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 MethodExperimental Method

Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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

Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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?

Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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: 1. Assigns names to variables based on a particular attribute 2. Divides data into discrete categories 3. No quantitative meaning

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

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

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

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

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 °

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

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

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

Agenda Roadmap Basic concepts Inferential statistics Scales of measurement Statistical notation

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

Summation Example  X = 3+1+7=11  X 2 = =59  (X) 2 =11*11=121 XX2X

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