EdPsy 511

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EdPsy 511

• August 28, 2007

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Common Research Designs

• Correlational
• Do two qualities go together.
• Comparing intact groups
• a.k.a. causal-comparative and ex post facto
  designs.
• Quasi-experiments
• Researcher manipulates IV
• True experiments
• Must have random assignment.
• Why?
• Researcher manipulates IV

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Measurement

• Is the assignment of numerals to objects.
• Nominal
• Examples Gender, party affiliation, and place of
  birth
• Ordinal
• Examples SES, Student rank, and Place in race
• Interval
• Examples Test scores, personality and attitude
  scales.
• Ratio
• Examples Weight, length, reaction time, and
  number of responses

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Categorical, Continuous and Discontinuous

• Categorical (nominal)
• Gender, party affiliation, etc.
• Discontinuous
• No intermediate values
• Children, deaths, accidents, etc.
• Continuous
• Variable may assume an value
• Age, weight, blood sugar, etc.

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Values

• Exhaustive
• Must be able to assign a value to all objects.
• Mutually Exclusive
• Each object can only be assigned one of a set of
  values.
• A variable with only one value is not a variable.
• It is a constant.

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Chapter 2 Statistical Notation

• Nouns, Adjectives, Verbs and Adverbs.
• Say what?
• Heres what you need to know
• X
• Xi a specific observation
• N
• of observations
• ?
• Sigma
• Means to sum
• Work from left to right
• Perform operations in parentheses first
• Exponentiation and square roots
• Perform summing operations
• Simplify numerator and divisor
• Multiplication and division
• Addition and subtraction

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• Pop Quiz (non graded)
• In groups of three or four
• Perform the indicated operations.
• What was that?

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Rounding Numbers

• Textbook describes a somewhat complex rounding
  rule.
• For this class, truncate at the thousandths
  place.
• e.g. 3.45678 ? 3.456

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Chapter 3

• Exploratory Data Analysis

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Exploratory Data Analysis

• A set of tools to help us exam data
• Visually representing data makes it easy to see
  patterns.
• 49, 10, 8, 26, 16, 18, 47, 41, 45, 36, 12, 42,
  46, 6, 4, 23, 2, 43, 35, 32
• Can you see a pattern in the above data?
• Imagine if the data set was larger.
• 100 cases
• 1000 cases

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Three goals

• Central tendency
• What is the most common score?
• What number best represents the data?
• Dispersion
• What is the spread of the scores?
• What is the shape of the distribution?

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Frequency Tables

• Let say a teacher gives her students a spelling
  test and wants to understand the distribution of
  the resultant scores.
• 5, 4, 6, 3, 5, 7, 2, 4, 3, 4

Value F Cumulative F Cum
7 1 1 10 10
6 1 2 10 20
5 2 4 20 40
4 3 7 30 70
3 2 9 20 90
2 1 10 10 100
N10
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As groups

• Create a frequency table using the following
  values.
• 20, 20, 17, 17, 17, 16, 14, 11, 11, 9

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As groups

• Create a frequency table using the following
  values.
• 20, 19, 17, 16, 15, 14, 12, 11, 10, 9

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Banded Intervals

• A.k.a. Grouped frequency tables
• With the previous data the frequency table did
  not help.
• Why?
• Solution Create intervals
• Try building a table using the following
  intervals
• lt13, 14 18, 19

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Stem-and-leaf plots

• Babe Ruth
• Hit the following number of Home Runs from 1920
  1934.
• 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46,
  41, 34, 22
• As a group let build a stem and leaf plot
• With two classes spelling scores on a 50 item
  test.
• Class 1 49, 46, 42, 38, 34, 33, 32, 30, 29, 25
• Class 2 39, 38, 38, 36, 36, 31, 29, 29, 28, 19
• As a group let build a stem and leaf plot

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Landmarks in the data

• Quartiles
• Were often interested in the 25th, 50th and 75th
  percentiles.
• 39, 38, 38, 36, 36, 31, 29, 29, 28, 19
• Steps
• First, order the scores from least to greatest.
• Second, Add 1 to the sample size.
• Why?
• Third, Multiply sample size by percentile to find
  location.
• Q1 (10 1) .25
• Q2 (10 1) .50
• Q3 (10 1) .75
• If the value obtained is a fraction take the
  average of the two adjacent X values.

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Box-and-Whiskers Plots (a.k.a., Boxplots)
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Shapes of Distributions

• Normal distribution
• Positive Skew
• Or right skewed
• Negative Skew
• Or left skewed

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How is this variable distributed?
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How is this variable distributed?
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How is this variable distributed?
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Descriptive Statistics
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Statistics vs. Parameters

• A parameter is a characteristic of a population.
• It is a numerical or graphic way to summarize
  data obtained from the population
• A statistic is a characteristic of a sample.
• It is a numerical or graphic way to summarize
  data obtained from a sample

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Types of Numerical Data

• There are two fundamental types of numerical
  data
• Categorical data obtained by determining the
  frequency of occurrences in each of several
  categories
• Quantitative data obtained by determining
  placement on a scale that indicates amount or
  degree

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Measures of Central Tendency
Central Tendency
Average (Mean)
Median
Mode
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Mean (Arithmetic Mean)

• Mean (arithmetic mean) of data values
• Sample mean
• Population mean

Sample Size
Population Size
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Mean

• The most common measure of central tendency
• Affected by extreme values (outliers)

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
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Mean 5
Mean 6
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Median

• Robust measure of central tendency
• Not affected by extreme values
• In an Ordered array, median is the middle
  number
• If n or N is odd, median is the middle number
• If n or N is even, median is the average of the
  two middle numbers

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
14
Median 5
Median 5
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Mode

• A measure of central tendency
• Value that occurs most often
• Not affected by extreme values
• Used for either numerical or categorical data
• There may may be no mode
• There may be several modes

0 1 2 3 4 5 6
0 1 2 3 4 5 6 7 8 9 10 11
12 13 14
No Mode
Mode 9