1. 1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 7.3 Dummy Variables

2. 2 Use of Dummy Variables is the skull length (mm) of the i th mouse:  X 1i sex: male or female (two categories),  X 2i specie (three categories), and  X 3 age.

3. 3 Use of Dummy Variables Model to estimate: Estimated Model:

4. 4 Use of Dummy Variables For a male mouse of the first specie: 110 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

5. 5 Use of Dummy Variables For a male mouse of the second specie: 101 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

6. 6 Use of Dummy Variables For a male mouse of the third specie: 100 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

7. 7 Use of Dummy Variables For a female mouse of the first specie: 010 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

8. 8 Use of Dummy Variables For a female mouse of the second specie: 001 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

9. 9 Use of Dummy Variables For a female mouse of the third specie: 000 D 11 : 1 if sex = Male, 0 otherwise D 21 : 1 if species = 1, 0 otherwise D 22 : 1 if species = 2, 0 otherwise

10. 10 Use of Dummy Variables measures the skull length for a female mouse of specie 3 at birth, i.e. age = 0 : The skull length for a female mouse of specie 3 at birth is 33 mm.

11. 11 Use of Dummy Variables measures the difference in skull length (for any age) between male and female for any specie : means that regardless of age, a male mouse will have a skull length 3.05 mm larger than a female mouse

12. 12 Use of Dummy Variables measures the difference in skull length between species one and three : means that a mouse of species 1 will have a skull length 4.9 mm smaller than a mouse of species 3, regardless of sex and age.

13. 13 Use of Dummy Variables measures the difference in skull length (male or female mice of any age) between species two and three : means that a mouse of species 2 will have a skull length 0.22 mm smaller than a mouse of species 3, regardless of sex and age.

14. 14 Use of Dummy Variables measures the difference in skull length (for male or female mice of any age) between species one and two (-4.9) – (-0.22) = -4.68 means the skull length for species 1 is 4.68 mm shorter than for species 2, regardless of age and sex.

15. 15 Use of Dummy Variables Dummy variables in models are often called “intercept shifters”