AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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

2. Use of Dummy Variables • is the skull length (mm) of the ith mouse: • X1i sex: male or female (two categories), • X2i specie (three categories), and • X3 age.

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

4. Use of Dummy Variables • For a male mouse of the first specie: 1 1 0 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

5. Use of Dummy Variables • For a male mouse of the second specie: 1 0 1 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

6. Use of Dummy Variables • For a male mouse of the third specie: 1 0 0 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

7. Use of Dummy Variables • For a female mouse of the first specie: 0 1 0 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

8. Use of Dummy Variables • For a female mouse of the second specie: 0 0 1 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

9. Use of Dummy Variables • For a female mouse of the third specie: 0 0 0 D11: 1 if sex = Male, 0 otherwise D21: 1 if species = 1, 0 otherwise D22: 1 if species = 2, 0 otherwise

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. 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. Use of Dummy Variables • measures the difference in skull length (for male mouse of any age) 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. 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. 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. Use of Dummy Variables • Dummy variables in models are often called “intercept shifters”