statistics

• Measurement


  The act of assigning numbers or symbols to characteristics of things according to rules
• Descriptive Statistics


  Methods used to provide concise description of a collection of quantitative information
• Inferential Statistics


  Method used to make inferences from observations of a small group of people known as sample to a larger group of individuals known as population
• Magnitude


  The property of "moreness"
• 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


  When nothing of the property being measured exists
• Scale


  A set of numbers who properties model empirical properties of the objects to which the numbers are assigned
• Continuous Scale


  Takes on any value within the range and the possible value within that range is infinite - used to measure a variable which can theoretically be divided
• Discrete Scale


  Can be counted; has distinct, countable values - used to measure a variable which cannot be theoretically be divided
• Error


  • Refers to the collective influence of all the factors on a test score or measurement beyond those specifically measured by the test or measurement
  • Degree to which the test score/measurement may be wrong, considering other factors like state of the testtaker, venue, test itself etc.
  • Measurement with continuous scale always involve with error
• Four Levels of Scales of Measurement

  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Nominal


  • Involve classification or categorization based on one or more distinguishing characteristics
  • Label and categorize observations but do not make any quantitative distinctions between observations
• Ordinal


  Rank ordering on some characteristics is also permissible
• Interval


  • Contains equal intervals, has no absolute zero point (even negative values have interpretation to it)
  • Zero value does not mean it represents none
• Ratio


  • Has true zero point (if the score is zero, it means none/null)
  • Easiest to manipulate
• Distribution


  Defined as a set of test scores arrayed for recording or study
• Raw Scores


  Straightforward, unmodified accounting of performance that is usually numerical
• Frequency Distribution


  All scores are listed alongside the number of times each score occurred
• Independent Variable


  Being manipulated in the study
• Quasi-Independent Variable


  • Nonmanipulated variable to designate groups
  • Factor: for ANOVA
• Post-Hoc Tests


  Used in ANOVA to determine which mean differences are significantly different
• Tukey's HSD test


  Allows the compute a single value that determines the minimum difference between treatment means that is necessary for significance
• Measures of Central Tendency

  • Mean
  • Median
  • Mode
• Mean


  • The average of all the raw scores
  • Equal to the sum of the observations divided by the number of observations
  • Interval and ratio data (when normal distribution)
  • Point of least squares
• Median


  • The middle score of the distribution
  • Ordinal, Interval, Ratio
  • Useful in cases where relatively few scores fall at the high end of the distribution or relatively few scores fall at the low end of the distribution
  • Identical for sample and population
  • Also used when there has an unknown or undetermined score
  • Used in "open-ended" categories (e.g., 5 or more, more than 8, at least 10)
  • For ordinal data
• Mode


  • Most frequently occurring score in the distribution
  • Bimodal Distribution: if there are two scores that occur with highest frequency
  • Not commonly used
  • Useful in analyses of qualitative or verbal nature
  • For nominal scales, discrete variables
  • Value of the mode gives an indication of the shape of the distribution as well as a measure of central tendency
• Variability


  An indication how scores in a distribution are scattered or dispersed
• Measures of Variability


  • Range
  • Quartile
  • Standard Deviation
• Range


  • Equal to the difference between highest and the lowest score
  • Provides a quick but gross description of the spread of scores
  • When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated
• Quartile


  • Dividing points between the four quarters in the distribution
  • Specific point
  • Quarter: refers to an interval
  • Interquartile Range: measure of variability equal to the difference between Q3 and Q1
  • Semi-interquartile Range: equal to the interquartile range divided by 2
• Standard Deviation


  • Equal to the square root of the average squared deviations about the mean
  • Equal to the square root of the variance
  • Variance: equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
  • Distance from the mean
• Normal Curve


  • Also known as Gaussian Curve
  • Bell-shaped, smooth, mathematically defined curve that is highest at its center
  • Asymptotically = approaches but never touches the axis
  • Tail – 2 – 3 standard deviations above and below the mean
• Symmetrical Distribution


  • Right side of the graph is mirror image of the left side
  • Has only one mode and it is in the center of the distribution
  • Mean = median = mode
• Skewness


  Nature and extent to which symmetry is absent
• Positive Skewed


  • Few scores fall the high end of the distribution
  • The exam is difficult
  • More items that was easier would have been desirable in order to better discriminate at the lower end of the distribution of test scores
  • Mean > Median > Mode
• Negative Skewed


  • When relatively few of the scores fall at the low end of the distribution
  • The exam is easy
  • More items of a higher level of difficulty would make it possible to better discriminate between scores at the upper end of the distribution
  • Mean < Median < Mode
• Skewed


  Associated with abnormal, perhaps because the skewed distribution deviates from the symmetrical or so-called normal distribution
• Kurtosis


  • Platykurtic
  • Leptokurtic
  • Mesokurtic
• Kurtosis


  • Steepness if a distribution in its center
  • High Kurtosis = high peak and fatter tails
  • Lower Kurtosis = rounded peak and thinner tails
• Standard Score


  Raw score that has been converted from one scale to another scale