CHAPTER 3 ALL PARTS: Business Statistics and Data Analytics Flashcards

Vocabulary flashcards covering core concepts of business statistics and data analytics, including populations, sampling, bias, descriptive statistics, probability distributions, hypothesis testing, t-tests, ANOVA, chi-square, correlation, and regression analysis.

Population

A group of phenomena or items that have something in common, composed of every item of interest in that group.

Parameter

A measure or characteristic that describes an entire population.

Sample

A representative subset of a population used to collect data and make inferences.

Statistic

A measure or characteristic calculated from a sample.

Inference

A conclusion drawn about the characteristics of a population based on sample data.

Descriptive Statistics

Measures that describe, summarize, and display the basic features of a data set from a sample or population.

Inferential Statistics

Measures calculated using sample data to test hypotheses and draw conclusions about a broader population.

Hypothesis

A proposed explanation made on the basis of limited evidence as a starting point for further investigation.

Simple Random Sampling

A sampling method where every observation in the population has an equal chance of selection.

Stratified Random Sampling

A sampling method where a population is divided into subgroups (strata) and a random sample is taken from each stratum to ensure proportional representation.

Cluster Sampling

A sampling method where a population is divided into groups (clusters), and only a select few clusters are chosen for study.

Convenience Sampling

A non-probability sampling method that selects easily accessible data points, often used when time or budget is constrained.

Data Reduction

The process of reducing the size of a data set to a manageable and suitable size for business analysis.

Filtering

A data reduction process in tools like Excel, Power BI, and Tableau that removes unwanted rows based on specific column attributes.

Bias

An intentional or unintentional prejudice in favor of or against a thing, person, group, or idea during data collection, analysis, or presentation.

Nonresponse Bias

Bias that occurs when individuals who opt out of responding to a survey differ systematically from those who do respond.

Selection Bias

Bias occurring when an analyst purposefully selects sample portions likely to yield answers supporting their personal beliefs or hypothesis.

Confirmation Bias

Bias that occurs when analysts evaluate or present data in a manner that confirms pre-existing beliefs while ignoring conflicting evidence.

Outlier Bias

The disproportionate impact exerted by extreme values (outliers) on statistical results and interpretations if left unexplained.

Continuous Data

Numerical data that can take on any real value within a range, including non-integers, representing an infinite set of potential values.

Discrete Data

Numerical data consisting only of whole numbers (integers), representing a finite set of values between observations.

Mean

A measure of central tendency representing the arithmetic average of a data set, calculated as total sum divided by $n$.

Median

The middle value in an ordered data set, representing the cutoff where $50\%$ of observations lie below and above.

Mode

The most frequently occurring observation in a data set, which serves as the primary measure of central tendency for categorical data.

Symmetry

A distribution shape where the mean, median, and mode are all equal, creating a balanced shape around the center.

Right-Skewed Distribution

A positively skewed distribution with a long tail to the right, where the mean is pulled above the median by high extreme values.

Left-Skewed Distribution

A negatively skewed distribution with a long tail to the left, where the mean is pulled below the median by low extreme values.

Kurtosis

A measure describing the thickness of the tails and the peakedness of a distribution relative to a normal shape.

Leptokurtic Distribution

A distribution characterized by positive excess kurtosis, featuring a taller peak and fatter tails with higher risk of extreme outcomes.

Platykurtic Distribution

A distribution characterized by negative excess kurtosis, presenting a flatter peak and thinner tails.

Range

A basic dispersion measure calculated as the difference between the maximum and minimum values in a data set ($\text{Maximum} - \text{Minimum}$).

Interquartile Range (IQR)

A dispersion measure focusing on the middle $50\%$ of a distribution, calculated as the difference between the third and first quartiles ($Q3 - Q1$).

Variance

A measure of dispersion calculated as the average of squared deviations from the mean for each observation.

Standard Deviation

The square root of variance, measuring data spread around the mean in the same units as the original observations.

Normal Distribution

A symmetric, bell-shaped continuous probability distribution where values close to the mean occur with highest frequency.

68-95-99.7 Rule

An empirical rule stating that $68\%$ of normal data lies within $\pm 1$ SD, $95\%$ within $\pm 2$ SDs, and $99.7\%$ within $\pm 3$ SDs of the mean.

Standard Normal Distribution

A theoretical normal distribution with a mean of $0$ and a standard deviation of $1$.

Z-Score

A standardized value measuring how many standard deviations an observation falls above or below the mean.

Uniform Distribution

A rectangular continuous probability distribution where every outcome within a defined interval is equally likely to occur.

Frequency Distribution

A tabular arrangement using bins or categories to list the frequency of occurrence for values in a sample.

