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Math 341

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Title Assessing the Goodness-of-Fit of Item Response Theory Models Using Bayesian Methods Author: Sherwin Toribio Last modified by: Sherwin Toribio – PowerPoint PPT presentation

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Title: Math 341


1
Math 341
  • January 24, 2007

2
Recap
  • Individuals are the objects described by a set
    of data. Individuals may be people, but they may
    also be animals or things.
  • Variable a characteristic of an individual. A
    variable can take different values for different
    individuals.
  • Categorical variable places an individual into
    one of several groups or categories. Gender,
    Blood Type
  • Quantitative variable takes numerical values
    for which arithmetic operations such as adding
    and averaging make sense. Height, Income, Time,
    etc.

3
Quantitative Variables
  • Discrete Variables There is a gap between
    possible values.
  • Counts (no. of days, no. of people, etc.)
  • Age in years
  • Continuous Variables Variables that can take on
    values in an interval.
  • Survival time, amount of rain in a month,
    distance, etc.

4
Distribution
  • - The distribution of a variable tells us what
    values it takes and how often it takes these
    values
  • Categorical Data
  • Table or Bar Chart
  • Quantitative Data
  • Frequency Table
  • Histogram
  • Stem-and-leaf plot

5
Length of Stay
5 1 15 9
3 7 2 12
4 18 9 13
28 24 13
1 6 10
5 6 9
6
Fifth-grade IQ Scores
145 101 123 106 117 102
139 142 94 124 90 108
126 134 100 115 103 110
122 124 136 133 114 128
125 112 109 116 139 114
130 109 131 102 101 112
96 134 117 127 122 114
110 113 110 117 105 102
118 81 127 109 97 82
118 113 124 137 89 101
7
Describing a distribution
  • Skewness
  • Symmetric
  • Skewed to the right (positively skewed)
  • Skewed to the left (negatively skewed)
  • Center/Spread
  • No of peaks (modes)
  • Unimodal, Bimodal, Multimodal.
  • Outliers
  • Extreme values.

8
Graphical Procedures
  • Categorical Data
  • Bar Chart
  • Pie Chart
  • Quantitative Data
  • Histogram
  • Stem-and-leaf plot (stemplot)
  • Time Plot (Time Series Data)
  • A time plot of a variable plots each
    observation against the time at which it was
    measured.
  • Consider example 1.7 on page 14.

9
Section 1.3
  • Measures of Center
  • Mean (Average)
  • 2.5, 3.2, 3.2, 3.4, 3.6, 3.7, 3.9, 3.9, 4, 4.2,
    4.2
  • - sensitive to outliers.
  • Median middle value
  • Mode most frequent occurring value.

10
Homework
Exercises Sec 1 4, 7, 8, 9. (pp. 10-11) Sec
2 10, 11, 15, 18, 20, 25, 29. (pp.23-28) Sec 3
34, 36, 41, 42. (pp.34-36)
11
Section 1.4
  • Consider 3 samples
  • 1,2,5,5,8,9
  • 3,4,5,5,6,7
  • 5,5,5,5,5,5
  • Measures of Dispersion (Spread)
  • Range
  • Variance
  • Standard Deviation
  • Five-number summary

12
Thank you!
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