A nonparametric statistical test that assesses the significance of a result by randomly reassigning the labels of observations.
Cross-Validation: A technique used to assess the performance of a predictive model by splitting the data into training and testing sets.
Statistical Learning Theory: A framework that combines statistical and computational techniques to analyse and predict patterns in data.
Resampling Methods: Statistical techniques that involve repeatedly drawing samples from a dataset to estimate a population parameter.
Statistical Inference: The process of making predictions or decisions about a population based on sample data.
Statistical Model: A mathematical representation of a real-world process that allows for inference or prediction based on observed data.
Maximum Likelihood Estimation (MLE): A method for estimating the parameters of a statistical model by maximising the likelihood function.
Bayesian Information Criterion (BIC): A criterion for model selection that penalises models based on their complexity.
Akaike Information Criterion (AIC): A criterion for model selection that balances goodness of fit and model complexity.
Multivariate Analysis: Statistical techniques used to analyse relationships between multiple variables simultaneously.
Factor Analysis: A statistical method used to identify underlying factors or latent variables that explain patterns of correlations among observed variables.
Principal Component Analysis (PCA): A dimensionality reduction technique that transforms data into a new coordinate system to identify patterns and relationships.
Canonical Correlation Analysis (CCA): A multivariate statistical technique used to assess the relationship between two sets of variables.
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