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. Medium 1 2 Time 12 18 12 18 2 2 8 27.5 38.0 27.2 29.3 & 9 29.7 37.6 27.1 30.6 1.0 1. Answer the following questions: a) Identify the factors, factor levels, treatment combinations, experimental units, response variable, and blocking factor (if any). 15.4 40.0 b) Describe and explain the relationship (no interaction, intermediate interaction, or strong/high interaction) of the factors based on the plot below. 26.8 31.6 Medium Data 21.0 37.3 28.6 32.8 Blue line 18 hours Red line 12 hours 20.8 40.9 31.1 32.5 12 M 18 s 19.1 38.8 25.4 33.6 20 c) Test the assumption of the parametric test at 5% level of significance. The R outputs are already given. Test Homogeneity of Variances Shapiro-Wilk Normality Test *TC1: *TC2: *TC3: | *TC4: *TC-Treatment Combination 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 = p-value p-value wk8_data$Medium wk8_data$Time Residuals Conclusion Conclusion data: Medium 1 & Time 18 Shapiro-Wilk normality test W = 0.91981, p-value Levene's Test for Homogeneity of Variance (center = "mean") Df F value Pr (>F) group 3 5.474 0.006521 ** 0.504 data: Medium 2 & Time 18. Shapiro-Wilk normality test W- 0.96619 p-value = 0.8503 > summary(aov(wk8_data$Data-wk8_data$Medium*wk8_data$Time)) Df Sum Sq Mean Sq F value Pr(>F) 1 3.8 1 633.5 wk8_data$Medium:wk8_data$Time 1 233.8 20 185.3 3.8 0.406 0.531 633.5 68.385 6.96e-08 *** 233.8 25.235 6.51e-05 *** 9.3 Signif. codes: ***** 0.001 **** 0.01 0.05 0.1¹1 0 Analysis of Variance Df Sum Sq Mean Sq F value Pr (>F) 3 871.0 290.32 31.34 9.35e-08*** 20 185.3 9.26 Treatment Combination Residuals Signif. codes: 0 **** 0.001 **0.01 0.05 0.11 Kruskal-Wallis Rank Sum Test data: wk8_data$Data by Treatment Combinations Kruskal-Wallis chi-squared- 19.007, df 3, p-value - 0.0002725
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. Medium 1 2 Time 12 18 12 18 2 2 8 27.5 38.0 27.2 29.3 & 9 29.7 37.6 27.1 30.6 1.0 1. Answer the following questions: a) Identify the factors, factor levels, treatment combinations, experimental units, response variable, and blocking factor (if any). 15.4 40.0 b) Describe and explain the relationship (no interaction, intermediate interaction, or strong/high interaction) of the factors based on the plot below. 26.8 31.6 Medium Data 21.0 37.3 28.6 32.8 Blue line 18 hours Red line 12 hours 20.8 40.9 31.1 32.5 12 M 18 s 19.1 38.8 25.4 33.6 20 c) Test the assumption of the parametric test at 5% level of significance. The R outputs are already given. Test Homogeneity of Variances Shapiro-Wilk Normality Test *TC1: *TC2: *TC3: | *TC4: *TC-Treatment Combination 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 = p-value p-value wk8_data$Medium wk8_data$Time Residuals Conclusion Conclusion data: Medium 1 & Time 18 Shapiro-Wilk normality test W = 0.91981, p-value Levene's Test for Homogeneity of Variance (center = "mean") Df F value Pr (>F) group 3 5.474 0.006521 ** 0.504 data: Medium 2 & Time 18. Shapiro-Wilk normality test W- 0.96619 p-value = 0.8503 > summary(aov(wk8_data$Data-wk8_data$Medium*wk8_data$Time)) Df Sum Sq Mean Sq F value Pr(>F) 1 3.8 1 633.5 wk8_data$Medium:wk8_data$Time 1 233.8 20 185.3 3.8 0.406 0.531 633.5 68.385 6.96e-08 *** 233.8 25.235 6.51e-05 *** 9.3 Signif. codes: ***** 0.001 **** 0.01 0.05 0.1¹1 0 Analysis of Variance Df Sum Sq Mean Sq F value Pr (>F) 3 871.0 290.32 31.34 9.35e-08*** 20 185.3 9.26 Treatment Combination Residuals Signif. codes: 0 **** 0.001 **0.01 0.05 0.11 Kruskal-Wallis Rank Sum Test data: wk8_data$Data by Treatment Combinations Kruskal-Wallis chi-squared- 19.007, df 3, p-value - 0.0002725
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:c) Test the assumption of the parametric test at 5% level of significance. The R outputs
are already given.
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.
Test
p-value
Conclusion
Homogeneity of Variances
Shapiro-Wilk Normality Test
"TC1:
p-value
Conclusion
Medium
Time
12
Data
*TC2:
"TC3:
27.5
29.7
15.4
21.0
20.8
19.1
1
37.6
27.1
37.3
28.6
*TC4:
*TC - Treatment Combination
18
38.0
40.0
40.9
38.8
12
27.2
26.8
31.1
25.4
2
data: Medium 1 & Time 12
data:
Medium 1 & Time 18
18
29.3
30.6
31.6
32.8
32.5
33.6
Shapiro-Wilk normality test
W = 0.93239,
Shapiro-Wilk normality test
W = 0.91981,
p-value = 0.5987
data:
p-value - 0.504
1. Answer the following questions:
Medium 2 & Time 12
data: Medium 2 & Time 18
a) Identify the factors, factor levels, treatment combinations, experimental units,
response variable, and blocking factor (if any).
Shapiro-Wilk normality test
W = 0.86098
p-value = 0.2318
Shapiro-Wilk normality test
W- 0.96619
p-value = 0.8503
Levene's Test for Homogeneity of Variance (center = "mean")
b) Describe and explain the relationship (no interaction, intermediate interaction, or
strong/high interaction) of the factors based on the plot below.
Df F value Pr (>F)
3
group
5.474 0.006521 **
> summary(aov(wk8_data$Data-wk8_data$Medium*wk8_data$Time))
Pr(>F)
Df Sum Sq Mean Sq F value
0.406
wk8_data$Medium
1
3.8
3.8
0.531
wk8_data$Time
633.5
633.5 68.385 6.96e-08 ***
wk8_data$Medium:wk8_data$Time 1
233.8
233.8 25.235 6,51e-05 ***
Residuals
20 185.3
9.3
Signif. codes:
0 ***** 0.001 **** 0.01 ** 0.05 '. 0.1 '1
10
Analysis of Variance
Df Sum Sq Mean Sq F value
3
Pr (>F)
31.34 9.35e-08 ***
Treatment Combination
871.0
290.32
2.0
Residuals
20
185.3
9.26
---
Medium
Signif. codes:
O ***** 0.001 *** 0.01 **' 0.05 '.' 0.1 '' 1
Blue line = 18 hours
Kruskal-Wallis Rank Sum Test
Red line = 12 hours
data: wk8_ data$Data by Treatment Combinations
Kruskal-Wallis chi-squared - 19.007, df = 3, p-value - 0.0002725
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