Statistics and the Research Process

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Statistics and the Research Process

• Chapter 2-Heiman

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Scientific Research

• The goal of science is to understand the
  ____________________
• We examine a specific _________ on a specific
  ___________ in a specific ___________
• Then, we ____________ back to the broader
  behaviors and laws with which we began.

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Review

• The entire group to which a law applies is the
  ___________________
• A _____________ is a relatively small subset of a
  population that is intended to represent, or
  stand for, the population
• The individuals measured in a sample are called
  the _____________________________

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Drawing Inferences

• We use the scores in a sample to _____________or
  to estimate the scores we would expect to find in
  the population.

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Representativeness

• In a ________________ sample, the characteristics
  of the ________________accurately reflect the
  characteristics of the __________________.

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Random Sampling

• Random sampling is a method of selecting a sample
  in which the individuals are _____________________
  ________ from the population.

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Unrepresentative Samples

• A random sample should be representative of the
  population, but never automatically assume that a
  sample is representative of the population.

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Examining Relationships

• A __________________ occurs when a change in one
  variable is accompanied by a _________________ in
  another variable.

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Strength of a Relationship

• The strength of a relationship is the extent to
  which one value of Y is ____________________ with
  one and only one value of X.

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Factors Affecting Strength

• A _______________ relationship may be due to
  additional extraneous influences and/or
  individual differences
• _________________________ refer to the fact that
  no two individuals are identical

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Graphing Relationships

• Describe a relationship using the general format
• Scores on the Y variable change as a function of
  changes in the X variable.
• The given variable in a study is the X variable.

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Four Sample Graphs

• A graph showing
• a perfectly
• consistent
• association.

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Four Sample Graphs

• A relationship
• that is not
• perfectly
• consistent.

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Four Sample Graphs

• A weak
• relationship.

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Four Sample Graphs

• No consistent
• pattern.

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Measurement Scales
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Characteristics of Variables

• Two important characteristics of variables are
• The __________________________ scale involved
• Whether it is continuous or discrete

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Measurement Scales

• 4 types of measurement scales
• _______________
• _________________
• __________________
• ___________________
• Differ in mathematical properties

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Nominal Scales

• ___________________ level of measurement
• Used with _______________ rather than
  ___________________ data
• Examples
• Gender, types of music, ethnicity, eye color

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Nominal Scales

• Variable is divided into categories
• Measured by determining which _____________person
  belongs to
• Classification
• Equivalence

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Example

• Interested in type of music people enjoy. Ask
  people to choose favorite type of music. You
  find that
• 15 like Rock
• 20 like Pop
• 12 like Country
• 10 like RB

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Ordinal Scale

• Next higher level of measurement
• ________________ depending on whether they
  possess more, less, or the same amount of the
  measured variable
• Is A gt B, B gt A, or A B?

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Examples of Ordinal Scale

• Rankings of contestants in a race
• Participant 1 came in first place
• Participant 2 came in second place
• Participant 3 came in third place
• Does not tell us about the _______________________
  _________

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Interval Scales

• Higher level than ordinal
• Possesses properties of ________________ and
  equal intervals b/w adjacent units
• Does not have an _____________________ point

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Interval

• Example
• Temperature
• Equal amounts of heat b/w each unit
• No absolute zero point

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Ratio

• ___________________level of measurement
• Same properties of the interval scale but also
  has an ___________________ point
• Examples
• Weight, height, age

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Figure 2.1
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Summary of Measurement Scales
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Inspecting data
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Inspection

• Before analyzing the data in any way, you should
  look at the data.
• Why might this be a good first step to take?

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How do we inspect our data?

• Order data in terms of magnitude
• From highest to lowest
• Or from lowest to highest

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Numerical Stroop Data

• There were 28 trials (questions)
• Response time (RT) for each is in seconds and
  tenths of seconds
• 3.5 means it took me 3.5 seconds to respond

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Look for Klinkers or Outliers

• Are the numbers out of range?
• If the top possible response is 7, 8 would be an
  invalid (purple)
• Did some responses take much too long? (yellow?)
• Were some responses very short? (blue?)

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Which Responses Will You Use?

• For Reaction Time (RT), we often use only correct
  responses
• It is not clear what processes were occurring
  with errors
• Delete errors from the RT data

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Score the Data

• Count the numbers condition
• Correct responses in Correct
• Put 1 if my Response matches Correct
• Otherwise, answer wrong (0)

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Stem and Leaf Plots (Displays)

• Decide what number to use as your stem
• It depends on how many digits
• If there are 2 digits (e.g., 15, 35), you
  probably will use the tens as the stem and the
  ones as the leaf
• If there are three digits (e.g., 126, 138), you
  probably will use the first two as the stem and
  the third as the leaf

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RT Data in Seconds

• 3.5 sec.
• 6.8 sec.
• 0.9 sec
• 1.6 sec
• Use the number of seconds as the stem and tenths
  of a second as the leaf

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Order your data from fastest to slowest

• Remove Errors
• Drop those fast times because they were errors

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Creating a Stem and Leaf Plot
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What Can We Learn from Stem and Leaf Plots?

• Look at the distribution
• Are most of the numbers very low with only a few
  high ones?
• With reaction time (RT) data, this is what you
  get
• Its called positively skewed because there are
  relatively few large scores
• Later well learn whether this is a problem

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What Can We Learn from Stem and Leaf Plots?

• Are there potential outliers
• The 11 looks much larger than the other scores
• Later well learn what to do about this