U9d1-64 – application of f tests – identify, describe, indicate &

In Unit 9, we will study the theory and logic of analysis of variance (ANOVA). Recall that a t test requires a predictor variable that is dichotomous (it has only two levels or groups). The advantage of ANOVA over a t test

is that the categorical predictor variable can have two or more groups. Just like a t test, the outcome variable in

ANOVA is continuous and requires the calculation of group means.

Logic of a “One-Way” ANOVA

The ANOVA, or F test, relies on predictor variables referred to as factors. A factor is a categorical (nominal)

predictor variable. The term “one-way” is applied to an ANOVA with only one factor that is defined by two or

more mutually exclusive groups. Technically, an ANOVA can be calculated with only two groups, but the t test is

usually used instead. Instead, the one-way ANOVA is usually calculated with three or more groups, which are

often referred to as levels of the factor.

If the ANOVA includes multiple factors, it is referred to as a factorial ANOVA. An ANOVA with two factors is

referred to as a “two-way” ANOVA; an ANOVA with three factors is referred to as a “three-way” ANOVA, and

so on. Factorial ANOVA is studied in advanced inferential statistics. In this course, we will focus on the theory

and logic of the one-way ANOVA.

ANOVA is one of the most popular statistics used in social sciences research. In non-experimental designs, the

one-way ANOVA compares group means between naturally existing groups, such as political affiliation

(Democrat, Independent, Republican). In experimental designs, the one-way ANOVA compares group means

for participants randomly assigned to different treatment conditions (for example, high caffeine dose; low

caffeine dose; control group).

Avoiding Inflated Type I Error

You may wonder why a one-way ANOVA is necessary. For example, if a factor has four groups ( k = 4), why not

just run independent sample t tests for all pairwise comparisons (for example, Group A versus Group B, Group

A versus Group C, Group B versus Group C, et cetera)? Warner (2013) points out that a factor with four groups

involves six pairwise comparisons. The issue is that conducting multiple pairwise comparisons with the same

data leads to inflated risk of a Type I error (incorrectly rejecting a true null hypothesis—getting a false positive).

The ANOVA protects the researcher from inflated Type I error by calculating a single omnibus test that

assumes all k population means are equal.

Although the advantage of the omnibus test is that it helps protect researchers from inflated Type I error, the

limitation is that a significant omnibus test does not specify exactly which group means differ, just that there is a

difference “somewhere” among the group means. A researcher therefore relies on either (a) planned contrasts

of specific pairwise comparisons determined prior to running the F test or (b) follow-up tests of pairwise

comparisons, also referred to as post-hoc tests, to determine exactly which pairwise comparisons are


Hypothesis Testing in a One-Way ANOVA

The null hypothesis of the omnibus test is that all k (group) population means are equal, or H0: μ1 = μ2 = … μk.

By contrast, the alternative hypothesis is usually articulated by stipulating that “at least one” pairwise

Unit 9 – One-Way ANOVA: Theory and Logic


comparison of population means is unequal. Keep in mind that this prediction does not imply that all groups

must significantly differ from one another on the outcome variable.

Assumptions of a One-Way ANOVA

The assumptions of ANOVA reflect assumptions of the t test. ANOVA assumes independence of observations.

ANOVA assumes that outcome variable Y is normally distributed. ANOVA assumes that the variance of Y scores

is equal across all levels (or groups) of the factor. These ANOVA assumptions are checked in the same process

used to check assumptions for the t test discussed earlier in the course—using the Shapiro-Wilk test and the

Levene test).

Effect Size for a One-Way ANOVA

The effect size for a one-way ANOVA is eta squared (η2). It represents the amount of variance in Y that is

attributable to group differences. Recall the concept of sum of squares ( SS ) from Unit 2. Eta squared for the

one-way ANOVA is calculated by dividing the sum of squares of between-group differences ( SS between) by the

total sums of squares in the model ( SS total), which is reported in SPSS output for the F test. Eta squared for the

one-way ANOVA is interpreted by referring to Table 5.2 in the Warner text (p. 208).

Journal Article Assignment

By the conclusion of Unit 9, you will have studied three fundamental statistics used in research, including

correlation, t tests, and one-way analysis of variance (ANOVA). You are now prepared to analyze a journal article

in your career specialization that reports one of these statistical tests. In the journal article assignment, you will

follow the general process used in completing DAA assignments:

1. Provide a brief summary of the research study and, in this assignment, why it is relevant to your career.

2. Identify the predictor variables and outcome variables including scales of measurement.

3. Articulate the research question, null hypothesis, and alternative hypothesis.

4. Report the test statistic and interpret it.

5. Provide conclusions as well as the strengths and limitations of the study.


Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand

Oaks, CA: Sage.


To successfully complete this learning unit, you will be expected to:

1. Analyze the use of one-way ANOVA in research situations.

2. Describe how ANOVA protects against the risk of inflated Type I error.

3. Analyze the assumptions, calculation, and effect size of one-way ANOVA.

[u09s1] Unit 9 Study 1- Readings

Use your Warner text, Applied Statistics: From Bivariate Through Multivariate Techniques , to complete

the following:

• Read Chapter 6, “One-Way Between-Subjects Analysis of Variance,” pages 219–260. This reading

addresses the following topics:

◦ Research situations using one-way ANOVA.

◦ Assumptions of one-way ANOVA.

◦ Calculation of one-way ANOVA.

◦ Effect size.

◦ Planned contrasts and post-hoc tests.

◦ Reporting and interpreting SPSS output.

PSY Learners – Additional Required Readings

In addition to the other required study activities for this unit, PSY learners are required to read the following:

Wang, P., Rau, P. P., & Salvendy, G. (2015). Effect of information sharing and communication on driver’s risk

taking. Safety Science , 77, 123–132. doi:10.1016/j.ssci.2015.03.013

SOE Learners – Suggested Readings

Wabed, A., & Tang, X. (2010). Analysis of variance (ANOVA). In N. J. Salkind (Ed.), Encyclopedia of research

design (pp. 27–29). Thousand Oaks, CA: Sage. doi:10.4135/9781412961288.n11


• DAA Template.

• SPSS Data Analysis Report Guidelines.

• IBM SPSS Step-by-Step Guide: One-Way ANOVA.

[u09d1] Unit 9 Discussion 1 – Application ofF Tests

For this discussion:

• Identify a research question from your professional life or career specialization that can be addressed

by a one-way ANOVA.

• Indicate why a one-way ANOVA would be the appropriate analysis for this research question.

• Describe the variables and their scale of measurement.

• Discuss the expected outcome.

Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Australia Assessments
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Smart response.
Customer 462457, April 13th, 2022
Great content. Thoroughly read all instructions.
Customer 462281, April 6th, 2022
Customer 463647, December 22nd, 2022
Business Studies
Very well done, thank you!
Customer 462533, February 6th, 2022
A job well done. The writer followed the instructions to detail.
Customer 463679, March 30th, 2023
Good job.
Customer 453707, May 8th, 2022
Business and administrative studies
Avoid plagiarism.
Customer 459305, March 29th, 2022
Be keen on plagiarism.
Customer 454463, March 28th, 2022
Thank you so much for the help. This work is everything I could have asked for and more.
Customer 454439, June 8th, 2020
Extremely well written, perfect for what I needed
Customer 454393, May 21st, 2020
Job well done!!!
Customer 453939, February 24th, 2020
Clean work!
Customer 463337, April 6th, 2023
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat