A comprehensive term that refers to the sum total of individual elements. Commonly used in various fields such as economics, statistics, and business to describe the collective or total amount.
In statistical testing, an alternative hypothesis is accepted if a sample contains sufficient evidence to reject the null hypothesis. It is usually denoted by H₁. In most cases, the alternative hypothesis is the expected conclusion, which is why the test was conducted in the first place.
A statistical model used to determine whether there are any statistically significant differences between the means of three or more independent groups.
A bar graph is a type of chart that displays information by representing quantities as rectangular bars of different lengths either vertically or horizontally. Bar graphs are widely used in statistics, finance, business, and other quantitative fields to visualize data distributions and comparisons.
The Bayesian Approach to Decision Making is a methodology that incorporates new information or data into the decision process. It is especially useful when making decisions for which insufficient empirical estimates are available.
A measure that indicates the typical value of a distribution. It is used in statistics to summarize a set of data by identifying the central point within that set.
A statistical method to test whether two (or more) categorical variables are independent or if they share a common proportion of observations. Frequently used in hypothesis testing and categorical data analysis.
Test statistic that quantifies the amount of variability in a dependent variable explained by the regression model's independent variable(s).
The Coefficient of Determination, denoted as R^2, measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is commonly used in the context of regression analysis to determine how well the model fits the data.
Combinations refer to the different subgroups that can be formed by sampling a larger group or population without considering the order of elements. Combinations are essential in probability, statistics, and various branches of mathematics.
A Combined Statistical Area (CSA) is defined by the U.S. Census Bureau as a combination of several adjacent Metropolitan Statistical Areas (MSAs) or Micropolitan Statistical Areas (μSAs), or a mix of the two, which are linked by economic ties.
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the interval.
A contingency table is a type of data matrix presenting sample observations classified by two or more characteristics, such as categories or attributes.
Correlation refers to the statistical measure that describes the degree to which two variables move in relation to each other. Its value ranges between -1 and 1, indicating the strength and direction of the relationship.
A statistical measure of the degree to which the movements of two variables are related. It quantifies the direction and strength of the relationship between variables.
Cost prediction involves forecasting future cost levels based on historical cost behavior using various statistical techniques, such as linear regression, to inform budgeting, decision-making, and strategic planning.
The Coupon Collector's Problem is a classic example in probability theory concerning how many trials are expected to collect all possible outcomes. This can be represented by the process of collecting coupons, each of which represents a unique outcome in a finite sample space.
Covariance is a statistical measure that indicates the extent to which two variables change together. A positive covariance suggests that the variables tend to increase or decrease in tandem, whereas a negative covariance indicates that as one variable increases, the other tends to decrease.
In the field of statistics, a dependent variable is the subject of an equation whose value depends on independent variables. Typically denoted as 'Y', the dependent variable is influenced or predicted by the independent variables, often denoted as 'X'.
A statistical method used in auditing and quality control to ensure that the proportion of units with a particular attribute (such as an error) does not exceed a predefined threshold in a population.
Disjoint events, also known as mutually exclusive events, are pairs of events in a probability space that cannot occur at the same time.
Economic indicators are key statistics that provide insight into the state of the economy. They help policymakers, business leaders, and investors make informed decisions about economic activities.
A division of the U.S. Department of Commerce that provides timely economic analysis, disseminates national economic indicators, and oversees the U.S. Census Bureau and the Bureau of Economic Analysis (BEA).
Expected Value (EV) is a fundamental concept in probability and statistics used in decision making, which represents the average outcome when accounting for all possible scenarios, weighted by their respective probabilities.
The concept of factorial is used both in statistics and mathematics to describe either a certain type of experimental design or the product of all positive integers up to a given number.
A frequency diagram is a type of bar diagram that illustrates how many observations fall within each category. It is a fundamental tool in statistics for data visualization.
The geometric mean is a measure of central tendency obtained by multiplying all the numbers in a set together and then taking the *n*th root of the resulting product, where *n* is the total number of values in the set.
The geometric mean is a type of mean that is calculated by taking the n-th root of the product of n numbers. It is particularly useful for sets of numbers whose values are meant to be multiplied together or are exponential in nature, such as rates of growth.
A statistical procedure used to test the hypothesis that a particular probability distribution adequately fits an observed set of data.
A histogram is a type of bar graph that represents the frequency of data occurrences within certain intervals or bins. It is a fundamental tool in statistics for illustrating the distribution of numerical data.
Independent events are two or more events whose occurrences do not affect one another. Understanding the independence of events is crucial in probability theory and statistics.
Two or more variables that are in no way associated with or dependent on each other.
An interval scale is a level of measurement in which the difference between observations provides meaningful information. Unlike nominal and ordinal scales, interval scales provide exact differences between values but lack a true zero point.
The Law of Large Numbers (LLN) is a mathematical principle that states that as the number of exposures increases, the results become more predictable and closer to the expected outcomes.
Life expectancy refers to the average age a person is expected to live based on actuarial calculations, which consider several factors including sex, heredity, and health habits. This metric is crucial for insurance companies in projecting benefit payouts and determining rates through actuarial analysis.
Management Science pertains to the study of management with a focus on using mathematics and statistics to resolve production and operations problems. It provides management with a quantitative basis for decision-making.
A matrix is a mathematical term describing a rectangular array of elements such as numerical data, parameters, or variables. Each element within a matrix has a unique position, defined by the row and column.
The Arithmetic Mean is a statistic calculated as the sum of all values in the sample divided by the number of observations. It is a fundamental measure of central tendency used in statistical analysis.
