Reference no: EM13869958
Design and Analysis of Completely Randomized Design
I. Objectives:
At the end of the exercise, the student should be able to:
a. Identify the treatment, experimental units and response variable of an experiment laid in CRD;
b. State the linear model and define each component in terms of the given problem;
c. Analyze and interpret data from an experiment laid out in CRD; and
d. Implement appropriate analysis for CRD using SAS.
II. Methods:
PART A:
The leaves of certain plants in the genus Albizzia will fold and unfold in response to various light conditions. We have taken 15 different leaves and subjected them to red light such that all 15 leaves began to receive red light exactly at the same time and the red light was removed after 3 minutes. The amount of red light was held constant and equal across all leaves. After 3 minutes, the leaves were divided into three groups of five at random. The leaflet angles were then measured 30, 45 and 60 minutes after light exposure. Other than time elapsed from light exposure to leaflet angle measurement, the leaves were treated identically. The objective of the experiment is to test the hypothesis that time elapsed from exposure to measurement does not affect leaflet angle. Mean results from preliminary computations were 139.6 for 30, 113.6 for 45 and 122.4 for 60. Moreover, sum of squares for experimental error was 9417.6.
1. Specify the treatment, experimental unit and response variable for this experiment.
2. What are the sources of variation in this experiment laid out in CRD?
3. Perform a possible randomization to allocate 5 leaves each to the treatment levels;
SV

df

SS

MS

Fc

Ftab

Decision















Total







4. Given results from preliminary computations, construct the ANOVA table using the format below.
PART B:
Scientists are interested in whether energy costs involved in reproduction affect longevity. In this experiment, 125 male fruit flies were grouped at random into five sets of 25. In one group, the males were kept by themselves. In two groups, the males were supplied with one or eight receptive virgin female fruit flies per day. In the other two groups, the males were supplied with one or eight unreceptive (pregnant) female fruit flies per day. The longevity of the flies (in days) was observed. Analyze the data shown below to test the null hypothesis that reproductive activity does not affect longevity.
Companion

Longevity (days)

none

35

37

49

46

63

39

46

56

63

65

56

65

70


63

65

70

77

81

86

70

70

77

77

81

77
















1 pregnant

40

37

44

47

47

47

68

47

54

61

71

75

89


58

59

62

79

96

58

62

70

72

75

96

75
















1 virgin

46

42

65

46

58

42

48

58

50

80

63

65

70


70

72

97

46

56

70

70

72

76

90

76

92
















8 pregnant

21

40

44

54

36

40

56

60

48

53

60

60

65


68

60

81

81

48

48

56

68

75

81

48

68
















8 virgin

16

19

19

32

33

33

30

42

42

33

26

30

40


54

34

34

47

47

42

47

54

54

56

60

44


Conduct a complete test of hypothesis (Ho and Ha, test procedure, test statistics, decision rule, ANOVA table from SAS output, decision and conclusion)