Histogram

A visual graph of a frequency distribution using contiguous vertical bars whose heights reflect counts in each bin.

Box Plot

A diagram displaying data spread across quartiles, showing the IQR box ($Q1$ to $Q3$), median line, mean marker ($\text{x}$), and whiskers.

Point Estimate

A single calculated sample statistic used as an estimate for an unknown population parameter.

Confidence Interval

A range around a point estimate calculated as $\text{Point Estimate} \pm \text{Margin of Error}$ at a chosen confidence level.

Margin of Error

The distance above and below a point estimate that defines a confidence interval, based on confidence level and standard error.

Null Hypothesis ($H_0$)

The base case statement assuming no relationship, effect, or significant difference exists between groups.

Alternative Hypothesis ($H_A$)

The claim tested against the null hypothesis asserting that a specific effect, difference, or relationship exists.

Two-Tailed Hypothesis Test

A statistical test evaluating whether a difference exists between groups in either direction.

One-Tailed Hypothesis Test

A statistical test evaluating a difference between groups in a specific directional orientation.

Significance Level ($\alpha$)

The probability threshold set by an analyst for rejecting the null hypothesis, representing the risk of a Type I error.

Type I Error

An error that occurs when the null hypothesis is rejected when it is actually true (acting on something that is false).

Type II Error

An error that occurs when failing to reject the null hypothesis when the alternative hypothesis is actually true (missing a true effect).

Hypothesis Testing Decision Matrix

A grid mapping hypothesis decisions (Different vs. Same) against population reality (Different vs. Same), identifying Type I error (Decision: Different, Reality: Same) and Type II error (Decision: Same, Reality: Different).

p-Value

The probability that sample test statistics occurred purely by chance under the assumption that the null hypothesis is true.

Independent t-Test

A statistical test comparing means between two unrelated or independent numerical groups.

Paired t-Test

A hypothesis test comparing means between two related or paired groups, such as pre-test and post-test scores on identical subjects.

ANOVA (Analysis of Variance)

A hypothesis test evaluating whether statistically significant differences exist among the means of three or more numerical groups.

Chi-Square Test

A statistical test examining differences or relationships between observed and expected categorical data distributions.

Correlation

A measure of linear association describing how two variables move together relative to one another.

Correlation Coefficient

A standardized statistic ranging from $-1$ to $1$ indicating the strength and direction of linear association between two variables.

Linear Regression Analysis

A statistical technique measuring the relationship between a dependent variable ($y$) and one or more independent variables ($x$) to predict outcomes.

Dependent Variable

The output variable ($y$) being predicted in a regression equation based on changes in independent variables.

Independent Variable

An input variable ($x$) in a regression model used to explain or predict variations in the dependent variable.

Line of Best Fit

The linear regression line ($y = mx + b$) that mathematically best represents the linear trend across data points.

R Square ($R^2$)

A goodness-of-fit measure ranging from $0$ to $1$ representing the proportion of variance in the dependent variable explained by independent variables.

Adjusted R Square

A modified goodness-of-fit statistic for multiple regression that increases only when new independent variables genuinely improve model prediction.

Binomial Distribution

A discrete probability distribution modeling scenarios with a fixed number of independent trials and exactly two possible outcomes.

Poisson Distribution

A discrete probability distribution modeling the count of occurrences of an event over a specified unit of time or space.

Standard Error (SE)

A measure quantifying the expected variability of sample means around the true population mean, calculated as $SE = \frac{s}{\sqrt{n}}$. Standard error shrinks as sample size increases.

Mesokurtic Distribution

A distribution shape with kurtosis equal to that of a standard normal distribution (excess kurtosis = $0$)—neither unusually peaked nor unusually flat.

Simple Linear Regression

A regression model that uses exactly one independent variable ($x$) to predict a continuous dependent variable ($y$).

Multiple Linear Regression

A regression model that uses two or more independent variables to predict a continuous dependent variable, improving predictive power over simple linear regression.

One-Sample t-Test

A hypothesis test used with numerical data to determine if a sample mean significantly differs from a known or hypothesized benchmark value.

Significance F

A regression output statistic testing overall model validity; a Significance F value below alpha ($\alpha$) indicates the regression model predicts significantly better than a baseline intercept-only model.

p-Value Hacking

The unethical practice of testing multiple sample subsets or altering significance thresholds after the fact to manipulate results until statistical significance ($p \le \alpha$) is achieved.

Correlation vs. Causation

A statistical principle stating that neither correlation nor regression proves a cause-and-effect relationship; they measure mathematical association and predictive alignment only, not causation.