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  • 1. 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
  • 2. Coding in a data matrix
  • 3. 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
  • 4. Levels of Measurement
    different kinds of variables
    (1) Nominal
    (2) Ordinal
    (3) Interval and Ratio
  • 5. 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
  • 6. 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)
  • 7. Interval (and Ratio) Variable
    All arithmetical operations are allowed
    intervals between each step are of equal size
    Examples:
    • length, weight, elapsed time, speed, temperature
  • 8. Levels of measurement
     
  • 9. 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
  • 10. Frequency table
  • 11. 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.
  • 12. Graphical presentation
    Pie charts
    Barcharts
    Line graphs
    Histograms
  • 13. 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.
  • 14. 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)
  • 15. Multiple barchart
  • 16. Compound or Component barchart
  • 17. Line graphs
    interval/ratio level variables that are discrete
    need to arrange the values in order
  • 18. 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
  • 19. Example: Histogram
  • 20. Graphs have the capacity to distort
  • 21. 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
  • 22. 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.
  • 23. 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.
  • 24. 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
  • 25. 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
  • 26. 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
  • 27. 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
  • 28. The range
    tells us over how many numbers altogether a distribution is spread
    • where
    • 29. r is the range
    • 30. h is the highest score in the data set
    • 31. l is the lowest score in the data set.
  • r = biggest value - smallest value = 55-10 = 45
  • 32. The mean deviation
    number which indicates how much, on average, the scores in a distribution differ from a central point, the mean.
    Mean deviation =
  • 33. 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
  • 34. The standard deviation (SD)
    represents the average amount of variability
    It is the average distance from the mean
    • sthe standard deviation
    • 35. find the sum of what follows
    • 36. Xeach individual score
    • 37. the mean of all the scores
    • 38. Nthe sample size
  • Standard deviations
  • 39. Shape of Normal Distribution
    Symmetrical
    Asymptotic tail
    Mean
    Median
    Mode
  • 40. 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
  • 41. SS2008N - Surveys
    Median
    50%
    50%
    Median
  • 42. SS2008N - Surveys
    Quartiles
    25%
    25%
    25%
    25%
    Median
    Quartile 1
    Quartile 3
  • 43. Standard Deviation