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

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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.

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

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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

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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

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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

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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

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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

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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

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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.

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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

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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.

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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.

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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.

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

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