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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCHPowerPoint Presentation

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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F Test

- State the hypotheses
- Determine the value of F*
- Choose the level of significance (α)
- Use tables to determine Fc
- Apply decision rule
r df of the numerator (number of restrictions),

n-k-1 df of the denominator (k –number of regressors in the unrestricted model)

Most Common Applications of F Test

- Some of the coefficients are equal to zero:
H0: β2 = β3 =0

H1: β2 and/or β3≠ 0

Models 1 and 3 in the table 14.1

- All coefficients are equal to zero:
H0: β1 = β2 = . . . =βk= 0

H1: βj≠ 0 for at least one j, j = 1, . . .,k

Most Common Applications of F Test

- F test for a set of dummy variables to be equal to zero:
Table 14.1 model 5

H0: β5 = β6 = β7 = 0

H1: β5≠ 0 and/or β6≠ 0 and/or β7≠ 0

- A single regression coefficient is equal to zero:
H0: βj = 0

H1: βj≠ 0

Most Common Applications of F Test

- Testing a hypothesis that specifies a relation among coefficients:
H0: β1 = β2

H1: β1≠ β2

CONi = β0 + β1 LABINCi + β2 PROPINCi + ui

CONi = β0 + β1 TOTINCi + ui , r=1

The Chow Test

- Test for equality of coefficients
Model 3 in table 14.1

The unrestricted form, allowing for differences, consists of two estimated regressions 3 one for blacks and one for whites

SSRu = 0.6713+16.9793=17.6506

Restricted form is regression 3 in table 14.1

The Chow Test

- In time-series data Chow test is the test for structural stability
H0: coefficients are the same in both periods

H1: Coefficients are different in both periods

LNMi = β0 + β1LNGNPi + ui

Two time periods: 1956-1970 and 1971-1980

H0: β01 = β02 and β11 = β12

H1: β01≠ β02 and β11≠β12

F-Test Example

F* = 27.06

Fcr2,131 at α=0.01≈ 4.78

Since the calculated F* is greater than the Fcr => you are 99% sure that both X1 and X2 have statistical impact on Y.

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