Types of Data: Ratio Specific intervals between consecutive numbers True zero value
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Transcript of Types of Data: Ratio Specific intervals between consecutive numbers True zero value
Types of Data:
Ratio• Specific intervals between consecutive numbers
• True zero value
Interval level:
• Specific intervals between consecutive values
• Zero is just a number in the string
Ordinal level:
• numbers establish rank order
• distance between numbers is not any specific interval
e.g., 1st , 2nd, 3rd...
Nominal level:
• Numbers only categorize data.
• Numbers have no mathematical value.
e.g., 1 = male, 2 = female
Chi Square Goodness of fit
• for nominal level data
• identifies if a sample of people conform to the categories as expected.
2
2
f ff
e o
e
2Where:
Chi Square
fe Frequency expected
fo Frequency observed
Frequency expected:
The amount of subjects that you would expect to find in each category based on known information.
Frequency observed:
The amount of subjects you actually find to be in each category in the present data.
2
2
f ff
e o
e
Let’s assume that:
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
First:
How many people do we expect to find in each category, based on these percentages?
Assume that the sample that you test has
n=50.
f ne %
The percentage needs to be written as a fraction or decimal.
ffe
e
.20 5010
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
ffe
e
..25 5012 5
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
ffe
e
.30 5015
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
ffe
e
..15 507 5
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
ffe
e
.10 505
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
f e 10 12.5 15 7.5 5
h.s. Some college MA Ph.D
college
20% 25% 30% 15% 10%
10 12.5 15 7.5 5
5 7 25 12 1 fo
fe
2
2
f ff
e o
e
10 12.5 15 7.5 5
5 7 25 12 1
h.s. Some college MA Ph.D
college
fe
fo
H S. .
10 510
2
H S
H S
. .
.
10 510
510
2
2
H S
H S
. .
. . .
25102 5
10 12.5 15 7.5 5
5 7 25 12 1
h.s. Some college MA Ph.D
college
fe
fo
12 5 712 5
2..
Some college:
12 5 712 5
5512 5
2
2
..
..
30 2512 5
2 42
..
.
1)
2)
3)
4)
10 12.5 15 7.5 5
5 7 25 12 1
h.s. Some college MA Ph.D
college
fe
fo
15 2515
2
15 2515
2
6 67.
1)
2)
3)
4)
College:
1015
2
15100
10 12.5 15 7.5 5
5 7 25 12 1
h.s. Some college MA Ph.D
college
fe
fo
7 5 127 5
2..
7 5 127 5
2..
4 57 5
2..
20 257 5..
M.A.
1)
2)
3)
4)70.2
10 12.5 15 7.5 5
5 7 25 12 1
h.s. Some college MA Ph.D
college
fe
fo
5 15
2
45
2
165
320.
5 15
2
Ph.D.
1)
2)
3)
4)
2 2 50 2 42 6 67 2 70 320 . . . . .
2 17 49 .
Critical Value:
Chi Square table
df = K-1 where k is # of groups
df=4
crit value = 9.488
17.49 > 9.48
Therefore there is a significant difference between the expected and observed frequencies.