Edpsy 511

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Edpsy 511

• Basic concepts
• Exploratory Data Analysis

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Populations vs. Samples

• Population
• The complete set of individuals
• Characteristics are called parameters
• Sample
• A subset of the population
• Characteristics are called statistics.
• In most cases we cannot study all the members of
  a population

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Descriptive vs. Inferential

• Descriptive statistics
• Summarize/organize a group of numbers from a
  research study
• Inferential statistics
• Draw conclusions/make inferences that go beyond
  the numbers from a research study
• Determine if a causal relationship exists between
  the IV and DV

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Random Sampling vs. Random Assignment

• Simple random sampling
• Each member of the population has an equal
  likelihood of being selected.
• Helps ensure that our sample will represent the
  population of interest.
• Random assignment
• Assigning subjects to different conditions in a
  way that they have equal chance of being placed
  in either condition.
• Controls for confounding

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Goals of Scientific Research

• Exploratory
• What is out there?
• Descriptive
• What does this group look like?
• Explanatory
• Why and how are these constructs related?
• Evaluation
• Does this program work?
• Prediction
• Who will become depressed?

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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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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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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

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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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A little on SPSS

• The assignments require hand calculations and
  SPSS practice
• Typically I have you check your answers using
  SPSS
• Do not buy SPSS
• Do not leave the SPSS work for night before the
  due date.
• You will need a TEC center account
• Do that after class today