Introduction to Statistics & Measurement

Introduction to Statistics & Measurement Lecture 1 Homework Ch 1: 1-3,6-8; Ch 2: 1-4, 6, 8, 10

Types of Statistics • Descriptive • organize • summarize • Inferential • drawing a conclusion about a group • based on data from subgroup ~

Domain of Statistics • What type of statements can be assessed by statistics? • Inductive statements • truth can be assessed by collecting and analyzing data • data --------------> conclusion • (specifics) (generalization) ~

Experimental/Statistical Method • Characteristics 1. Inspiration comes from observations 2. Interested in whole group e.g., all college statistics students not just small group 3. Meaningful results from fluctuating data ~

Samples from Populations • Population: all members of group • size depends on our interest • Usually impractical to assess population • Parameter: measure from population • Sample = subset of population • representative of population • Statistic: any measurement from a sample ~

Variables & Measurement • Variable: any measurable characteristic • and can take on many different values • can assign arbitrary values • Measurement: • procedure for assigning values to a variable • must be mutually exclusive • unambiguous result for each individual ~

Levels of Measurement • 4 types of variables & measurement levels • Nominal scale • qualitative: do not represent magnitudes • order NOT important • Ordinal scale • have a logical order • qualitative: undefined distance between • If assign numerical value, must reflect order ~

Levels of Measurement • Interval scale - quantitative • requires logical order • width of all categories must be equal • Ratio scale • same characteristics as interval • scale must have true zero point • Interval/ratio treated same for course • nominal, ordinal, interval/ratio distinction important • some statistics not relevant for a scale ~

Discrete & Continuous Variables • Discrete • no possible intermediate points b/n adjacent values • integers, counting numbers • e.g., # of children in family • Nominal level: always discrete ~

Discrete & Continuous Variables • Ordinal & interval/ratio can be discrete OR continuous • Continuous variable • has infinite number of values b/n adjacent scale values • e.g., height, weight, temperature • review in text • rounding rules • significant figures ~

Notation • Assign symbol to variable name • convenience, shorthand • Most common: single variable = X • 2 variables: X and Y • 3 variables: X, Y, and Z • or other logical symbols: height = H ~

Notation • Data set • set of measurements of variable(s) • each measurement = a data point • Index variable • particular measurement’s position in data set • i = 1 refers to the first subject • i = 2, the second subject, etc • order is usually arbitrary ~

Notation • n = # of measurements in sample • e.g. n = 5 • Use subscript when referring to specific data point • Xi = i th value of X • X2 = 2d value of X ~

Summation Notation • Often sum data points in set • S means to summate • S Xi = X1 + X2 + X3 + X4 + X5 • shorthand: S Xi = X1 + X2 + ... + X5

Computations • Sometimes need to perform calculations before summation • e.g., S 3X = 3X1 + 3X2 + 3X3 + 3X4 + 3X5 • S X2i = X21 + X22 + X23 + X24 + 2X5 ~

Computations: Suggestion • Box 2.2, pp. 18,19 • Do calculations one step at a time • e.g., S 3X2 • 1st find X2 for each data point • then make new column multiply by 3 • fewer mistakes • easier to find mistakes ~

3X2 i 1 2 3 4 5 X 2 2 1 3 2 X2 Computations: Suggestion 4 12 4 12 1 3 9 27 4 12 66 S

Computations • S X2i versus (S Xi)2 • SXY versus SX SY • SX + 1 versus S(X + 1) ~

Introduction to Statistics & Measurement