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Subject
Statistics
Date
Apr 30, 2024
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Pages
6
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11/20/23, 11
:
02 AM
Assignment_07
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Biostatistics in R
Assignment 7: Analysis of Variance
(ANOVA)
Lesson Setup
Run the next cell to load the necessary R packages for this lesson.
[1] "My current working directory is /Users/megancuevas/STATS1403/R assignme
nts/Assignment_07"
If your current working directory is not correct, you can run the code in the following cell
to change it. However, you will need to modify this code to match the folder location on
your particular computer system.
In [1]:
print
(
paste
(
"My current working directory is"
, getwd
()))
In [2]:
# Do NOT run the code in the cell unless you need to change your current wor
# You must edit the pathname to match the location of this assignment on YOU
# You must also remove the pound sign # befor the setwd() command before it # setwd("C:/Users/David/Biostats/Assignments/Assignment_04")
11/20/23, 11
:
02 AM
Assignment_07
Page 2 of 6
about:srcdoc
Introduction to ANOVA (One-Way)
The analysis of variance (ANOVA) can be thought of as an extension to the t-test. The
independent t-test is used to compare the means of a condition between 2 groups.
ANOVA is used when one wants to compare the means of a condition between more
than 2 groups. ANOVA is an omnibus test, meaning it tests the data as a whole. Another
way to say that is this, ANOVA tests if there is a difference in the mean somewhere in the
model (testing if there was an overall effect), but it does not tell one where the
difference is if the there is one. To find out where the difference is between the groups,
one has to conduct post-hoc tests. This is also covered in this section.
Although it can be thought of as an extension of the t-test, in terms of when to use it,
mathematically speaking, it’s more of a regression model and is considered a
generalized linear model (GLM).
ANOVA Assumptions
There are 3 assumptions that need to be met for the results of an ANOVA test to be
considered accurate and trust worthy. It’s important to note the the assumptions apply
to the residuals and not the variables themselves. The ANOVA assumptions are the same
as for linear regression and are:
Normality
Caveat to this is, if group sizes are equal, the F-statistic is robust to violations of
normality
Homogeneity of variance
Same caveat as above, if group sizes are equal, the F-statistic is robust to this
violation
Independent observations
11/20/23, 11
:
02 AM
Assignment_07
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about:srcdoc
Data Using in this Assignment
The data file "Cushing.txt" is part of the R Package called MASS
. The data file has 27
rows and 3 columns:
TCort
The urinary excretion rate (mg/24 hr) of Tetrahydrocortisone
PregN
The urinary excretion rate (mg/24 hr) of Pregnanetriol
Type
The type of adrenal cortical tumor coded as a (adenoma), b (bilateral hyperplasia), c
(carcinoma) or u for unknown.
The date was taken from the following reference
J. Aitchison and I. R. Dunsmore (1975) Statistical Prediction Analysis. Cambridge
University Press, Tables 11.1–3. (NOTE: The column names have been shorten from the
original dataset to make coding easier)
The R code in the cell below loads the Cushing's data into dataframe called CushDat
and then uses the head()
function to print out the first six enteries.
TCort
PregN
Type
3.1
11.70
a
3.0
1.30
a
1.9
0.10
a
3.8
0.04
a
4.1
1.10
a
1.9
0.40
a
In [3]:
# Loading data
CushDat =
read.csv
(
"Cushings.txt"
)
head
(
CushDat
)
Your preview ends here
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Related Questions
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12.9
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864
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921
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Tough to graduate colleges
547
495
550
526
451
480
470
533
617
429
554
529
524
568
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550
650
535
519
506
486
540
494
509
513
459
615
526
524
377
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543
608
490
537
513
550
466
520
544
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497
480
520
531
533
470
455
400
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494
603
395
578
445
459
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372
575
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564
480
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520
530
542
670
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590
440
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510
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419
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• sex-coded 1 = male and 2 = female
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●
.
