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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 n Descriptive l organize l summarize n Inferential l drawing a conclusion about a group l based on data from subgroup ~

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

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Experimental/Statistical Method n 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 n Population: all members of group l size depends on our interest l Usually impractical to assess population l Parameter: measure from population n Sample = subset of population l representative of population l Statistic: any measurement from a sample ~

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

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

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

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

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

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

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

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

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Summation Notation n Often sum data points in set means to summate X i = X 1 + X 2 + X 3 + X 4 + X 5 shorthand: X i = X 1 + X 2 +... + X 5

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Computations n Sometimes need to perform calculations before summation e.g., 3X = 3X 1 + 3X 2 + 3X 3 + 3X 4 + 3X 5 X 2 i = X 2 1 + X 2 2 + X 2 3 + X 2 4 + 2 X 5 ~

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Computations: Suggestion n Box 2.2, pp. 18,19 n Do calculations one step at a time e.g., 3X 2 u 1st find X 2 for each data point u then make new column multiply by 3 l fewer mistakes l easier to find mistakes ~

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Computations: Suggestion i12345i12345 X22132X22132 X2X2 4 4 1 9 4 3X 2 12 3 27 12 66

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Computations X 2 i versus ( X i ) 2 XY versus X Y X + 1 versus X + 1) ~

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