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Introduction to Statistics: Quantitative Methods in HPELS

This lecture provides an introduction to statistics and quantitative methods in the field of Health, Physical Education, Recreation, and Leisure Studies (HPELS). Topics covered include basic concepts, inferential statistics, scales of measurement, and statistical notation.

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Introduction to Statistics: Quantitative Methods in HPELS

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  1. Introduction to Statistics Quantitative Methods in HPELS HPELS 6210

  2. Agenda • Roadmap • Basic concepts • Inferential statistics • Scales of measurement • Statistical notation

  3. Roadmap • Descriptive Statistics • Central tendency • Variability • Inferential Statistics • Parametric • Nonparametric Correlational Method Experimental Method

  4. Agenda • Roadmap • Basic concepts • Inferential statistics • Scales of measurement • Statistical notation

  5. 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

  6. 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

  7. 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

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

  9. Agenda • Roadmap • Basic concepts • Inferential statistics • Scales of measurement • Statistical notation

  10. 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

  11. 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?

  12. 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

  13. 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?

  14. Agenda • Roadmap • Basic concepts • Inferential statistics • Scales of measurement • Statistical notation

  15. 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

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

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

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

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

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

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

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

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

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

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

  26. 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

  27. 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

  28. Agenda • Roadmap • Basic concepts • Inferential statistics • Scales of measurement • Statistical notation

  29. Statistical Notation • Textbook  progressive introduction of statistical notation • Summation = 

  30. Summation Example • X = 3+1+7=11 • X2 = 9+1+49=59 • (X)2=11*11=121

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

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