1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 14: F Tests

2 F Test State the hypotheses Determine the value of F* Choose the level of significance (α) Use tables to determine F c 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)

3 Most Common Applications of F Test Some of the coefficients are equal to zero: H 0 : β 2 = β 3 =0 H 1 : β 2 and/or β 3 ≠ 0 Models 1 and 3 in the table 14.1 All coefficients are equal to zero: H 0 : β 1 = β 2 =... =β k = 0 H 1 : β j ≠ 0 for at least one j, j = 1,...,k

4 Most Common Applications of F Test F test for a set of dummy variables to be equal to zero: Table 14.1 model 5 H 0 : β 5 = β 6 = β 7 = 0 H 1 : β 5 ≠ 0 and/or β 6 ≠ 0 and/or β 7 ≠ 0 A single regression coefficient is equal to zero: H 0 : β j = 0 H 1 : β j ≠ 0

5 Most Common Applications of F Test Testing a hypothesis that specifies a relation among coefficients: H 0 : β 1 = β 2 H 1 : β 1 ≠ β 2 CON i = β 0 + β 1 LABINC i + β 2 PROPINC i + u i CON i = β 0 + β 1 TOTINC i + u i, r=1

6 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 SSR u = = Restricted form is regression 3 in table 14.1

7 The Chow Test In time-series data Chow test is the test for structural stability H 0 : coefficients are the same in both periods H 1 : Coefficients are different in both periods LNM i = β 0 + β 1 LNGNP i + u i Two time periods: and H 0 : β 01 = β 02 and β 11 = β 12 H 1 : β 01 ≠ β 02 and β 11 ≠ β 12

8 F-Test Example Ŷ i = X X 2 Test: H 0 : β 1 = β 2 =0 H a : β 1 and/or β 2 ≠ 0

9 F-Test Example RSS = SSE =

10 F * = F cr 2,131 at α=0.01≈ 4.78 Since the calculated F * is greater than the F cr => you are 99% sure that both X 1 and X 2 have statistical impact on Y. F-Test Example