C784 STATISTICS FULL COURSE REVIEW|37 QUESTIONS AND ANSWERS.

Lurking Variable Associated with the explanatory and the response variables that is not directly being studied. Simpson's Paradox Occurs when a trend or result that appears in groups of data disappears when we combine the data. Regression Analysis A process for estimating and analyzing the relationship between variables. Least-Squares Regression Line AKA the line of best fit. y = mx + b "rise over run" Interpolation Using existing data along with the Least-Squares Regression Line to make a prediction. Extrapolation Estimation by projecting OUTSIDE known data points. p-value the probability that a result occurred by chance Significance Levels in Hypothesis Testing Statistically Significant: If a measured p-value is less than the significance level. NOT Statistically Significant: If a measured p-value is MORE than the significance level. Empirical Rule 68 - 95 - 99.7 68% is w/in 1 standard deviation of the mean 95% is w/in 1 standard deviation of the mean 99.7% is w/in 1 standard deviation of the mean Used for Categorical (Qual) Data Bar Chart Pie Chart Mean Average - adding series then dividing by the total number in that series Center & Spread Measures SYMMETRIC - Mean (center) / Standard Deviation (spread) SKEWED - Median (center) / IQR (spread) CATEGORICAL - Mode (center) / no spread What is the difference between a bar chart and a histogram? BAR CHART - Categorical data distributed over groups of categories HISTOGRAM - Quantitative data distributed over various intervals Outlier Formula 1.5 x IQR above Q3 or below Q1 Graphical Displays for Quantitative Variables HISTOGRAMS - large data sets STEM PLOTS - keeps individual data points DOT PLOTS - smaller data sets BOX PLOTS - center, spread and 5 number summary SCATTER PLOTS - x,y axis 5 Number Summary Min - Q1 - Median - Q3 - Max Graphical Displays and Corresponding Numerical Analysis Tools for Examining Data Relationships C > C - Two-way Frequency Tables (aka Contingency Table) use conditional percentages and relative frequencies C > Q - Side-by-Side Boxplots use 5 number summaries Q > Q - Scatterplots use correlation coefficients InterQuartile Range (IQR) Q3-Q1 Standard Deviation Average distance each data point is from the mean 3 Types of Percentages on a Two-Way Frequency Table OVERALL% - (aka Relative Frequencies) When all of the counts are divided by the overall total CONDITIONAL ROW% - when the explanatory variable is in rows; calculated by dividing the joint frequencies of each row by the row total CONDITIONAL COLUMN% - when the explanatory variable is in the columns; calculated by dividing joint frequencies of each column by column total Right and Left Skew Right Skewed is positive (tail li.) Left Skewed is negative (tail .iI) Define Explanatory vs Response Variable EXPLANATORY VARIABLE (x/independent) - presumed to possible cause change in the response variable RESPONSE VARIABLE (y/dependent) presumed to be affected by the explanatory variable Correlation Coefficient aka "r", describes the direction and strength of the relationship of variables on a scatterplot. Between -1 and +1 0 = no correlation -1 = perfect negative correlation 1 = perfect positive correlation Linear Regression Equation aka the line of best fit, y = mx + b slope is m b is y intercep y is y (response) variable x is x (explanatory) variable Qualitative Descriptions with their Quantitative Probability Impossible = 0% possibility Unlikely = 1% to 30% probability As likely as unlikely = 40% to 60% probability Likely - 70% to 99% probability Certain - 100% probability Sample Space Denoted by "S", this is all possible outcomes in an experiment 3 ways of finding S: Lists, Trees and Tables Theoretical (Classical) Probability P(A) = # of outcomes of event / total # of outcomes in S (in this formula, A represents the event) Example: rolling a 2 on a 6 sided die P(2) = 1/6 P(2) = .17 Empirical (Observational) Probability This is based on an experiment. Relative frequency of an event = number of times event occurs / total number of trials The Law of Large Numbers as the number of trials increases, the relative frequency approaches the theoretical probability Complementary Event an event NOT happening Disjoint Event Event that cannot overlap or occur at the same time. P (A and B) = 0 P(A and B) = P(A) + P(B) Example: rolling a 5 AND a 6 with one die cannot both occur at the same time Multiplication Rule for Independent Events (AND) IF events A and B are independent AND disjoint: P(A and B) = P(A) * P(B) General Addition Rule for Independent Events (you are asked for "or") If events are independent and NOT disjoint and you are asked for events A OR B: P(A or B) = P(A) + P(B) - P(A and B) Conditional Probability of Dependent Events P(B | A) = probability of event B happening given that A occurred P(B | A) = P(A and B)/P(A) this is "both" divided by "given" Recap of disjoint and non disjoint probability formulas If A and B are disjoint events: P(A and B) = 0 P(A or B) = P(A) + P(B) If A and B are not disjoint events but are independent: P(A and B) = P(A) * P(B) P(A and B) = P(A) + P(B) - P(A and B) Probability and Complementary Rule w/ Formulas Number of desired events/Total number of events + the complement/Total number of events =1 OR P(A) + P(not A) = 1 1 - P(A) = P(not A) 1 - P(not A) = P(A) Because "at least one X" and "no X" are complements, it is always true that P(at least one X) = 1 - P(no X)