The branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data to uncover patterns, quantify uncertainty, and make informed, evidence-based decisions.
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A statement that contradicts the null hypothesis, proposing that there is a significant difference, effect, or relationship between variables in the population. It represents what the researcher typically wants to find evidence for.
A variable that places individuals into one of several distinct groups or categories, typically represented by labels rather than numerical values. Examples include gender, color, or type of car.
A fundamental theorem stating that the distribution of sample means (or sums) from any population will approach a normal distribution as the sample size increases, regardless of the original population's distribution.
A range of values, calculated from sample data, that is likely to contain the true value of an unknown population parameter with a specified level of confidence. It provides an estimated interval for the parameter.
A quantitative variable that can take any value within a given range or interval, including fractions and decimals. Its values are typically obtained by measurement, such as height or temperature.
Methods used to organize, summarize, and present data in a meaningful way, often through graphs, tables, and summary measures like means and percentages. Its goal is to describe the main features of a dataset.
A quantitative variable whose possible values are countable and often represent counts of items or occurrences. There are gaps between its possible values, like the number of children in a family.
A formal statistical procedure used to make decisions about a population parameter based on sample data. It involves formulating hypotheses, collecting data, and calculating a test statistic to evaluate the evidence.
Methods that use data from a sample to make generalizations, predictions, or decisions about a larger population. It involves hypothesis testing and confidence intervals to draw conclusions beyond the observed data.
A measure of statistical dispersion, representing the range of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
A level of measurement where data can be ordered, and the differences between values are meaningful and consistent. However, there is no true zero point, so ratios are not meaningful. Examples include temperature in Celsius or Fahrenheit.
The arithmetic average of a set of numbers, calculated by summing all values in the dataset and then dividing by the total count of values. It is sensitive to extreme outliers.
The middle value in a dataset that has been ordered from least to greatest, effectively dividing the data into two equal halves. It is less affected by extreme outliers than the mean.
The value or category that appears most frequently in a dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode if all values appear with the same frequency.
A level of measurement where data can be categorized into distinct groups, but these categories have no inherent order or ranking. Examples include gender, hair color, or religious affiliation.
A continuous probability distribution characterized by its symmetric, bell-shaped curve, where the mean, median, and mode are all equal. It is widely used to model natural phenomena and errors.
A statement that assumes there is no significant difference, no effect, or no relationship between variables in the population. It is the hypothesis that researchers aim to test and potentially reject.
A level of measurement where data can be categorized and ranked in a meaningful order, but the differences or intervals between categories are not uniform or quantifiable. Examples include letter grades or satisfaction ratings.
The probability of obtaining observed results, or results more extreme, if the null hypothesis were true. A small p-value suggests strong evidence against the null hypothesis.
A numerical characteristic or measure that describes an entire population, often unknown and estimated using data from a sample. Examples include the population mean or standard deviation.
The entire group of individuals, objects, or events that a researcher is interested in studying and about which conclusions are to be drawn. It represents the complete set of possible observations.
A numerical measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
A mathematical function that describes all possible values and the likelihoods that a random variable can take within a given range. It can be discrete or continuous.
A variable that takes numerical values for which arithmetic operations such as addition and averaging make sense. These variables measure a quantity or amount.
A variable whose value is a numerical outcome of a random phenomenon or experiment. Its specific value cannot be predicted with certainty before the event occurs.
A measure of spread calculated as the difference between the maximum and minimum values in a dataset. It provides a quick, but often limited, idea of the total variability.
A level of measurement where data can be ordered, differences between values are meaningful, and there is a true and absolute zero point, allowing for meaningful ratios. Examples include height, weight, or income.
A subset of individuals, objects, or events selected from a larger population, intended to represent the characteristics of that population. It is used to make inferences about the larger group.
A measure of the typical amount of variation or dispersion of data values around the mean. It is the square root of the variance and is expressed in the same units as the original data.
A numerical characteristic or measure calculated from sample data, used to describe the sample or to estimate a population parameter. Examples include the sample mean or standard deviation.
The scientific discipline focused on the collection, analysis, interpretation, presentation, and organization of data. It provides methods for drawing conclusions from data and making decisions in the face of uncertainty.
The error of rejecting a null hypothesis when it is actually true. This is often considered a 'false positive' and its probability is denoted by alpha (α), the significance level.
The error of failing to reject a null hypothesis when it is actually false. This is often considered a 'false negative' and its probability is denoted by beta (β).
A characteristic, attribute, or quantity that can be measured or observed and can take on different values or categories for different individuals or objects. It is the fundamental unit of data collection.
A measure of how spread out a set of data is from its mean, calculated as the average of the squared differences from the mean. A higher variance indicates greater variability.