Mr. Meinzen - Introduction to Statistics Terminology

Chapter 1 Terminology

Fathom Software

• Toolbar
• Inspection Window
• Formula Editor
• Collection
• Case or Cases
• Table (or Case Table)
• Graph
• Summary Table
• Attribute
• Value

Excel Software

• Graphs & Labeling (horizontal and vertical axes, title)

Statistical Terms

• Data
• Summary Statistic (mean, median, mode, etc.)
• Analyze

Chapter 2 Terminology

• univariate data

• quantitative variable (aka attribute in Fathom software)
• categorical (or qualitative) variable (aka attribute in Fathom software)

• graphs (plots)

• bar chart
• dotplot
• stemplot
• histogram or relative frequency plot
• boxplot (box-and-whisker plot) and modified boxplot
• outlier (resistant vs sensitive to) , clusters, gaps

• shape of distribution

• symmetric
• uniform (or rectangular) distribution
• normal distribution
• skewness
• left skewed distribution
• right skewed distribution
• other
• bimodal distribution

• CENTER [summary statistic: single value measurement or computation]

• mean
• median
• mode (only for bimodal)

• SPREAD [summary statistic: single or multiple valued measurement or computation]

• deviation (or residue)
• standard deviation
• variance
• quartiles (ranges)
• 5-number summary [min, Q1, Q2 (median), Q3, max]
• interquartile range (IQR)

• statistical (math or calculator) symbols and terms

• x-bar [also the formula to calculate]
• s or SD [also the formula to calculate]
• z-score [also the formulat to calculate as well as re-centering and re-scaling]
• percentages calculated from normal curve
• normalcdf ( leftbound, rightbound, mean, SD )
• invNorm ( area, mean, SD )

Chapter 3 Terminology

• bivariate data (from Chapter 3): shape -> trend -> strength -> variability

  • plausible explanation : causation, common response, or confounding
  • lurking variable
  • residual plots
  • outliers

• scatter plots : shape -> trend -> strength -> variability

  1. data's shape : linear, curved, or none
  1. y = a₁ + b₁*x [equivalent to algebra equation of line : y = mx + b]
  2. shape's trend : positive slope, negative slope, or none
  1. b₁ : measure of slope
  3. trend's strength : strong trend (tight cluster), moderate trend (some clustering), or weak trend (no cluster)
  1. correlation : a measure of a trend's strength
  4. strength's variability : uniform or heteroscedasticity (fan-shaped)

• summary line

• • Least Squares Regression Line (also called LSRL)
  • Line of Best Fit (best guess or LSRL)
  • Regression Line (LSRL)
  • Trend Line (LSRL)
  • Fitted Line (best guess)

• statistical (math or calculator) symbols and terms

• randomNormal ( mean, SD )
• least squares regression line ("regression line" or just LSRL) : y = a₁ + b₁*x
• explanatory variable or predictor variable, x
• response variable or observed variable, y
• slope, b₁
• y-intercept, a₁
• predicted value, ŷ
• interpolations, extrapolation
• influential point
• residual
• sum of square errors (SSE)
• r : correlation coefficient
• r² : coefficient of determination
• "correlation does not imply causation" due to lurking variable

Chapter 4 Terminology

• units (and population size)
• population
• census & sample
• parameter & statistic

• sample bias

• selection bias
• size bias
• volunteer bias
• convenience bias
• judgement bias
• nonresponsive bias
• questionnaire bias
• wording or language bias
• incorrect response bias

• samples - unbiased representatation of population

• simple random sample (SRS)
• stratified random sample
• cluster sample
• two-stage cluster sample
• systematic sample with random start

• experiment vs observational study

• blind experiment, double blind experiment
• treatment
• factor (categorical)
• level
• experimental unit
• response variable
• designs of experiments
• completely randomized design
• randomized paired comparison design
• randomized block design
• variables in experiments
• explanatory variable or factor (if catagorical)
• response variable
• lurking variable
• confounding variable
• variability
• between-treatment
• within-treatment

Chapter 5 Terminology

• event
• table of random digits
• venn diagrams

• Probability

• event, P(A)
• complement of event, P(A_c)
• distribution
• model
• mutually exclusive [disjoint categories]
• conditional events
• independent events
• "of at least one"
• variance & standard deviation

• Sampling

• space
• with Replacement
• without Replacement

• Mathematical

• Law of Large Numbers
• Fundamental Counting Principle
• Terminology with Probabilities
  • Complement of Event : P(A_c) = 1 - P(A)
  • P("of at least one") = 1 - P("exactly none")
  • Mutually Exclusive Events [i.e. disjoint] : P(A and B) = 0
  • Conditional Events : P(A|B) = P(A and B) / P(B) often written as P(A and B) = P(A|B) * P(B)
  • Independent Events : P(A|B) = P(A)
• Addition Rules ["or"]
  • Full Rule : P(A or B) = P(A) + P(B) - P(A and B)
  • Simplified Rule for Mutually Exclusive Events [disjoint] : P(A or B) = P(A) + P(B)
• Multiplication Rules ["and"]
  • Full Rule : P(A and B) = P(A) * P(B|A) can also be writen as P(A and B) = P(B) * P(A|B)
  • Simplified Rule for Independent Events : P(A and B) = P(A)*P(B)

Chapter 6 Terminology

• Probability Distributions
• Random Variable, X
• Expected Value, E(X)
• mean, u_x
• standard deviation, s_x
• from Collected Data
• using Known Data Frequencies that model Your Situation
• simulation using Random selection from a known data
• from Theory
• assumptions + Basic Mathematical Principles
• Binomial Distributions
• n = number of trials
• p = probability of success on any one trial
• 1-p = q = probability of failure on any one trial
• P(X = k) = _nC_k p^k (1 - p)^{n - k}
• binompdf(number of trials, probability of success, number of successes)
• Normal Distribution ~ BINS (binomial, independant, number of trials is fixed, success probabilities is known)