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**Introduction to Statistics & Measurement**

Lecture 1 Homework Ch 1: 1-3,6-8; Ch 2: 1-4, 6, 8, 10

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**Types of Statistics Descriptive organize summarize Inferential**

drawing a conclusion about a group based on data from subgroup ~

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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) ~

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**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 ~

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**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 ~

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**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 ~

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**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 ~

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**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 ~

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**Discrete & Continuous Variables**

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

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**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 ~

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**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 ~

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**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 ~

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**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 ~

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**Summation Notation S Xi = X1 + X2 + X3 + X4 + X5**

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

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**Computations S X2i = X21 + X22 + X23 + X24 + 2X5 ~**

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

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**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 ~

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**Computations: Suggestion**

1 2 3 4 5 X 2 1 3 X2 3X2 4 12 4 12 1 3 9 27 4 12 S 66

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

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