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Introduction to Statistics Quantitative Methods in HPELS 440:210

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Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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Roadmap Descriptive Statistics Central tendency Variability Inferential Statistics Parametric Nonparametric Correlational MethodExperimental Method

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Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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Basic Concepts Statistics: A set of mathematical procedures for organizing, summarizing and interpreting information Statistics generally serve two purposes: Organize and summarize information Descriptive statistics Answer questions (interpretation) Inferential statistics

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Basic Concepts Population: The set of all individuals or subjects of interest in a particular study Sample: The set of individuals or subjects selected from a population intended to represent the population of interest Parameter: A value that describes a population Statistic or test statistic: A value that describes a sample

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Basic Concepts Inferential statistics: Procedures that allow you to make generalizations about a population based on information about the sample Figure 1.1, p 6

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Basic Concepts Sampling error: The discrepancy that exists between a sample statistic and the population parameter Figure 1.2, p 8

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Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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Inferential Statistics Statistical Inference: Statistical process that uses probability and information about a sample to make inferences about a population Two Main Methods Correlational Method Experimental Method

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Correlational Method Process: Observe two variables naturally Quantify strength and direction of relationship Advantage: Simple and elegant Disadvantage: Does not assume “cause and effect” Shoe size and IQ in elementary students?

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Experimental Method Process: Manipulate one variable Observe the effect on the second variable Advantage: A well controlled experiment can make a strong case for a “cause and effect” relationship Disadvantage: Difficult to control for all “confounding” variables

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Experimental Method Which variable is manipulated? Independent variable Treatment (not always a pill) Which variable is observed? Dependent variable Measure or test What is the effect of the IV on the DV?

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Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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Scales of Measurement The scales of measurement describe the nature/properties of data The scale of measurement affects the selection of the test statistic The are four scales of measurement: 1. Nominal 2. Ordinal 3. Interval 4. Ratio

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Scales of Measurement: Nominal Characteristics of Nominal Data: 1. Assigns names to variables based on a particular attribute 2. Divides data into discrete categories 3. No quantitative meaning

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Scales of Measurement: Nominal Example: Gender as a variable 1. Names assigned to variables based on particular attribute -Male or female 2. Divides data into discrete categories -Male or female (not both) 3. No quantitative meaning -Males cannot be quantified as “more or less” than girls

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Scales of Measurement: Ordinal Characteristics of Ordinal Data: 1. Has quantifiable meaning 2. Intervals between values not assumed to be equal

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Scales of Measurement: Ordinal Example: Likert Scales UNI Teacher Evaluations: “Does the instructor show interest...” Never Seldom Frequently Always

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Scales of Measurement: Ordinal Example: Likert Scales 1. Has quantifiable meaning -”Never” is less than “seldom” -Values can be rank ordered 2. Intervals between values not assumed to be equal NeverSeldomFrequentlyAlways ??

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Scales of Measurement: Ordinal Other examples: Small, medium, large sizes Low, medium, high performance

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Scales of Measurement: Interval Characteristics of Interval Data: 1. Has quantifiable meaning 2. Intervals between values are assumed to be equal 3. Zero point does not assume the absence of a value 4. Values do not originate from zero 5. Values cannot be expressed as multiples or fractions

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Scales of Measurement: Interval Example: Temperature (Fahrenheit or Celcius) 1. Has quantifiable meaning -10 C° is less than 20 C° 2. Intervals between values are assumed to be equal -The difference between 5 and 10 C° = difference between 15 and 20 C° 3. Zero point does not assume the absence of a value -0 C ° does not mean absence of temperature 4. Values do not originate from zero -0 C ° is arbitrary based on freezing point 5. Values cannot be expressed as multiples or fractions -10 C ° is not twice as cold as 5 C °

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Scales of Measurement: Ratio Characteristics: 1. Has quantifiable meaning 2. Intervals between values are assumed to be equal 3. Zero point assumes the absence of a value 4. Values originate from zero 5. Values can be expressed as multiples or fractions

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Scales of Measurement: Ratio Example: Length 1. Has quantifiable meaning 2. Intervals between values are assumed to be equal 3. Zero point assumes the absence of a value 4. Values originate from zero 5. Values can be expressed as multiples or fractions

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Scales of Measurement How do the scales of measurement affect the selection of the test statistic? Bottom Line: Nominal and ordinal data Nonparametric Interval and ratio data Parametric

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Scales of Measurement Parametric statistics: Definition: Statistical techniques designed for use when the data have certain specific characteristics in regards to: Scale of measurement: Interval or ratio Distribution: Normal More powerful Nonparametric statistics: Definition: Statistical techniques designed to be used when the data are: Scale of measurement: Nominal or ordinal or Distribution: Nonnormal

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Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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Statistical Notation Textbook progressive introduction of statistical notation Summation =

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Summation Example X = 3+1+7=11 X 2 = 9+1+49=59 (X) 2 =11*11=121 XX2X2 39 11 77

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Textbook Problem Assignment Problems: 2, 8, 12a, 12c, 16, 20.

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