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+
Life Expectancy by Birth Rate
80 -
70 -
10
20
30
40
BirthRate
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Call:
Im (formula =
LifeExpectancy
BirthRate, data = SampCountries)
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Min
10
Median
30
Маx
-7.0592 -2.3047
0.9123
2.5019
5.8358
Coefficients:
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1.03301
82.54
BirthRate
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0.04492
-14.09
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Adjusted R-squared:
0.8012
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account_circle
Math
StatisticsQ&A LibraryPolokwane Butchery supplies Vienna sausages in the entire of KZN province. An Inspector from the CCSA has been sceptical of the mass of the Vienna sausage packs after receiving numerous complaints. He wants to investigate the marked mass shown on Vienna sausages. A pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. How many packs should the Inspector sample in order to be 99% confident that the sample mean will differ by at most 0.2kg?
Polokwane Butchery supplies Vienna sausages in the entire of KZN province. An Inspector from the CCSA has been sceptical of the mass of the Vienna sausage packs after receiving numerous complaints. He wants to investigate the marked mass shown on Vienna sausages. A pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. How many packs should the Inspector sample in order to be 99% confident that the sample mean will differ by at most 0.2kg?…
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●
genhelf - variable recording general self-reported health coded 1 = very good, 2 =
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●
sbp - variable recording systolic blood pressure
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●
hi_sbp - indicator of high blood pressure coded 1 if the respondent's sbp is 130 or
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- Student Absences and Grades on the Final Exam Dr. V. noticed that the more frequently a student is late or absent from class the worse he or she performs on the final exam. He decided to investigate. Dr. V. collected a random sample of 22 students. This sample includes the number of times a student is absent and their grades on the final exam. The data can be found in the Excel file Assignment10_R1.xlsx on the Exercise1_Excel_Built-in f. worksheet. Do not use any software that I did not assign. Question 1: Which or the two variables (times absent or grades on the final exam) is the independent variable and which is the dependent variable? Question 2: Using Microsoft Excel: (Excel file Assignment10_R1.xlsx on the Exercise1_Excel_Built-in f.xlsx worksheet) Count the number of XY variables. Calculate the mean and sample standard deviation of both the independent and dependent variables. Calculate the correlation coefficient, r, using Excel’s CORREL function. Explain…arrow_forwardAbsenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. The file ‘absenteeism FinEx’ contains the data on these selected 100 organizations. Question: How does the MLR analysis compare with the t-test for Av Shift in predicting absenteeism? Comment on the similarities and/or differences. (both MLR and t-test are provided below) Data: Wage Pct PT Pct U Av Shift U/M Rel Absent 22477 8.5 57.1 1 1 5.4 29939 1.9 41.5 0 1 4.1 22957 12.2 52.6 1 0 11.5 18888 30.8 65.1 0 1 2.1 15078 6.8 68.8 0 1 5.9 15481 5.1 46.4 0 0 12.9 21481 25.3 38.9 0 1 3.5 29687 9.2 17.2 0 0 2.6 13603 8.4 12.9 0 0 8.6 18303 4.9…arrow_forwardStudent Absences and Grades on the Final Exam Dr. V. noticed that the more frequently a student is late or absent from class the worse he or she performs on the final exam. He decided to investigate. Dr. V. collected a random sample of 22 students. This sample includes the number of times a student is absent and their grades on the final exam. The data can be found in the Excel file Assignment10_R1.xlsx on the Exercise1_Excel_Built-in f. worksheet. Do not use any software that I did not assign. : Using Excel, conduct a NHST to determine whether there is a correlation in the population. Use a 0.05 significance level. Use the Excel file Assignment10_R1.xlsx, Exercise1_Correlation NHST worksheet) Test Set-Up: What type of Null Hypothesis Test should you use? It this a left-tailed, two-tailed, or right-tailed test. Significance Level: Use a 5% significance level. What is/are the Critical Value(s)? Write the Null & Alternate Hypotheses (Follow the examples shown in…arrow_forward
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