Introduction to Statistics

Introduction to Statistics Quantitative Methods in HPELS 440:210

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

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

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

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

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

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

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

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?

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

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?

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

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

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

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

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

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

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

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

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°

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

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

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

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

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

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

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

Introduction to Statistics