Quants
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    Quants Quants Presentation Transcript

    • What is a Variable?
      any entity that can take on different values
      not always 'quantitative' or numerical, but we can assign numerical values
      attribute = a specific value of a variable
      Examples:
      gender: 1=female; 2=male
      attitudes: 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree; 5 = strongly agree
    • Coding in a data matrix
    • Coding in a data matrix
      Gender: Male = 1; Female=2
      Political Orientation: Traditionalist=1; Moderate=2; Progressive=3
      Social Class: Working=1; Upper working=2; Lower middle=3; Middle=4; Upper middle=5
    • Levels of Measurement
      different kinds of variables
      (1) Nominal
      (2) Ordinal
      (3) Interval and Ratio
    • Nominal Variable
      used to classify things
      represents equivalence (=)
      adding, subtracting, multiplying or dividing nominal numbers is meaningless
      tells you how many categories there are in the scheme
    • Ordinal Variable
      ordering or ranking of the variable
      the relationship between numbered items
      ‘higher’, ‘lower’, ‘easier’, ‘faster’, ‘more often’
      equivalence (=) and relative size (greater than) and < (less than)
    • Interval (and Ratio) Variable
      All arithmetical operations are allowed
      intervals between each step are of equal size
      Examples:
      • length, weight, elapsed time, speed, temperature
    • Levels of measurement
       
    • Frequency distributions
      count number of occurrences that fall into each category of each variable
      allow you to compare information between groups of individuals
      also allow you to see what are the highest and lowest values and the value at which most scores cluster
      variables of any level of measurement can be displayed in a frequency table
    • Frequency table
    • Percentages
      number of cases belonging to particular category divided by the total number of cases and multiplied by 100.
      the total of percentages in any particular group equals 100 per cent.
    • Graphical presentation
      Pie charts
      Barcharts
      Line graphs
      Histograms
    • Pie chart
      illustrates the frequency (or percentage) of each individual category of a variable relative to the total.
      Pie charts are not appropriate for displaying quantitative data.
    • 15
      Barcharts
      the height of the bar is proportional to the category of the variable - easy to compare
      used for Nominal or Ordinal level variables (or discrete interval/ratio level variables with relatively few categories)
    • Multiple barchart
    • Compound or Component barchart
    • Line graphs
      interval/ratio level variables that are discrete
      need to arrange the values in order
    • Histograms
      represents continuous quantitative data
      The height of the bars corresponds to the frequency or percentage of cases in the class.
      The width of the bars represents the size of the intervals of the variable
      The horizontal axis is marked out using the mid points of class intervals
    • Example: Histogram
    • Graphs have the capacity to distort
    • Measures of Central Tendency
      describe sets of numbers briefly, yet accurately
      describe groups of numbers by means of other, but fewer numbers
      Three main measures:
      mean
      median
      mode
    • The Mean
      • most common type of average that is computed.
    • When to use the Mean
      When values in a particular group cluster closely around a central value, the mean is a good way of indicating the ‘typical’ score, i.e. it is truly representative of the numbers.
      If the values are very widely spread, are very unevenly distributed, or clustered around extreme values, than the mean can be misleading, and other measures of central tendency should be used instead.
    • The Median
      Also an average, but of different kind.
      It is defined as the midpoint in a set of scores. It is the point at which one-half, or 50% of the scores fall above and one-half, or 50%, fell below.
      Computing the Median:
      (1) List the scores in order, either from highest to lowest or lowest to highest.
      (2) Find the middle score. That’s the median.
    • The Median: Pros and Cons
      time-consuming
      if one of the numbers near the middle of the distribution moves even slightly, than the median would alter, unlike the mean, which is relatively unaffected by a change in one of the central numbers
      if one of the extreme values changes, than the median remains unaltered.
      • 2, 80, 100, 120, 130, 140, 160, 200, 3150
      single scores which are quite clearly ‘deviant’ when compared with others, are known as outliers – 2 and 3150
    • The Mode
      the value in any set of scores that occurs most often
      example 1:
      5, 6, 7, 8, 8, 8, 9, 10, 10, 12 – the mode = 8
      example 2:
      5, 6, 7, 8, 8, 8, 9, 10, 10, 10, 12 –two modes: 8 and 10 – bimodal
      very unstable figure
      1,1,6,7,8,10 – mode = 1
      1,6,7,8,10,10 – mode = 10
    • When to Use What?
      depends on the type of data that you are describing
      for nominal data - only the mode
      for ordinal data - mode and median
      for interval data - all of them
      but, for extreme scores - use the median
    • Measure of dispersion (spread)
      better impression of a distribution’s shape
      measures indicate how widely scattered the numbers are
      how different scores are from one particular score – the mean
      variability - a measure of how much each score in a group of scores differs from the mean
    • The range
      tells us over how many numbers altogether a distribution is spread
      • where
      • r is the range
      • h is the highest score in the data set
      • l is the lowest score in the data set.
    • r = biggest value - smallest value = 55-10 = 45
    • The mean deviation
      number which indicates how much, on average, the scores in a distribution differ from a central point, the mean.
      Mean deviation =
    • 210
      368
      364
      319
      -210
      -368
      -319
      -364
      Mean=370
      X - mean= (-210)+210+(-368)+368+(-364)+364+(-319)+319 = 0
      X - mean= 210+210+368+368+364+364+319+319 = 2522
      mean deviation = 2522/8 = 315.25
    • The standard deviation (SD)
      represents the average amount of variability
      It is the average distance from the mean
      • sthe standard deviation
      • find the sum of what follows
      • Xeach individual score
      • the mean of all the scores
      • Nthe sample size
    • Standard deviations
    • Shape of Normal Distribution
      Symmetrical
      Asymptotic tail
      Mean
      Median
      Mode
    • The area under the curve
      A normal distribution always has the same relative proportions of scores falling between particular values of the numbers involved.
      Areas under the curve = proportion of scores lying in the various parts of the complete distribution
    • SS2008N - Surveys
      Median
      50%
      50%
      Median
    • SS2008N - Surveys
      Quartiles
      25%
      25%
      25%
      25%
      Median
      Quartile 1
      Quartile 3
    • Standard Deviation