Introduction to Statistics Questions and Answers 2023

Introduction to Statistics Questions and Answers 2023 Statistics A set of tools and techniques that is used for describing, organizing, and interpreting information or data Example of statistics Number of students in a particular curriculum speed of problem-solving, or average cost of dinner Purpose of statistics Making decisions with incomplete data Data A record of an observation or an event such as a test score, grade in a class, or response time, one! Data Set A collection of observations or events such as test scores, grades on a test, or response times Descriptive statistics Used to organize and describe the characteristics of a collection of data; measures of central tendency (CT) and measures of variability Inferential statistics Used to make generalizations from a smaller group of subjects (a sample to a larger group of subjects (a population); won't have access to the entire population Population A group of people that have at least one characteristic in common (All Aggies) Sample A subset of a population (Certain subset of Aggies) Statistic A summarized value of a sample (Avg. Age of Aggies) Parameter A summarized value of a population (avg. age of the entire population of aggies) Variables A characteristic (of a person, place, or thing) that takes on different values (Achievement, attitude, knowledge, etc) Types of variables Quantitative (Numerical) and Qualitative (Categorical Quantitative Variable Represent differing amounts of the characteristic (Age, intelligence, or run time, etc.) Qualitative Variable Represent differing kinds rather than amounts (Gender, marital status, or breed of dog, etc.) Continuous Variables Variables that can take on any value (number of free throws made, GRE score, or number of students in class) Discrete Variables Variables that can take of a finite number of values (marital status, gender, or a year in school) Dichotomous variable either male or female Univariate Data When a study involved studying only one variable (Speed) Bivariate Data When a study involves studying two variables simultaneously (Strength and throwing distance) Purpose four levels of measurement Help the research determine what types of statistical analyses are appropriate for a given set of data Nominal Scale (Names) Values merely name the category to which the object under study belongs, interpretations are limited to statements of kind rather than amount (Italian, Irish...) Ordinal Scale Outcomes can be ordered or ranked to reflect differing degrees or amounts of the characteristic being studied (first vs. second vs. third) Does not give info about the difference between first and second, second and third Interval Scale Value assigned is based on some underlying continuum that has equal intervals (The 2-point difference between 3 and 5 and 7 and 8, drop in temp from 30C to 10C same as 50C to 30C) (Includes meas. of aptitude, achievement, or attitude) Social Sciences Parametric statistical techniques underlying distributions assumed to be normal Ratio Scale Has the same characteristics as the interval scale and also has an absolute zero, absolute zero implies that there can be an absence of the trait being measured (Height, weight or light) 0 can be the starting point. Symbol - X Symbol - What we are going to be studying (Ex. Age or motivation) Symbol - ∑ Symbol - "Sum of" Symbol - ∑X Symbol - "Sum of X" Symbol - N Symbol - Number of people in a population Symbol - n Symbol - Number of people in a sample Symbol - (∑X)"2" Symbol - (Sum of X Quantity) squared Symbol - ∑(X"2") Symbol - Square each X and then sum it up Symbol - X(-above) - M Symbol - Measures of CT - Mean Symbol - Md - Q"2" - P50 Symbol - Measures of CT - Median Symbol - M"2" Symbol - Measures of CT - Mode Symbol - SD - S Symbol - Measures of Variability - Standard Deviation Symbol - IQR Symbol - Measures of Variability - Interquartile Range Symbol - R Symbol - Measures of Variability - Range Symbol - S"2" - MS Symbol - Variants of Means Squared Symbol - SS Symbol - Sums of Squares (also variations) Symbol - Q Symbol - Quartile Symbol - P Symbol - Percentile Symbol - Q Q Q* Symbol - 25th quartile, 50th quartile, 75th quartile Symbol - P P P* Symbol - 25th percentile, 50th percentile, 75th percentile Abuse of power The use of more participants than necessary in a controlled experiment