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  1. Raw scores
    they are meaningless because we dont know whats good or bad, high or low
  2. Relative scale
    • most test scores are judged on a relative scale
    • relative to other test takers
  3. Summary statistics
    • about summarizing single variables
    • focus on quantitative (numerical)variables
    • start with a "bag of data" (collection of numbers)
    • consists of one or (usually) more variables
  4. what does summarizing mean
    • making information more concise (shorter)
    • summarizing depends on the sample size (N)
    • if N is large, we need to be very concise
    • if N is small, we can be less concise (more complete)
  5. Sorting
    • the simpliest summary technique is to sort the data
    • works with small sets of numbers
    • easier to see the distribution when the data are sorted
    • no information is lost; the presentation is merely simplified
  6. Histogram
    • a bar graph of a grouped frequency distribution of quantitative variable
    • the apperance of a histogram can vary depending on how many categories you use
  7. how to create a histogram
    • create categories or groups of bins
    • count the number of people or items in each group
    • make a bar graph, one bar for each group
  8. Frequency polygons
    • the same as histograms, but midpoints connected by lines, rather than using bars
    • not used very much
  9. raw frequencies
    • counts
    • are the original numbers
  10. relative frequencies
    • the numbers divided by N (the total)
    • percentages are the same relative frequency, except with the decimal point shifted over two places
  11. Symmetrical
    • left side is the mirror image of the right side
    • many distributions are symmetrical
  12. Shapes of distributions
    • Symmetrical
    • Uniform
    • Bell-shaped
    • Floor and Ceiling effects
    • Skewed
    • Bimodal
  13. Uniform
    • equal probabilities in all categories
    • uniform distribution is symmetrical
    • bars are close together in uniform
  14. Bell-shaped
    • most common
    • another examole of a symmetrical distribution
    • bars are close togther in a bell shape
  15. Floor effects
    • there is a lower limit to the possible numbers
    • usually this is 0
    • examples: incomes, which generally cannot be negative
  16. ceiling effect
    an upper limit to the possible numbers
  17. Skewed
    • to the right (positively skewed)
    • to the left (negatively skewed)
    • skew us frequentky due to floor and ceiling effects
  18. Bimodal
    • two humps or central points
    • like two bell shaped put together
  19. Boxplots (or box-and-whisker plots)
    • includes median (a small square)
    • outliers (small circle)
    • non-outlier range (in the shape of a capital I)
    • and the percentage (a big box)
  20. measures of central tendency
    • these measure where the "middle" or "center" is, or where most of the action is in the distribution
    • includes the mean, median, and mode
  21. measures of dispersion or variability
    theses measure how spread out the data are
  22. mean
    • arithmetic average- add them up and divide by N
    • most sensitive to outliers
  23. median
    • middle-most number (same as the 50th percentile)
    • if there is an even amount of numbers, average the middle two
    • sort the numbers first
    • less sensitive to outliers
  24. mode
    • the most frequently occuring number.
    • the hump in the histograms
    • the only measure that works with qualitative data
    • the only measure of central tendency where there can be two (eg. bimodal)
  25. when a distribution is symmetrical and bell-shaped
    the mean median and mode are the same
  26. when distributions are skewed
    mean, median, and mode are separate
  27. measures of dispersion of variability
    • these measure how spread out the data are
    • a data set: 3 3 3 3 (0 variability)
    • another data set: 1 2 3 4 5 (medium variability)
    • another data set: -1 1 3 5 7 (larger variability)
  28. Ordinal measures of variability
    • these depend only on the order of the numbers
    • range, interquartile range, and semi-interquartile range
  29. range
    highest to lowest
  30. interquartile range
    • chop off the top 25% (upper quartile)
    • chop off the bottom 25% (lower/bottom quartile)
    • take the difference
  31. semi-interquartile range
    half of the interquartile range
  32. quantitative measures of variability
    • these are based on the actual numbers, not just their orders
    • variance and standard deviation
  33. variance
    average squared deviation from the mean
  34. Standard deviation
    square root of the variance
  35. Norms
    • are summary statistics of test results-they tell us what is "normal" or average
    • we can tell how far an individual score is from average using summary statistics
    • Z scores are commonly used

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2012-10-15 18:43:46

chapter 4.1
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