Video Lecture: Descriptive and Inferential Statistics - Vocabulary Flashcards

Vocabulary flashcards covering core concepts from descriptive statistics, distributions, and inferential statistics as discussed in the video notes.

Central Limit Theorem (CLT)

States that the sum (or average) of a large number of independent, identically distributed random variables tends toward a normal distribution regardless of the original distributions.

Normal distribution (Gaussian)

A symmetric bell-shaped distribution that many statistical methods assume; characterized by its mean and standard deviation.

Type I Error

Rejecting a true null hypothesis (false positive); the probability of this error is denoted by alpha.

Type II Error

Failing to reject a false null hypothesis (false negative); the probability of this error is denoted by beta.

Significance level (alpha)

The probability threshold for rejecting the null hypothesis when it is true (commonly 0.05).

Power of a test

The probability of correctly rejecting a false null hypothesis; equal to 1 minus beta.

R-squared (coefficient of determination)

Measures the proportion of variance in the dependent variable explained by the model; ranges from 0 to 1, with 1 indicating a perfect fit.

Correlation

A measure of the strength and direction of a linear relationship between two variables; does not imply causation.

Causation

A cause-and-effect relationship where changes in one variable bring about changes in another.

Lurking variable (confounding variable)

An outside factor that affects both variables of interest, potentially creating a spurious association.

Parametric tests

Statistical tests that assume a specific population distribution (often normal), e.g., t-tests, ANOVA.

Non-parametric tests

Tests that do not assume a specific population distribution; e.g., Mann-Whitney U, Kruskal-Wallis.

p-value

The probability of observing the data (or more extreme) under the null hypothesis; used to decide on reject/fail to reject.

Cross-validation

A model evaluation method that partitions data into training and validation sets to assess performance.

k-fold cross-validation

A form of cross-validation where data are split into k subsets; train on k-1 and test on the remaining fold, rotating.

Bootstrapping

A resampling technique (sampling with replacement) used to estimate the distribution of a statistic.

Descriptive statistics

Techniques that summarize data (e.g., central tendency and dispersion) without making inferences about a population.

Mean

Arithmetic average of a set of numbers.

Median

The middle value in an ordered data set.

Mode

The most frequently occurring value in a data set.

Population

The entire group of interest in a study.

Sample

A subset drawn from a population used to estimate population characteristics.

Parameter

A numerical characteristic of a population (e.g., population mean).

Statistic

A numerical characteristic computed from a sample (e.g., sample mean).

Handling missing data by deletion

Removing records with missing values (listwise or pairwise deletion).

Imputation

Replacing missing values with estimated values (mean/median/mode or model-based).

Interquartile Range (IQR)

Q3 minus Q1; a robust measure of dispersion not affected by extreme values.

Skewness

A measure of asymmetry in a distribution; negative means left tail longer, positive means right tail longer.

Box plot

A graphical display showing the median, Q1, Q3, and whiskers (min/max) of a dataset.

Variance

Average of the squared deviations from the mean.

Standard deviation

Square root of the variance; measures spread in the same units as the data.

Range

Difference between the maximum and minimum values in a dataset.

Z-score

The number of standard deviations a value is from the mean: z = (X − μ) / σ.

Covariance

A measure of how two variables vary together; not standardized.

Pearson correlation coefficient (r)

A standardized measure of linear relationship between two variables, ranging from -1 to 1.

Kurtosis

A measure of the tailedness or extremity of a distribution's tails.

Simpson's Paradox

A trend observed within subgroups reverses when data are aggregated across groups.

Outliers

Values far from the rest of the data that can distort statistics like the mean.

Log transformation

Applying a logarithm to data to reduce skew and stabilize variance.

Histogram

A bar chart showing the frequency distribution of data divided into bins.

Probability Density Function (PDF)

A function describing the probability distribution of a continuous random variable.

Probability Mass Function (PMF)

A function describing the probabilities of the discrete outcomes of a random variable.

Poisson distribution

A discrete distribution for counting rare events; parameter λ equals the mean rate.

Binomial distribution

Distribution of the number of successes in n independent Bernoulli trials with probability p.

Hypothesis testing

A framework for testing assumptions about a population using sample data.

A/B testing

An experimental design comparing two versions (A and B) to determine which performs better.

Null Hypothesis (H0)

A statement of no effect or no difference to be tested against.

Alternative Hypothesis (HA)

A statement that there is an effect or difference to be detected.

Independent samples t-test

Tests whether the means of two independent groups are different.

Paired t-test

Tests whether the means of paired observations (e.g., before/after) differ.

ANOVA (Analysis of Variance)

A test comparing means across three or more groups to see if at least one differs.

Chi-square test

Tests independence between categorical variables or goodness-of-fit of observed frequencies.