## Conducting Analysis of Variance to Determine the Significance of Experiments

The solutions below demonstrate how to use ANOVA to find the significance of experiment results. The first problem delves into the effects of drug dosage on muscle soreness while the second one compares five different groups. All answers in both cases are correct and neat. You may use them as sources of reference during revision.

## ANOVA - Post-hoc comparison problem

A researcher is studying the effects of drug dosage on delayed muscle soreness following a 30-minute standardized step-test exercise. The researcher randomly assigns 48 subjects to four different groups. Immediately after the exercise, the subjects are given one of three levels of a drug or a placebo. The following data are the mean levels of perceived pain for the four groups (higher score means greater pain), measured six hours after the exercise (n = 12 per group). The error means square for the ANOVA is 14.36. Using the Tukey HSD test the minimum significant difference is calculated as 4.15.

- Placebo = 82.5 mm
- 4 mL dose = 63.4 mm
- 8 mL dose = 56.6 mm
- 12 mL dose = 55.2 mm

Please complete the following 3 questions

1. c = the number of comparisons is 6.

2. Which group comparisons exceed the minimum significant difference?

Group Comparisons:

Placebo-4mL dose= 19.1

Placebo-8mL dose= 25.9

Placebo- 12mL dose= 27.3

4mL dose - 8mL dose = 6.8

4mL dose- 12mL dose = 8.2

8mL dose- 12mL dose = 1.4

All group differences exceed minimum significant difference except the difference between 8mL and 12 mL dose

3. What is the smallest, most effective dose?

The most effective dose is 12mL as it reduces the pain to 55.2.

## Completing missing values for One-way ANOVA

Complete the missing values in this table. You may use the slides and Portney Chapter 25 for guidance. Then provide short answers for the following six questions.

The study was a comparison of 5 groups. Assume equal-size groups. The numbers in bold are given.

1. How many participants are in each group?

**There are 5 groups that mean degrees of freedom for Between groups is 4 which means total observations are **

**20+4+1=25
**

**As each group contains an equal number, participants in each group are 5.
**

2. Write the null hypothesis for this study.

**Null Hypothesis: There is no significant difference between different group means
**

3. Do you accept or reject the null hypothesis? Explain what this means.

**We reject the null hypothesis as the p-value is less than 0.05. That means there is a significant difference between at least two group means.
**

4. Identify the type of ANOVA.

**One Way ANOVA
**

5. How many independent variables?

**One Independent variable is there.
**

6. What was the probable study design?

**The probable study design is Complete Randomised Design
**