Question

An experiment was conducted for better understanding of the effectiveness of a particular type of drug for reducing bad cholesterol (LDL) level. The purpose of the experiment was to determine whether different dosages used have significant different outcomes in average LDL reduction. Twenty subjects with LDL at around 250 to 300 mg/dL had participated in the study and were randomly divided into four groups. Each group was given a specific level of dosage of the drug each day for one month, with a control group that only provided with placebo. The reduction in LDL was recorded and showed in the following table. Positive number indicates reduction and negative numbers indicates increasing in DLD. Use statistical software to analyze the data and answer the following question.

Control |
Light Dosage Level |
Medium Dosage Level |
Heavy Dosage Level |

7 |
25 |
73 |
81 |

-3 |
17 |
60 |
71 |

6 |
22 |
55 |
79 |

5 |
21 |
41 |
60 |

15 |
12 |
36 |
85 |

- Use statistical software to determine whether the average reduction in LDL differ among people who used different dosages of the drug. Perform a one-way ANOVA F-test and report p-value of the test and draw a conclusion using the level of significance at 5%.

Null hypothesis:

Alternative hypothesis:

Report the value of the F-test statistic =

Report p-value from the F-test and the conclusion:

[Place your software output here.]

- Verify the assumptions behind the ANOVA F-test using statistical software and explain your result.

[Place your software output here.]

- Use Tukey’s multiple comparison methods to compare all the treatment groups to see where the differences are and also identify homogeneous subsets from these treatment groups.

[Place your software output here.]

Answer #1

Null hypothesis: H0: The mean reduction in LDL is same for control group and all dosage levels.

Alternative hypothesis: Ha: At least one of the dosage levels or control group have different mean reduction in LDL.

Report the value of the F-test statistic = 51.44

Report p-value from the F-test and the conclusion: p-value = 1.94e-08

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that at least one of the dosage levels or control group have different mean reduction in LDL.

By Tukey’s multiple comparison method output, the significant mean differences of reduction in LDL is found in,

Control and Medium Dosage Level , Control and Heavy Dosage Level , Light and Medium Dosage Level, Light and Heavy Dosage Level, Medium and Heavy Dosage Level

The homogeneous subsets are,

Subset 1 - {Control , Light Dosage Level}

Subset 2 - {Medium Dosage Level }

Subset 3 - {Heavy Dosage Level}

On running the below R code, we get the following output.

R code -

**# Load the data
LDL <- c(7,-3,6,5,15,
25,17,22,21,12,
73,60,55,41,36,
81,71,79,60,85)
# Create vectors of factors (4 levels) for Dosage levels
Dosage=factor(c(rep(1,5),rep(2,5),rep(3,5),rep(4,5)))**

**# Fit a regression model on scale for different factors of
Dosage levels and run the anova test
summary(model <- aov(LDL ~ Dosage))**

**# Run the TukeyHSD test
TukeyHSD(model, "Dosage", ordered = TRUE)**

*> summary(model <- aov(LDL ~ Dosage))
Df Sum Sq Mean Sq F value Pr(>F)
Dosage 3 14891 4964 51.44 1.94e-08 ***
Residuals 16 1544 96
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’
1*

*> # Run the TukeyHSD test
> TukeyHSD(model, "Dosage", ordered = TRUE)
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered*

*Fit: aov(formula = LDL ~ Dosage)*

*$Dosage
diff lwr upr p adj
2-1 13.4 -4.375201 31.1752 0.1777685
3-1 47.0 29.224799 64.7752 0.0000062
4-1 69.2 51.424799 86.9752 0.0000000
3-2 33.6 15.824799 51.3752 0.0003061
4-2 55.8 38.024799 73.5752 0.0000007
4-3 22.2 4.424799 39.9752 0.0121973*

An experiment was done to see the effects of diet and a drug on
Type II Diabetes in men in the 50’s. Men in the 50’s who were
diagnosed with Type II Diabetes that was under moderate control
were randomly selected and randomly assigned to one of 4 treatment
groups (8 per group). The groups were a Control group, those given
a special diet, those given the drug, and those given the diet and
the drug. The control group was...

