Foundations of Behavioral Statistics

1
Foundations of Behavioral Statistics

• Ch. 1 Introductory Terms and Concepts

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Statistics

• Statistics is about thinking, being reasonable
  and reflective.
• One must understand the significance of the data
  collected and be able to communicate it.
• Statistics help the researcher communicate the
  results of the data to others.
• The way a researcher interprets the data depends
  largely on his purpose for the study and what he
  wishes to accomplish.
• Language in statistics may be confusing since
  various meaning may be used for a single word and
  certain terms have multiple names.

3
Variables vs. Constants

• Variable scores that fall into at least 2
  categories.
• Constant scores that fall within a single
  category.
• In research, at least two variables are always
  used because we want to identify relationships.
  Constants may not always be used.

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Dependent vs. Independent Variables

• We are mostly interested on the dependent
  variable (also called criterion, outcome, or
  response). Changes on this variable are
  determined by the independent variables.
• The independent variable (also called predictor
  variable) determines the change in the dependent
  variable.
• Although the dependent variable always happens
  after or at the same time as the independent
  variable, a researcher selects the dependent
  variable first.

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Quiz 1

• A study is conducted to determine the effects of
  three sets of instructional materials on
  fourth-grade reading achievement. Three random
  samples of fourth-grade boys are selected within
  the same school. These three groups are then
  taught by three different teachers, each teaching
  only one group and using one set of instructional
  materials. At the end of ten weeks of
  instruction, the students are tested on reading
  achievement.
• Identify the constant(s), independent
  variable(s), and dependent variable(s) of this
  study.

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Answers

• Constants
• Grade level, gender, school
• Independent Variable
• Instruction materials
• Dependent Variable
• Reading achievement

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Univariate vs. Multivariate Analyses

• Studies may include more than two variables. In
  some cases, more than one independent variables
  or more than one dependent variables may be
  involved.
• When only one dependent variable but two or more
  independent variables are involved in a study we
  call it univariate statistics.
• If two or more dependent variables are involved,
  a researcher may opt to analyze them at the same
  time and their relationship with each other. We
  call this multivariate statistics.

8
Symbols

• Researchers often use Roman or Greek letters as
  symbols to represent their interpretation of the
  data.
• Roman letters are used for representing variables
• Independent variables are represented by letters
  positioned in the alphabet before the letters
  used for dependent variables (predictors happen
  before outcomes!)
• Symbols may be combined (those used for
  statistical characterization and for variables).

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Moderator vs. Mediator Variables

• A moderator variable may affect the relationship
  between a dependent and an independent variable,
  thus redirecting the study.
• Sometimes independent variables affect an outcome
  directly and sometimes indirectly. A mediator
  variable is used to determined the type of effect
  caused.

10
Population vs. Samples

• If we conduct a study and collect data from
  members in this investigation and then we
  generalize our finding to others not in the
  study, our dataset is called a sample. We
  interpret our findings through statistics.
• If we do not wish to generalize our findings to
  others not in our study and wish for this data to
  only affect those in the study, then this dataset
  is called the population. We call this
  interpretation parameters.

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Levels of Scale

• Nominal or Categorical
• Ordinal or Ranked
• Interval or Continuous
• Ratio

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Nominal Scale

• Nominal Scale
• Categorizes or shows difference without order
• Ex
• Gender

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Ordinal

• Ordinal
• Categorizes and shows rank or order
• Ex Military Rank

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Interval

• Interval
• Difference, order, and unit of equal differences
• Ex IQ scores

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Ratio

• Ratio
• Difference, order, unit of equal differences, and
  comparison in terms of a ratio
• Ex Age

16
Quiz

• Classify each of the following variables in in
  terms of type of measurement scale (nominal,
  ordinal, interval, or ratio)
• Performance on the essay section of an American
  history test.
• Ordinal
• Ratings assigned by supervisors to the
  performance of student teachers.
• Ordinal
• Strength of junior high boys on a physical task,
  as measured in pounds of force by an electron
  device.
• Ratio
• Score on a teacher-constructed, multiple-choice
  test of seventy-five items, for which all items
  are weighted equally.
• Interval
• Ethnic background
• Nominal

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Normative versus Ipsative Measurement

• Normative
• Responses do not mechanically constrain other
  responses
• Ipsative
• Responses mechanically constrain other responses

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Designs

• Experiment
• One intervention group and one control
• Only experimental designs can determine causality

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Designs Continued

• Design Symbols
• X
• Intervention
• R
• Random group assignment
• O
• Measurement

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Validity

• Accurate interpretability and generalizable
  results
• Internal design validity
• Did the intervention cause the observed effects
• External design validity
• How can the effects be generalized

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Threats to Design Validity

• Selection
• Biases in selection or grouping
• Experimental mortality
• Loss of participants
• History
• Occurrence of unplanned events
• Maturation
• Effects do to the passages of time
• Testing
• Impacts of pre-posttest
• Instrumentation
• Using different measures for different groups

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Threat to External validity

• Reactive measurement effects
• When pre-testing affects sensitivity to the
  intervention
• Hawthorne Effects
• Participants in an intervention altering their
  behavior because they are aware that they are in
  an intervention
• John Henry effects
• When participants in the control group when alter
  their behavior because they know their in the
  control group

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Reference

• Thompson, B. (2006). Foundations of behavioral
  statistics An insight-based approach. New York
  Guilford.
• Wiersma, W. (1991). Research methods in
  education. Boston Allyn and Bacon.