Introduction to Probability and Statistics for Engineers and Scientists

462 Chapter 10:Analysis of Variance

Station

Year 123456

1970 53 35 31 37 40 43

1971 36 34 17 21 30 18

1972 47 37 17 31 45 26

1973 55 31 17 23 43 37

1974 40 32 19 26 45 37

1975 52 42 20 27 26 32

1976 39 28 21 21 36 28

1977 40 32 21 21 36 35

The p-values in a Two-Way ANOVA

Start

Quit

1 2 3 4 5 6

A

53

36

47

55

40

52

35

34

37

31

32

43

31

17

17

17

19

38

B C D E F

37

21

31

23

26

27

40

30

45

43

45

36

43

18

26

37

37

22

The value of the F-statistic for testing that there is no row effect is 3.72985

The p-value for testing that there is no row effect is 0.00404

The value of the F-statistic for testing that there is no column effect is

22.47898

The p-value for testing that there is no column effect is less than 0.0001

FIGURE 10.2

To test the hypotheses that the data are unchanging (a) from year to year, and (b) from
station to station, run Program 10.5. Results are shown in Figure 10.2. Thus both the
hypothesis that the data distribution does not depend on the year and the hypothesis that
it does not depend on the station are rejected at very small significance levels. ■