UNIT 5

• Names

  • Buot, Blueminous Mitzi
  • Limco, Jannarine
  • Reyes, Jose Angelo
• Topics

  • Scales of Measurement
  • Frequency Distribution
  • Percentile Ranks
  • Percentiles
  • Distributions
  • Norms
  • Correlation and Regression
• Tests are devices used to translate observations into numbers
• Learning Objectives

  • Discuss three properties of scales of measurement
  • Determine why properties of scales are important in the field of measurement
  • Identify methods for displaying distributions of scores
  • Calculate the mean and the standard deviation for a set of scores
  • Define a Z score and explain how it is used
  • Relate the concepts of mean, standard deviation, and Z score to the concept of a standard normal distribution
  • Define quartiles, deciles, and stanines and explain how they are used
  • Tell how norms are created
  • Relate the notion of tracking to the establishment of norms
• WHY WE NEED STATISTICS?
• Statistical methods serve two important purposes in the quest for scientific understanding
• First, statistics are used for purposes of description
• Second, we can use statistics to make inferences, which are logical deductions about events that cannot be observed directly
• Scientific study requires systematic observations and an estimation of the extent to which observations could have been influenced by chance alone
• Statistics and the basic principles of measurement lie at the center of the modern science of psychology
• Descriptive statistics are methods used to provide a concise description of a collection of quantitative information
• Inferential statistics are methods used to make inferences from observations of a small group of people known as a sample to a larger group of individuals known as a population
• Properties of Scales of Measurement

  • Magnitude
  • Equal Intervals
  • Absolute 0
• Magnitude is the property of “moreness”
• A scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance
• The concept of equal intervals is a little more complex than that of magnitude
• A scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning
• Equal Intervals


  The difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units
• Absolute 0


  Obtained when nothing of the property being measured exists
• Types of Scales

  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Nominal scale


  Does not have the property of magnitude, equal intervals, or an absolute 0. Used to name objects
• Ordinal scale


  Has the property of magnitude but not equal intervals or an absolute 0. Used to rank individuals or objects
• Interval scale

  Has the properties of magnitude and equal intervals but not absolute 0
• Ratio scale

  Has all three properties (magnitude, equal intervals, and an absolute 0)
• For nominal data, each observation can be placed in only one mutually exclusive category
• Ordinal measurements can be manipulated using arithmetic; however, the result is often difficult to interpret because it reflects neither the magnitudes of the manipulated observations nor the true amounts of the property that have been measured
• Interval data cannot be used to make statements about ratios
• The frequency distribution displays scores on a variable or a measure to reflect how frequently each value was obtained
• For most distributions of test scores, the frequency distribution is bell-shaped, with the greatest frequency of scores toward the center of the distribution and decreasing scores as the values become greater or less than the value in the center of the distribution
• Grouped Data VS Ungrouped Data

  • Ungrouped Data
  • Grouped Data
• Percentile ranks replace simple ranks when adjusting for the number of scores in a group. They answer the question, "What percent of the scores fall below a particular score (Xi)?"
• Steps for calculating Percentile Rank

  1. Determine how many cases fall below the score of interest

  2. Determine how many cases are in the group

  3. Divide the number of cases below the score of interest by the total number of cases in the group, and

  4. Multiply the result by 100
• Percentiles are the specific scores or points within a distribution. They divide the total frequency for a set of observations into hundredths
• Basic Concepts of Distributions

  • Population vs Sample
  • Terms and Symbols
• Population

  The entire group that you want to draw conclusions about
• Population

  • All 87 students of 3rd year Psychology students
• Sample


  The specific group that you will collect data from
• Sample

  • 40 out of all 3rd year Psychology students
• Mean


  Also known as the arithmetic average
• Variance


  It tells whether the scores are clustered close together or spread out over a large distance from its mean