Ask Question, Ask an Expert

+61-413 786 465

info@mywordsolution.com

Ask Statistics and Probability Expert

Please follow these instructions carefully, read them first! Your answers should be well structured and concise, and written in complete English sentences. Include your graphs and your code (in typepreparer font), comment it. Do not forget to number your answers to refer to the corresponding tasks below.

Tasks

problem1)

Create a data frame in R that will look like this:

fact variable1
A .
A .
. .
B .
B .
. .
C .
. .
D .
. .
The final dimension of the data set should be 48 rows by 2 columns. Each factor level (A, B, C, D) is replicated 12 times. For variable 1, use the following code:
                          variable1=rnorm(48,10)*(rep(rpois(4,.2),each=12)/8+1)
Give this data frame a name of your choice and show the code you used to create it. describe as much of the code to populate variable 1 with numbers. Comment on the details of the code.

problem 2)

Think of a situation (an experiment or observational study) within your (future) area of research that could produce such a data set. describe (hypothetically) what was done and how the data were obtained. Throughout the rest of this assignment, pretend these are real data. However, in your interpretation, you may comment at any stage on how the data were created.

problem 3)

Explore your data set using at least 2 commands to summarise your data and at least 2 commands to visually depict your data (plots, histograms,...). At each step / for each plot you create, comment on what you see and what you learn from it.

problem 4)

Compare the maximum and minimum values within each group (factor level) to their respective group means. What is the largest absolute difference between one of your values and its group mean? What are the chances of obtaining such a value, assuming the data are normally distributed and centered around the respective group mean with a standard deviation of 1?

problem 5)
 Formulate a hypothesis based on task 1 that you can test using ANOVA. Perform the analysis. Briefly describe what the F-value tells you and interpret the p-value. Draw a conclusion.

problem 6)

Regardless of whether you found significant differences between groups or not, perform a Tukey’s HSD test to determine what groups are significantly different from each other (even if none are). Briefly interpret this result in view of the nature of your data.

problem 7)

describe why the output contains an ‘adjusted p-value’. What does it adjust for? Can you outline a simulation experiment in R (you don’t need but you can show how you would program it) that illustrates the problem of multiple comparisons?

problem 8)

Compute the group means and then the variance of the group means for variable1 and assign this number to an object called ‘betweenVar’, meaning ‘between group variance’. Also compute the within-group variance of variable1 and assign this number to an object called ‘withinVar’ for ‘within group variance’.

problem 9)

Using the within- and between groups variances from the task above, conduct a power test for your ANOVA. Regardless of whether your ANOVA result was significant or not, discuss all aspects of the power test (sample size, type I and type II error, power, within- and between group variance) in accordance with the outcome of your ANOVA (as in task 4) and the nature of your data as you described it in task 1. For ex, if your ANOVA did not find a significant difference between groups, discuss how you could change your experimental set-up to find an expected difference. Or, if your ANOVA was significant, discuss the power of your test and (for ex) your type I error probability and whether / how you could reduce it. Talk about what the design of a larger experiment could look like based on the results of your pilot study, e.g. by bringing in financial aspects.

problem 10)

Show the differences between groups in a bar plot with standard errors. Mark those groups that do not differ significantly with the same letters. Adjust the margins, the label and tick size and position etc. until you think this graph could be published in a journal. Draft a figure caption that contains all the needed information: What is shown? Where? How was it measured? When? What test are the letters referring to?

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M9427

Have any Question? 


Related Questions in Statistics and Probability

Seedlings come in packages of 10 and consist of the

Seedlings come in packages of 10 and consist of the following: 2 Douglas-fir, 3 spruce, and 5 pines. In any given package, how many ways can the 10 seedlings be arranged if seedlings that are the same species cannot be d ...

Jen and barry get sued by ben amp jerrys for trademark

Jen and Barry get sued by "Ben & Jerry's" for trademark infringement. Jen and Barry lose, and they need a LOT of money. They decide to play Tennetucky's "Mega-6" lottery. They'll win the jackpot if they correctly choose ...

41 of the doctors in america are dentists if a random

41% of the doctors in America are dentists. If a random sample of size 826 is selected, what is the probability that the proportion of doctors who are dentists will be less than 40%?

A population has a mean of 150 and a standard deviation of

"A population has a mean of 150 and a standard deviation of 21. If a random sample of 49 is taken, what is the probability that the sample mean is between 152.5 and 157.5 using z scores?"

With a die being rolled the set of equally likely outcomes

With a die being rolled. The set of equally likely outcomes is? {1, 2? 3, 4? 5, 6}. Find the probability of getting a 10.

You are in charge of numbering the homes in a new

You are in charge of numbering the homes in a new subdivision. If we were to ue 0 through 9 as our number to use and we want to have 3 digit house numbers, how many unique homes numbers would we potentially be able to pr ...

The times that customers spend in a book store are normally

The times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of 15.9 minutes. A random sample of 25 customers has a mean of 36.1 minutes or less. Would this ...

Let x be a random variable with range rx -1 0 1 and let px

Let X be a random variable with range RX = {-1, 0, 1} and let P(X = 1) = P(X = -1) = p/2 for some p ∈ [0, 1]. a) Compute P(X = 0). b) Compute the expectation E[X] and variance Var(X) of X as a function of p, and determin ...

Question 1 a sample of 81 account balances of a credit

Question 1: A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126. 1. Formulate the hypotheses that can be used to determine whether the mean of all acc ...

A random sample of 40 hotel reviews is drawn from a large

A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the hot ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As