The median is a statistical measure that represents the middle value in a data set, effectively dividing the dataset into two equal halves. It is particularly useful in representing a data set without the distortion that large deviations can cause with the average (mean).
Mode refers to the manner of existing or acting; way, method, or form. In statistics, it represents the most commonly occurring value in a data set.
The nominal scale is a level of measurement where observations are distinguished by name alone. Examples include types of housing such as single-family, patio home, condominium, or townhouse. It is considered the weakest form of measurement.
Normal distribution, in statistics, is a continuous probability distribution that is perfectly symmetrical around the mean, signifying that data near the mean are more frequent in occurrence than data far from the mean. It is completely defined by its mean and standard deviation.
In statistical hypothesis testing, the null hypothesis (H0) is the default or initial statement assumed to be true, often stating that there is no effect or no difference. The null hypothesis is only rejected if the evidence from the data significantly contradicts it.
A p-value is a statistical measure that helps researchers determine the significance of their results. This value helps assess whether the observed data supports the null hypothesis or not.
A parameter is a measure used to describe a population, such as the number of rental units in a given city. Parameters are known for certain, whereas estimates are derived from samples.
A statistical term used to express a quantity as a portion of the whole, which is assigned a value of 100. Price changes are often reported as percentage increases or declines.
A statistical ranking designation where the pth percentile of a list is the number such that p percent of the elements in the list are less than that number.
Permutations refer to the different arrangements or orderings of a set of items, where the order of elements is crucial in their selection.
The Poisson distribution is a type of probability distribution that typically models the count or number of occurrences of events over a specified interval of time or space.
Population refers to the entire pool of individuals or entities that share a common characteristic from which statistical samples can be drawn for a study.
A term used in statistics to describe the direct association between two variables, indicating that as one variable increases, the other variable also increases. Positive correlation is typically represented by correlation coefficients greater than 0.
Probability is the likelihood that a particular outcome will occur, quantified on a scale from 0 (indicating certainty that it will not occur) to 1 (indicating certainty that it will occur). It is a key concept in decision-making models, often subjective in nature.
In statistics, a probability density function (PDF) defines the likelihood of a discrete or continuous random variable taking specific values or a range of values, respectively.
Quantitative Analysis involves using mathematical and statistical methods to evaluate investments, business operations, and financial data.
Quartiles are statistical measures dividing a data set into four equal parts. Each quartile represents a rank order segment in the distribution of the data. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) or the median represents the 50th percentile, the third quartile (Q3) represents the 75th percentile, and the fourth quartile (Q4) represents the upper range of data.
A random sample is a subset of individuals selected from a larger population in such a way that every individual has an equal and independent chance of being chosen.
A random variable is a fundamental concept in statistics used to describe quantities that have no fixed value but instead are subject to variability due to random phenomena.
A program that generates a sequence of numbers that seem to be completely random. Random numbers provide a way of selecting a sample without human bias.
Range is a key metric used in various fields, such as investment and statistics, to measure the scope of data or price fluctuations within a specific period.
The highest level of measurement in which not only the differences between observations are quantifiable, but the observations can themselves be expressed as a ratio. It is the most powerful measurement scale.
A regression line is a line calculated in regression analysis that is used to estimate the relationship between two quantities, the independent variable and the dependent variable.
Sampling is a fundamental aspect of fields like marketing research and sales promotion, facilitating the study and testing of small groups to draw conclusions or stimulate usage in larger populations cost-effectively.
Simple Linear Regression: Method for Analyzing the Relationship Between One Independent Variable and One Dependent Variable
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. It is widely used in situations where comparing variability between different data sets or understanding the consistency of data points is crucial.
The standard error measures the accuracy with which a sample distribution represents a population by indicating the degree of variability or dispersion present in the sample.
A statistic is a descriptive measure calculated from data sampled from a population, used to make inferences about the overall population. It serves as a fundamental element in the field of statistics, aiding in data analysis, hypothesis testing, and predictive modeling.
Statistical modeling refers to the process of applying statistical analysis to a set of data in order to identify patterns, understand relationships, and make predictions.
Statistically significant is a term used in hypothesis testing to determine whether a test statistic meets or exceeds a predetermined threshold, leading to the rejection of the null hypothesis.
Statistics is the study of ways to analyze data. It consists of Descriptive Statistics and Statistical Inference.
Stratified Random Sampling is a method used to divide a population into distinct subgroups or strata, which are independently sampled to achieve more precise estimates.
The T-statistic is a statistical measure used to compare the means of two groups or to assess if a sample mean significantly differs from a known value. It is instrumental in hypothesis testing, particularly when the sample size is small, and the population standard deviation is unknown.
A measure calculated from data sampled from a population, used to either reject or fail to reject the null hypothesis.
The use of historical data and mathematical techniques to model the historical path of a price, demand for a good, or consumption. Time series analysis is based on the premise that by knowing the past, the future can be forecast.
A two-tailed test, also known as a two-sided or nondirectional test, is a method in hypothesis testing that examines whether two estimates of parameters are equal without considering which one is smaller or larger. This type of test rejects the null hypothesis if the test statistic is significantly small or large.
Two-Way ANOVA is a statistical test procedure that assesses the effect of two independent variables on a dependent variable by examining the interaction between these variables.
An unbiased estimator is a statistical term referring to a method of estimating a population parameter, where the average of several random samples results in an estimate equal to the population parameter itself.
In statistics, the term 'universe' represents all possible elements within a particular set. For example, the universe of shoppers in a country would encompass every individual who engages in shopping activities within that country.
A variable is a data item that can change its value; it is also referred to as a factor or an element in various fields such as statistics, computer science, and mathematics.
