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.