Elements of Statistics II

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STIIDiscissionModule5.docx

Module 5: Discussion Forum: ANOVA

Instructions

This space has been created for you to share the link of a newspaper or blog article that discusses the importance for companies of using ANOVA testing with your classmates.

1. Write a summary about the blog or article.

2. Write at least two paragraphs.

3. The paragraph must have at least 3 sentences.

4. Read your classmates blogs and select two of them to discuss.

5. Establish a dialogue with them.

General Instructions for the Discussion Forum

1. Post your answer as established by your instructor on the course calendar. Your comments must be written in your own words. You can offer examples and quotes to support your proposals. Citations of other authors must be properly documented (author's name, title, date, etc.).

2. Post your comments to the response of at least two (2) of your classmates on or before the day set by your instructor on the course calendar. Your reaction may be based on personal experiences, study material, or additional information obtained from the Online Library or others, and may include:

· Some understanding received from what is published that synthesizes the information and offers new perspectives or suggestions.

· The validation or rejection of the idea (supported by your experience or research).

· New information that broadens, adds or contrasts perspectives (based on reading and evidence).

3. Remember that your work must be original and must not contain material copied from books or the internet. You must respect the intellectual property of the authors and not commit plagiarism.

4. Examine the criteria used to evaluate your assignment to find out how to get the highest grade for your work. The assignments are graded or evaluated through rubrics or by the distribution of points.

5. Before submitting your entry, read your message several times. This will ensure that it contains the exact information you want to communicate.

Remember to review the academic expectations for your submission.

Submission Instructions:

· Submit your initial discussion post by 11:59 PM Eastern on Wednesday.

· Contribute a minimum of 350 words for your initial post. It should include at least 2 academic sources, formatted and cited in APA.

· Respond to at least two of your classmates' discussion posts by 11:59 PM Eastern on Sunday. Ask a question, and provide a different viewpoint.

STIIModule5Class.docx

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

STIIModule5Class.docx

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)

Example:

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

STIIDiscissionModule5.docx

Module 5: Discussion Forum: ANOVA

Instructions

This space has been created for you to share the link of a newspaper or blog article that discusses the importance for companies of using ANOVA testing with your classmates.

1. Write a summary about the blog or article.

2. Write at least two paragraphs.

3. The paragraph must have at least 3 sentences.

4. Read your classmates blogs and select two of them to discuss.

5. Establish a dialogue with them.

General Instructions for the Discussion Forum

· Some understanding received from what is published that synthesizes the information and offers new perspectives or suggestions.

· The validation or rejection of the idea (supported by your experience or research).

· New information that broadens, adds or contrasts perspectives (based on reading and evidence).

3. Remember that your work must be original and must not contain material copied from books or the internet. You must respect the intellectual property of the authors and not commit plagiarism.

5. Before submitting your entry, read your message several times. This will ensure that it contains the exact information you want to communicate.

Remember to review the academic expectations for your submission.

Submission Instructions:

· Submit your initial discussion post by 11:59 PM Eastern on Wednesday.

· Contribute a minimum of 350 words for your initial post. It should include at least 2 academic sources, formatted and cited in APA.

· Respond to at least two of your classmates' discussion posts by 11:59 PM Eastern on Sunday. Ask a question, and provide a different viewpoint.

STIIModule5Class.docx

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)

Example:

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

STIIDiscissionModule5.docx

Module 5: Discussion Forum: ANOVA

Instructions

This space has been created for you to share the link of a newspaper or blog article that discusses the importance for companies of using ANOVA testing with your classmates.

1. Write a summary about the blog or article.

2. Write at least two paragraphs.

3. The paragraph must have at least 3 sentences.

4. Read your classmates blogs and select two of them to discuss.

5. Establish a dialogue with them.

General Instructions for the Discussion Forum

· Some understanding received from what is published that synthesizes the information and offers new perspectives or suggestions.

· The validation or rejection of the idea (supported by your experience or research).

· New information that broadens, adds or contrasts perspectives (based on reading and evidence).

3. Remember that your work must be original and must not contain material copied from books or the internet. You must respect the intellectual property of the authors and not commit plagiarism.

5. Before submitting your entry, read your message several times. This will ensure that it contains the exact information you want to communicate.

Remember to review the academic expectations for your submission.

Submission Instructions:

· Submit your initial discussion post by 11:59 PM Eastern on Wednesday.

· Contribute a minimum of 350 words for your initial post. It should include at least 2 academic sources, formatted and cited in APA.

· Respond to at least two of your classmates' discussion posts by 11:59 PM Eastern on Sunday. Ask a question, and provide a different viewpoint.

STIIModule5Class.docx

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)

Example:

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

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