Yk μ = 8 di = = Bi - = (αβ) Specify the appropriate linear model and define each component in the context with the problem. Yijk = μ + a₁ + B₁ + (aß) +&i=1,2; j = 1,2; k=1,2,3,4 & ijk = =
Yk μ = 8 di = = Bi - = (αβ) Specify the appropriate linear model and define each component in the context with the problem. Yijk = μ + a₁ + B₁ + (aß) +&i=1,2; j = 1,2; k=1,2,3,4 & ijk = =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 30E
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Question
A virologist is interested in studying the effects of 2 preselected different culture media and 2 preselected different times on the growth of a particular virus. She performs a balanced design with 6 plates for each of the treatment combinations. The 24 measurements were taken in a completely randomized order.
Transcribed Image Text:Medium Time
12
1
2
18
12
18
27.5
38.0
27.2
29.3
data: Medium 1 & Time 12
Shapiro-Wilk normality test
W = 0.93239,
p-value = 0.5987
data: Medium 2 & Time 12
Shapiro-Wilk normality test
W = 0.86098
p-value 0.2318
Levene's Test for Homogeneity
29.7
37.6
27.1
30.6
Treatment Combination
Residuals
signif. codes: 0 ***** 0.001 **** 0.01
15.4
group 3 5.474 0.006521 **
40.0
data: Medium 1 & Time 18
Shapiro-Wilk normality test
W = 0.91981,
p-value 0.504
26.8
31.6
data: Medium 2 & Time 18.
Shapiro-Wilk normality test
W- 0.96619
p-value 0.8503
of Variance (center = "mean")
Df F value Pr (>F)
Data
> summary(aov(wk8_data$Data-wk8_data$Medium*wk8_datasTime))
Df Sum Sq Mean Sq F value Pr(>F)
wk8_data$Medium
1 3.8
0.531
wk8_data$Time
1 633.5
wk8_data$Medium: wk8_data$Time 1 233.8
Residuals
20 185.3
Signif. codes: 0 **** 0.001*** 0.01 * 0.05.¹0.1
Analysis of Variance
Df Sum Sq Mean Sq F value Pr (>F)
3 871.0 290.32
20 185.3
9.26
Kruskal-Wallis Rank Sum Test
3.8 0.406
633.5 68.385 6.96e-08 ***
233.8 25.235 6.51e-05 ***
9.3
1
31.34 9.35e-08 ***
0.05 0.11
data: wk8_data Data by Treatment Combinations
Kruskal-Wallis chi-squared = 19.007, df = 3, p-value = 0.0002725
21.
0
37.
3
28.
6
32.
8
Medium
1
1
1
1
1
1
1
1
1
1
1
1
722NNN
2
22222
20.
8
40.
9
31.
1
32.
5
Time
12
∞∞∞∞ ∞ ∞NNNNNN ∞ ∞ ∞ ∞ ∞ ∞ NNNNNN
12
12
12
12
12
18
18
18
18
18
18
12
12
12
12
12
12
18
18
18
18
18
18
19.1
38.8
25.4
Data
33.6
27.5
29.7
15.4
21
20.8
19.1
38
37.6
40
37.3
40.9
38.8
27.2
27.1
26.8
28.6
31.1
25.4
29.3
30.6
31.6
32.8
32.5
33.6
Transcribed Image Text:Yijk =
μ
=
di =
=
Specify the appropriate linear model and define each component in the
context with the problem.
Bi =
(aß),
Sijk
=
Yijik = μ + a₁ + B₁ + (aß) +&i=1,2; j = 1,2; k = 1,2,3,4
j
17
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