P-A: Levels of Measurement, Sampling Techniques, Hypothesis

• Statistics


  The branch of mathematics that deals with the collection, presentation, analysis and interpretation of numerical data
• Statistics


  • Making inferences or generalizations about the population characteristics from data gathered from sample
  • Making it possible to predict the likelihood of events from data
• Data


  A set of qualitative and quantitative values; made up of variables
• Variable


  Any thing that can be measured; something that can take different values between individuals or in the same individual at different time points
• Typically the result of measurements
• Diekhoff, 1992: 'Concerned with the presentation of information in a convenient, usable, and understandable form.'
• Mendelhall & Ott, 1972 cited in Leonard, 1976: 'Concerned with the collection, organization and analysis of numerical facts or observations. Its purpose is to describe and draw inferences about numerical properties of a group of population.'
• McClave & Sincich, 2009: 'Statistics is the science of data. This involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information.'
• Descriptive Statistics

  Procedures for summarizing, graphing and, in general, describing quantitative information
• Inferential Statistics


  Procedures that allow the drawing of conclusions and generalizations about the population on the basis of data gathered from a sample
• Determining the appropriate statistical techniques to be used in analyzing the collected information/data and in testing hypothesis
• Sample research variables/topics where descriptive statistics could be used

  • Average I.Q. of students
  • Incidents of violent behavior among students
  • Cheating behavior
• Sample research variables/topics where inferential statistics could be used

  • Anxiety, coping styles and depression
  • Relationship between emotional intelligence and intelligence quotient
  • Effect of aerobic exercise training on brain structure and psychological well-being in young adults
  • Impact of training on performance
• Measurement


  The assignment of numbers to objects or events
• Nominal


  Differentiates between items based on categories or subjects
• Nominal


  • Gender: male, female
  • Civil status: single, married
  • Religion: Christian, Muslim, Buddhist, Jews, etc
  • Employment status: permanent/regular, temporary, casual, contractual/job-order, co-terminus, part-time
  • Political orientation
  • Organization: profit, non-profit
  • Health profession (medical doctor, psychologist, social worker)
  • Psychological disorder (schizophrenia, anxiety disorder, mood disorder, etc)
• Ordinal


  Allows ranking of objects or observations; data consisting of spectrum of values
• Examples of Ordinal

  • Performance rating: (poor to excellent)
  • Brand preference (1st choice, 2nd choice, so on)
  • Educational attainment
  • Position
  • Salary grade
  • University rankings
  • Socio-economic class
• Interval


  Allows for the degree of difference between observations; equal distance
• Ratio


  Has fixed intervals between scores, and has a fixed zero point, which means that the values can be compared with each other with zero as a reference point
• Examples of Ratio

  • Amount of savings
  • Crime incidence
  • Number of convictions
  • Bacteria in a specimen
  • Number of passers in the board exams
  • Number of children
  • Years of work experience
  • Sales figures
• One-sample


  Procedures used to test statistics for only one sample
• Two-sample


  Procedures used to test statistics for two samples or groups of subjects
• Independent Samples


  Between subjects; mutually exclusive groups
• Independent Samples


  • Difference in the motives for teaching between the male teachers and female teachers
  • Difference in study habits across students from various programs
  • Quality of education of PUPSPC as assessed by school officials, professors, external alumni, students
• Dependent / Related / Paired Samples


  Within subjects; two or more sets of data are either correlated or coming from the same sample
• Dependent / Related / Paired Samples


  • Studies on attitudinal change; measuring difference in the achievement scores before and after intervention
  • Difference in the marital satisfaction between husbands and wives; relationship between IQ scores and performance rating
• Discrete Variable


  Made up of distinct and separate units or categories; it can only take on a finite value
• Dichotomous Variable


  Categorical variable that has been divided into two categories
• Continuous Variable


  Can be expressed by a large (often infinite) number of measures
• Dichotomized Variable


  A continuous variable that has been divided into two categories
• Independent Variable


  The presumed cause in a study; a variable that can be used to explain or predict the values of another variable
• Dependent Variable


  The presumed effect in a study; the variable whose values are predicted by the independent variable
• Mediating Variable


  A variable that accounts for the relation between the predictor and the criterion; it explains the relation, or provides the causal link between other variables
• Moderating Variable


  A variable that influences or "moderates" the relation between an independent and a dependent variable, producing an interaction effect
• Lecture 2: Sampling Techniques and Sample Size Determination
• Population


  A collection of sampling (events, persons, institutions, or other subjects of study) that one wants to describe or about which one wants to generalize
• Sample


  A subset of the population from which observations are actually obtained, and from which conclusions about the population are drawn
• Independent (or criterion) variables

  • Achievement in Mathematics
  • Intelligence
  • Other School Factors
  • Gender
  • Computer-Aided Instruction
  • Stress
  • Social Support
  • Stress + Social support
• Fairchild, A. J. & MacKinnon, D. P. (2009). A general model for testing mediation and moderation effects. Prevention Science, 10(2): 87-99.