The writer is very fast, professional and responded to the review request fast also. Thank you.
Presentation/PPT
27/08/2022
Module 5:
ANOVA
The Analysis of Variance (ANOVA) is a statistical procedure to test the hypothesis that the means of three or more populations are equal. The ANOVA requires the F-distribution.
(Triola, 2018)
If there is only one explanatory variable, the ANOVA procedure is called one-way or single factor ANOVA, in which this variable is a continuous variable with three or more categories called groups.
Hypotheses:
Null Hypothesis: H0 : μ1 = μ2 = μ3 = · · · = μk
Alternative Hypothesis: H1 : μ1 ≠ μ2 ≠ μ3 ≠ · · · ≠ μk
If the null hypothesis is rejected, we conclude that with a particular significance level (α) the population means are not all equal.
The Assumptions of the ANOVA are:
· All populations are normally distributed.
· The variances among all the populations are the same.
· The random error terms are independent and normally distributed with mean equal to zero (μ = 0), and standard deviation σ.
ANOVA Hypothesis Test:
Basics of Hypothesis Testing:
1. Given a claim, identify the Null Hypothesis H0 and the Alternative Hypothesis H1.
2. State the conclusion (reject the Null Hypothesis of fail to reject the Null Hypothesis).
Null Hypothesis: H0 : μ1 = μ2 = μ3 = · · · = μk
Alternative Hypothesis: H1 : μ1 ≠ μ2 ≠ μ3 ≠ · · · ≠ μk
Decision Rule: Reject Ho if p-value is less than the significance level
(p-value < α)
p-value is a measure of the strength of the evidence provided by the data against the null hypothesis Ho. The smaller the p-value, the stronger is the sample evidence for rejecting the null hypothesis Ho.
Example:
Autor Readability. Pages were randomly selected by the author from The Bear and the Dragon
by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J.K. Rowling, and War and Peace by Leo Tolstoy. The Flesch Reading Ease scores for those pages are listed below. With a significance level of 5%, do the authors appear to have the same level of readability?
|
Clancy |
Rowling |
Tolstoy |
|
58.2 |
85.3 |
69.4 |
|
73.4 |
84.3 |
64.2 |
|
73.1 |
79.5 |
71.4 |
|
64.4 |
82.5 |
71.6 |
|
72.7 |
80.2 |
68.5 |
|
89.2 |
84.6 |
51.9 |
|
43.9 |
79.2 |
72.2 |
|
76.3 |
70.9 |
74.4 |
|
76.4 |
78.6 |
52.8 |
|
78.9 |
86.2 |
58.4 |
|
69.4 |
74.0 |
65.4 |
|
72.9 |
83.7 |
73.6 |
(Triola, 2018)
We will assume that the assumptions of the model are met:
· The three populations are normally distributed.
· The variances among all the populations are the same.
· The random error terms are independent and normally distributed with mean equal to zero (μ = 0), and standard deviation σ.
We are going to evaluate the ANOVA, with the support of the MS Excel program (
steps are listed in the Read Section of this module-Word and Excel documents attached).
From Excel ANOVA Single Factor:
Anova: Single Factor
ANOVA Hypothesis Testing Steps:
1) Given a claim, identify the Null Hypothesis H0 and the Alternative Hypothesis H1.
Null Hypothesis: H0 : μC = μR = μT
Alternative Hypothesis: H1 : μC ≠ μR ≠ μT
2) State the conclusion (reject the Null Hypothesis of fail to reject the Null Hypothesis).
Decision Rule: Reject Ho if p-value is less than the significance level
(p-value < α)
α = 5% or 0.05
From the Excel output: p-value = 0.000562
0.000562 < 0.05
Conclusion: Reject Ho, with a significance level of 5% there is statistical evidence that the readability population means of the three authors are different.
References:
Rajaretnam, T. (2016).
Statistics for social sciences. Sage Publications, Inc. ISBN-13: 9789351506560
Triola, M. F. (2018).
Elementary statistics (13th ed.). Pearson. ISBN-13: 978-0134462455
https://librarylogin-carolina.uagm.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=e000xww&AN=1214457&site=ehost-live&ebv=EB&ppid=pp_Cover
The writer is very fast, professional and responded to the review request fast also. Thank you.
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more