ANOVA: One Way: A drug trial using different levels of a drug to
reduce blood pressure is conducted to determine the best dosage. A
one Way ANOVA is conducted. Claim: The reduction of blood pressure
differs by dosage.
The results of the study are given in the ANOVA table
ANOVA
Source of Variation
SS
df
MS
F
P-value
Between Groups
360
4
D
E
0.0138
Within Groups
A
B
C
Total
660
19
Complete the Table:
A...

An experiment was done to test the effectiveness of a drug that
is being considered for possible use in the treatment of people who
experience chronic anxiety. Fifty people who are chronically
anxious are identified through a local health clinic. Twenty-five
people are randomly assigned to the experimental group, and they
receive the new drug for six weeks. The other 25 people are
randomly assigned to the control group, and they receive the
commonly used drug for six weeks. After...

An experiment was conducted to test the effect of a new drug on
a viral infection. After the infection was induced in 100 mice, the
mice were randomly split into two groups of 50. The first group,
the control group, received no treatment for the
infection, and the second group received the drug. After a 30-day
period, the proportions of survivors, p?1 and
p?2, in the two groups were found to be 0.38 and 0.66,
respectively.
(a) Is there sufficient...

1. ) Suppose a
researcher is interested in the effectiveness of a new drug that is
intended to naturally increase hours of sleep for elderly patients
experiencing insomnia above 5 hours. Suppose he collects
information from a group of 64 patients, and calculates a sample
mean of 6.4 hours of sleep and a standard deviation of
s=0.8.
Write out your null and alternative
hypotheses.
Carry out the appropriate statistical test to determine
if the new treatment is effective (One sided)?...

A pharmaceutical company performs an experiment to test a new
drug against Coronavirus (SARS2-COV). Their scientists
predict that this drug will reduce the length of hospital stay for
patients, compared to the current standard
treatment. One group of patients (Group A) is given the
new drug. One group of patients (Group B) is given the
current standard treatment. The average length of
hospital stays were as follows: Group A: 6
days. Group B: 11 days.
What is the hypothesis?
What is the control?
What is the...

ANOVA F test was conducted to test whether the means
of four groups are the same against at least one group mean is
different. The total number of subjects in four samples were 50.
The F ratio (test statistics) was 2.45
a) What is the p-value?
b) What is your conclusion at 5% significance level?
Are all group means the same?

A new drug has been developed that claims to prevent
seasickness completely! Design an experiment that would determine
how effective it is.
Do you need to define any terms for your experiment
(operationally define)? If so, define them here.
What is your independent variable?
What is your dependent variable?
Who are your subjects/participants?
How will you select and assign your subjects/participants to a
group?
What treatment will the experimental group be given?
What treatment will the control group be given?...

5. A study was conducted to investigate the
risk factors for peripheral arterial disease among persons 55-74
years of age. Data were collected pertaining to LDL cholesterol
levels (mmol/liter) from four different subgroups of subjects:
Group
Sample Size
Sample Mean
(intermittent) Patients with intermittent claudication
25
6.28
(major) Major asymptomatic disease cases
35
5.70
(minor) Minor asymptomatic disease cases
27
5.04
(no) Those with no disease
30
5.16
It is assumed that LDL values are approximately normally
distributed in each...

A drug company is
investigating a new pain relief medicine for migraine. To test the
effectiveness of the new drug, 10 volunteers were selected and
randomly assigned to receive either the new medication or a
placebo. The subjects were instructed to take the drug or placebo
during their next migraine headache episode and to report their
pain on a scale of 1 to 10 (10 being most pain). The following
table summarize the results:
Placebo
Group
Treatment
Group
9
4...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 2 minutes ago

asked 7 minutes ago

asked 11 minutes ago

asked 11 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 24 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 36 minutes ago

asked 47 minutes ago