# Introduction to Research_2_ by pptfiles

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```									  Introduction to
Statistics
Quantitative Methods in HPELS
440:210
Agenda
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Descriptive Statistics                       Inferential Statistics
•Central tendency                           •Parametric
•Variability                                •Nonparametric

Correlational Method   Experimental Method
Agenda
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Basic Concepts
n Statistics: A set of mathematical
procedures for organizing, summarizing
and interpreting information
n Statistics generally serve two purposes:
¨ Organize     and summarize information
n   Descriptive statistics
n   Inferential statistics
Basic Concepts
n   Population: The set of all individuals or subjects
of interest in a particular study
n   Sample: The set of individuals or subjects
selected from a population intended to represent
the population of interest
n   Parameter: A value that describes a population
n   Statistic or test statistic: A value that describes a
sample
Basic Concepts
n   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
n   Sampling error: The discrepancy that exists
between a sample statistic and the
population parameter
¨ Figure   1.2, p 8
Agenda
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Inferential Statistics
n Statistical Inference: Statistical process
that uses probability and information about
a sample to make inferences about a
population
n Two Main Methods
Method
¨ Correlational
¨ Experimental Method
Correlational Method
n   Process:
¨ Observe  two variables naturally
¨ Quantify strength and direction of relationship

n Disadvantage: Does not assume “cause
and effect”
¨ Shoe   size and IQ in elementary students?
Experimental Method
n   Process:
¨ Manipulate one variable
¨ Observe the effect on the second variable
n Advantage: A well controlled experiment
can make a strong case for a “cause and
effect” relationship
n Disadvantage: Difficult to control for all
“confounding” variables
Experimental Method
n   Which variable is manipulated?
¨ Independent variable
¨ Treatment (not always a pill)

n   Which variable is observed?
¨ Dependent variable
¨ Measure or test

n   What is the effect of the IV on the DV?
Agenda
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Scales of Measurement
n   The scales of measurement describe the
nature/properties of data
n   The scale of measurement affects the selection
of the test statistic
n   The are four scales of measurement:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Scales of Measurement: Nominal

n   Characteristics of Nominal Data:
n   Assigns names to variables based on a
particular attribute
n   Divides data into discrete categories
n   No quantitative meaning
Scales of Measurement: Nominal
n   Example: Gender as a variable
n   Names assigned to variables based on
particular attribute
-Male or female
n   Divides data into discrete categories
-Male or female (not both)
n   No quantitative meaning
-Males cannot be quantified as “more or less” than
girls
Scales of Measurement: Ordinal
n   Characteristics of Ordinal Data:
n   Has quantifiable meaning
n   Intervals between values not assumed to
be equal
Scales of Measurement: Ordinal
n Example: Likert Scales
n UNI Teacher Evaluations:
n “Does the instructor show interest . . .”
¨ Never
¨ Seldom
¨ Frequently
¨ Always
Scales of Measurement: Ordinal
n      Example: Likert Scales
n      Has quantifiable meaning
-”Never” is less than “seldom”
-Values can be rank ordered
n      Intervals between values not assumed to
be equal
?                                 ?

Never             Seldom         Frequently       Always
Scales of Measurement: Ordinal
n   Other examples:
¨ Small,medium, large sizes
¨ Low, medium, high performance
Scales of Measurement: Interval
n   Characteristics of Interval Data:
n   Has quantifiable meaning
n   Intervals between values are assumed to be
equal
n   Zero point does not assume the absence of a
value
n   Values do not originate from zero
n   Values cannot be expressed as multiples or
fractions
Scales of Measurement: Interval
n   Example: Temperature (Fahrenheit or Celcius)
n   Has quantifiable meaning
-10 C° is less than 20 C°
n   Intervals between values are assumed to be equal
-The difference between 5 and 10 C° = difference between 15
and 20 C°
n   Zero point does not assume the absence of a value
-0 C° does not mean absence of temperature
n   Values do not originate from zero
-0 C° is arbitrary based on freezing point
n   Values cannot be expressed as multiples or fractions
-10 C° is not twice as cold as 5 C°
Scales of Measurement: Ratio
n   Characteristics:
n   Has quantifiable meaning
n   Intervals between values are assumed to be
equal
n   Zero point assumes the absence of a value
n   Values originate from zero
n   Values can be expressed as multiples or
fractions
Scales of Measurement: Ratio
n   Example: Length
n   Has quantifiable meaning
n   Intervals between values are assumed to be
equal
n   Zero point assumes the absence of a value
n   Values originate from zero
n   Values can be expressed as multiples or
fractions
Scales of Measurement
n How do the scales of measurement affect
the selection of the test statistic?
n Bottom Line:
¨ Nominal   and ordinal data à Nonparametric
¨ Interval and ratio data à Parametric
Scales of Measurement
n   Parametric statistics:
¨ Definition:Statistical techniques designed for use
when the data have certain specific characteristics in
regards to:
n   Scale of measurement: Interval or ratio
n   Distribution: Normal
¨ More    powerful
n   Nonparametric statistics:
Statistical techniques designed to be used
¨ Definition:
when the data are:
n   Scale of measurement: Nominal or ordinal or
n   Distribution: Nonnormal
Agenda
n Basic concepts
n Inferential statistics
n Scales of measurement
n Statistical notation
Statistical Notation
n Textbook à progressive introduction of
statistical notation
n Summation = S
Summation Example
n SX = 3+1+7=11     X   X2

n SX2 = 9+1+49=59   3   9
n S(X)2=11*11=121
1   1

7   7
Textbook Problem Assignment
n   Problems: 2, 8, 12a, 12c, 16, 20.

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