In Unit 10, we will apply our understanding of the one-way ANOVA to the SPSS data set.

Proper Reporting of the One-Way ANOVA

Reporting a one-way ANOVA in proper APA style requires an understanding of several elements. To provide

context for the F test, provide a means plot, as well as the means and standard deviations for each level of a

given factor. The following elements are included in reporting the F test:

• The statistical notation for a one-way ANOVA ( F).

• The degrees of freedom.

• The F value.

• The probability value ( p).

• The effect size.

If the omnibus F test is significant, follow with a discussion of post-hoc tests. Consider the following example

from Warner (2013, p. 254):

The overall F for the one-way ANOVA was statistically significant, F(3, 24) = 11.94, p < .001. This

corresponded to an effect size of η2 = .60; that is, about 60% of the variance in anxiety scores was

predictable from the type of stress intervention. This is a large effect. . . .

In addition, all possible pairwise comparisons were made using the Tukey HSD test. Based on this

test. . . .

F, Degrees of Freedom, and F Value

The statistical notation for a one-way ANOVA is F, and following it is the degrees of freedom for this statistical

test, such as (3, 24) reported above. Unlike correlation or a t test, there are two degrees of freedom reported

for a one-way ANOVA. The first reported df is the between-groups df, or dfbetween, which is the number of

groups (or levels) minus one ( k − 1). In the example above, the factor consists of k = 4 levels (4 − 1 = 3). The

second reported df is the within-groups df, or dfwithin, which is the sample size minus the number of groups or

levels ( N − k). In the example above, N = 28, so 28 − 4 = 24. The F value is calculated as a ratio of mean

squares, which are both positive. Therefore, any non-zero F value is always positive.

Probability Value

Appendix C (pp.1058–1061) of the Warner text provides critical values of F for rejecting the null hypothesis. In

the example above, with (3, 24) degrees of freedom and alpha level set to .05 (one-tailed versus two-tailed is

not relevant to ANOVA), the table indicates a critical value of ± 3.01 to reject the null hypothesis. The obtained

F value above is 11.94, which exceeds the critical value required to reject the null hypothesis. SPSS determined

the exact p value to be .000, which is reported as p < .001. (Remember that SPSS only calculates a p value out

to three decimal places.) This p value is less than .05, which indicates that the null hypothesis should be rejected

for the alternative hypothesis—that is, at least one of the four group means is significantly different from the

other group means.

Unit 10 – One-Way ANOVA: Application

INTRODUCTION

Effect Size

The effect size for a one-way ANOVA is eta squared (η2). The effect size is not provided in SPSS output. It is

calculated by hand by dividing SSbetween by SStotal from the SPSS ANOVA output. In the example above,

SSbetween = 182.107 and SStotal = 304.107, which means that 182.107 ÷ 304.107 = .60. The effect size is

interpreted using Table 5.2 in the Warner text (p. 208).

Post-Hoc Tests

When the omnibus F is significant, it does not indicate exactly which pairwise comparisons are significant. A

Tukey’s honestly significant difference (HSD) test is one of many post-hoc tests used. The SPSS output for the

Tukey’s HSD indicates which pairwise comparisons are statistically significant, and this information can be

reported in narrative form (that is, without p values or other specific statistical notation) as shown in the fourth

paragraph of the “Results” section in the Warner text (p. 254).

The Warner text provides a “Results” example at the end of each chapter for all statistics studied in this course.

You are encouraged to review these examples and follow their structure when writing up Section 4,

“Interpretation,” of the DAA Template.

Reference

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

Oaks, CA: Sage.

OBJECTIVES

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

1. Interpret the one-way ANOVA output.

2. Apply the appropriate SPSS procedures to check assumptions and calculate the one-way ANOVA to

generate relevant output.

3. Analyze the assumptions of the one-way ANOVA.

4. Articulate a research question, null hypothesis, alternative hypothesis, and alpha level.

[u10s1] Unit 10 Study 1- Readings

Use your IBM SPSS Statistics Step by Step text to complete the following:

• Read Chapter 12, “The One-Way ANOVA Procedure.” This reading addresses the following topics:

◦ Introduction to one-way ANOVA.

◦ SPSS commands.

◦ Post-hoc tests in SPSS.

◦ Planned contrasts in SPSS.

◦ Reporting and interpreting SPSS output.

[u10d1] Unit 10 Discussion 1 – Course Reflection

For this discussion, address the following:

• Reflect on your experiences upon completing this course.

• Evaluate your current level of statistics anxiety relative to your initial level in Unit 1 of the course.

• Describe how your view of statistics has changed from the beginning of the course.

• Discuss how you can use statistics in your career. Do you have a different perception than you initially

did? Justify your answer.