# One-Way Analysis of Variance and Post Hoc Tests

## One-way ANOVA and Scheffe Post Hoc Test

Directions:
Read the entire homework prior to starting the homework. Using the information from the following scenario, conduct a one-way ANOVA and specify the Scheffe post hoc test. (Assume a non-directional research hypothesis (two-tailed test) and a level of significance of .05). Assume a two-tailed test.
Scenario:
A newly hired assistant professor wanted to explore university faculty salaries. One aspect she wanted to explore was the difference in salaries by rank. She was curious to see if there was a statistical difference in the salary of an assistant professor, an associate professor, and a full professor. When running the One-Way ANOV, she used a non-directional hypothesis and an alpha coefficient of .05. Answer the following questions.
1. What is the mean salary of each group? (2 points each)
a. Assistant Professor
b. Associate Professor
c. Professor
2. What is the standard deviation of the salaries of each group?(2 points each)
a. Assistant Professor
b. Associate Professor
c. Professor

## One-way ANOVA Assumptions

3. What are the assumptions of the One-Way ANOVA? (2 points)
4. a. State an appropriate null hypothesis for this analysis (in word form). (1.5 points)
b. State a directional research hypothesis (in word form). (1.5 points)
5. What is the observed or computed value of F? (do not round)(2 points)
6. What are the reported degrees of freedom for the Between Groups variance? (2 points)
7. What are the reported degrees of freedom for the Within Groups variance? (2 points)
8. What is the reported level of significance? (do not round)(2 points)
9. Based on the results of the one-way ANOVA, would you accept or reject the null hypothesis? (2 points)
10. Calculate eta squared (η2). How do you interpret this value? (2 points)
11. Based on the results of the Scheffepost hoc test, identify which groups are significantly different. Explain your answer. (2 points)

## One-way ANOVA Rural Topics

12. Find a data set on your rural topic of interest (or another rural topic if you cannot find one specific to your interest) that could appropriately be assessed with a One Way Anova. Copy the URL link to the data file here. What would the null hypothesis be? (4 points)
13. Present a table with the results, a paragraph reporting the results, and a discussion of the meaning of the results as they might appear in an article.
a. The results and discussion must be written in APA format at a doctoral level, free from errors.
b. The results must include a table and narrative that provides a thorough description of the central tendency and distribution of levels of professorship salaries as well as the One Way ANOVA and post hoc results.
c. The discussion should
1) explain the results,
2) identify limitations to the study or data analysis,
3) possible reasons for the data results, and 4) suggest future studies. Include citations from the literature (a minimum of three (3)). Emphasize the importance of the topic to “rural” (education, health, economics, etc.)
d. Refer to the text, Research Methods, Statistics, and Applications for results and discussion examples. Refer to the APA Manual for instructions on tables.
(15 points)
Note: The table must be created using your word processing program. The table should be created using APA format. Tables that are copied and pasted from SPSS are not acceptable and will receive NO credit.