Statistics Exam Review

These flashcards cover key concepts and terminology from the statistics lecture notes, aiding in the understanding and retention of important definitions and principles.

Statistics

A set of mathematical tools and techniques used for collecting, analyzing, interpreting, presenting, and organizing data to understand patterns and trends.

Descriptive Statistics

A subset of statistics that focuses on summarizing and organizing data to provide a clear overview, often through numerical measures and visual aids.

Inferential Statistics

A branch of statistics that uses sample data to make generalizations, predictions, or inferences about a larger population, incorporating concepts like hypothesis testing.

Sample

A carefully selected group or subset of individuals or items from a larger population, used to represent that population in statistical analysis.

Population

The complete set of individuals, items, or observations that you are interested in studying and drawing conclusions about in your research.

Variable

Any characteristic, number, or quantity that can be measured or counted and can vary among subjects in a study, such as height, age, or test scores.

Data

Information collected from observations or measurements that can be qualitative (descriptive) or quantitative (numerical), forming the basis for analysis.

Central Tendency

A statistical measure that identifies a single score as representative of an entire distribution, including measures such as mean, median, and mode.

Mean

The average value of a set of numbers, calculated by summing all values and dividing by the total number of values.

Median

The middle value in a data set when the numbers are arranged in ascending or descending order; it divides the data into two equal halves.

Mode

The value or values that occur most frequently in a data set. A set can be unimodal (one mode), bimodal (two modes), or multimodal (multiple modes).

Standard Deviation (SD)

A statistic that quantifies the amount of variability or dispersion of a set of data points around the mean; a low SD indicates data points are close to the mean, while a high SD indicates they are spread out.

Range

The difference between the highest and lowest values in a data set, providing a measure of the spread of the data.

Variance

A statistical measure that describes how much individual data points differ from the mean; it is calculated as the average of the squared differences from the mean.

Outlier

A data point that significantly deviates from the other observations in a data set, which may indicate variability in measurement, experimental errors, or novel phenomena.

Histograms

A type of bar graph that represents the frequency distribution of a set of continuous data, showing how data points are distributed across different ranges.

Correlation Coefficient

A numerical value (ranging from -1 to 1) that quantifies the strength and direction of the relationship between two variables, indicating how changes in one variable might be associated with changes in another.

Reliability

The degree to which a measurement instrument consistently produces stable and repeatable results across different instances or samples.

Validity

The extent to which a test or measurement accurately assesses what it is designed to measure, ensuring the results are meaningful and applicable to the context.

Nominal Scale

A type of measurement scale that categorizes data into distinct, non-overlapping groups that do not have a meaningful order or ranking.

Ordinal Scale

A measurement scale that ranks data points in a specific order, indicating relative positioning, but does not provide information about the distance between ranks.

Interval Scale

A scale utilized for measuring data that has ordered values with equal intervals between them, but lacks a true zero point, making certain ratio comparisons meaningless.

Ratio Scale

A measurement scale that possesses all the properties of an interval scale but includes a true zero point, allowing for meaningful comparisons of absolute magnitudes.

Quantitative Data

Data that can be quantified and measured, often represented in numerical form, allowing for statistical analysis and mathematical operations.

Qualitative Data

Descriptive, non-numerical data that provides insights into characteristics, properties, and patterns; often gathered through interviews, surveys, or observation.

Data Set

An organized collection of related data points or values, often structured in a table format, enabling easier analysis and interpretation.

Statistical Significance

A determination regarding whether the observed results of an analysis are likely due to chance alone or if they reflect genuine effects within the population.

Sampling Error

The discrepancy that arises when a sample does not accurately reflect the characteristics of the entire population from which it was drawn, potentially leading to invalid conclusions.

Hypothesis Testing

A systematic method in statistics for making data-driven decisions, involving the formulation of a null hypothesis and an alternative hypothesis and determining the likelihood of the null being true.

P-value

A statistical measure that helps determine the significance of results in hypothesis testing, representing the probability of obtaining test results at least as extreme as those observed, under the null hypothesis.

Confidence Interval

A range around a sample statistic that provides an estimated range of values for a population parameter, reflecting the level of uncertainty associated with the estimate.

Regression Analysis

A statistical process for estimating the relationships among variables; it examines the effect of one or more independent variables on a dependent variable to predict outcomes.

Chi-Square Test

A statistical test employed to assess whether there is a significant association or difference between categorical variables, often used in research to analyze contingency tables.