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EDU 660. Methods of Educational Research Descriptive Statistics John Wilson Ph.D. Definitions. Quantitative data numbers representing counts or measurements. Definitions. Quantitative data numbers representing counts or measurements - PowerPoint PPT PresentationTRANSCRIPT
EDU 660
Methods of Educational ResearchDescriptive Statistics
John Wilson Ph.D.
DefinitionsQuantitative data
numbers representing counts or measurements
DefinitionsQuantitative data
numbers representing counts or measurements
Qualitative (or categorical or attribute) data
can be separated into different categories that are distinguished by some non-numeric characteristics
DefinitionsQuantitative data
the incomes of college graduates
DefinitionsQuantitative data
the incomes of college graduates
Qualitative (or categorical or attribute) data
the genders (male/female) of college graduates
Discrete data result when the number of possible values is
a ‘countable’ number0, 1, 2, 3, . . .
Definitions
Discrete data result when the number is or a ‘countable’
number of possible values0, 1, 2, 3, . . .
Continuous (numerical) data result from infinitely many possible
values that correspond to some continuous scale
Definitions
2 3
Discrete
The number of students in a classroom.
Definitions
Discrete
The number of students in a classroom.
ContinuousThe value of all coins carried by the students in the classroom.
Definitions
nominal level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high)
Example: Your car rental is a: Ford, Nissan, Honda, or Chevrolet
Levels of Measurement of Data
ordinal level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless.
Example: Course grades A, B, C, D, or F. Your car rental is an: economy, compact, mid-size, or full-size car.
Levels of Measurement of Data
interval level of measurement like the ordinal level, with the additional property that the
difference between any two data values is the same. However, there is no natural zero starting point (where
none of the quantity is present)
Example: The temperature outside is 5 degrees Celsius.
Levels of Measurement of Data
ratio level of measurementthe interval level modified to include the natural zero
starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful.
Examples: Prices of textbooks.
The Temperature outside is 278 degrees Kelvin.
Levels of Measurement of Data
Levels of Measurement Nominal - categories only
Ordinal - categories with some order
Interval – interval are the same, but no natural starting point
Ratio – intervals are the same, and a natural starting point
a value at the centre or middle of a data set
MeanMedianMode
Measures of the centre
Mean(Arithmetic Mean)
AVERAGEThe number obtained by adding the values and dividing the total by the number of
values
Definitions
Notation denotes the addition of a set of values
x is the variable usually used to represent the individual data values
n represents the number of data values in a sample
N represents the number of data values in a population
Notationis pronounced ‘x-bar’ and denotes the mean of a set of sample values
x =n x
x
Notation
µ is pronounced ‘mu’ and denotes the mean of all values in a population
is pronounced ‘x-bar’ and denotes the mean of a set of sample values
x =n x
x
Nµ =
x
Definitions
Medianthe middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
The Median is used to describe house prices in Toronto. Why not the Mean?
Definitions Mode
the score that occurs most frequentlyBimodal
MultimodalNo Mode
denoted by M
the only measure of central tendency that can be used with nominal data
a. 5 5 5 3 1 5 1 4 3 5
b. 1 2 2 2 3 4 5 6 6 6 7 9
c. 1 2 3 6 7 8 9 10
Examples
Mode is 5
Bimodal - 2 and 6
No Mode
Waiting Times of Bank Customers at Different Banks(in minutes)
TD
RBC
6.5
4.2
6.6
5.4
6.7
5.8
6.8
6.2
7.1
6.7
7.3
7.7
7.4
7.7
7.7
8.5
7.7
9.3
7.7
10.0
TD
RBC
6.5
4.2
6.6
5.4
6.7
5.8
6.8
6.2
7.1
6.7
7.3
7.7
7.4
7.7
7.7
8.5
7.7
9.3
7.7
10.0
TD
7.15
7.20
7.7
7.10
RBC
7.15
7.20
7.7
7.10
Mean
Median
Mode
Midrange
Waiting Times of Bank Customers at Different Banksin minutes
Measures of Variation
RangeVarianceStandard Deviation
Measures of Variation
Range
valuehighest lowest
value
Measures of Variation
Variance
• Mean Squared Deviation from the Mean
(Root Mean Squared Deviation)
Measures of Variation
Standard Deviation
Population Standard Deviation Formula
Root Mean Squared Deviation
(x - x)2
N s=
Basketball Starting LineHeight (inches)
78
77
75
74
71