“Assessing the Goodness-of-Fit of Item Response Theory Models

```Math 145
September 11, 2006
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.
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
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.}
Quantitative Variables

Discrete Variables – There is a gap
between possible values.
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Counts (no. of days, no. of people, etc.)
Age in years
Continuous Variables – Variables that can
take on values in an interval.
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Survival time, amount of rain in a month,
distance, etc.
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
Length of Stay
5
1
15
9
3
7
2
12
4
18
9
13
28
24
13
1
6
10
5
6
9
Describing a distribution
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Skewness
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No of peaks (modes)
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Symmetric
Skewed to the right
Skewed to the left
Unimodal, Bimodal, Multimodal
Outliers
Consider # 1.15, 1.17, 1.18 on page 29.
Graphical Procedures

Categorical Data

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Quantitative Data

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Bar Chart
Pie Chart
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 1.11 on page 22.
Homework
Exercises:
Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20
Section 1.2

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}
 Median


Range
 Standard Deviation
 Five-number summary
Consider example 1.11 on page 22.

Homework
Exercises:
Sec 1: 1.1, 1.2, 1.3, 1.9, 1.11, 1.17, 1.19, 1.20
Sec 2: 1.42, 1.45, 1.47, 1.55-1.57*, 1.60, 1.62
Sec3: 1.78, 1.80, 1.81, 1.82, 1.83, 1.85*, 1.87,
1.89, 1.90*, 1.93-95, 1.97, 1.110, 1.115
Thank you!
```