Hypothetical Study Example Using One-Way Between-Subjects ANOVA

 

 

Hypothetical Study Example Using One-Way Between-Subjects ANOVA

Study Overview

Topic

The hypothetical study aims to examine the effect of different types of study environments on student performance in a mathematics test.

Research Question

How do different study environments affect student test scores?

Hypothesis

– Null Hypothesis (H0): There is no significant difference in the mean test scores of students studying in different environments. This can be expressed as: ( \mu_{A} = \mu_{B} = \mu_{C} ), where:

– ( \mu_{A} ): Mean test score for students studying in a quiet library.
– ( \mu_{B} ): Mean test score for students studying in a noisy café.
– ( \mu_{C} ): Mean test score for students studying at home with background music.

– Alternative Hypothesis (H1): At least one group mean is significantly different from the others, i.e., ( \mu_{A} \neq \mu_{B} \neq \mu_{C} ).

Experimental Design

Groups

This study will involve three groups of participants, each assigned to a different study environment:

1. Group A: Students who study in a quiet library.
2. Group B: Students who study in a noisy café.
3. Group C: Students who study at home with background music.

Conditions

Participants will be randomly assigned to one of the three groups, ensuring that each group has an equal chance of being assigned to any condition. After a designated study period (e.g., one week), all participants will take the same mathematics test designed to assess their understanding of the material studied.

Outcome Measure

The primary outcome measure will be the students’ scores on the mathematics test, which will be analyzed using one-way between-subjects ANOVA.

Statistical Considerations

Null Hypothesis and Rejection

The null hypothesis states that there are no differences in mean scores among the groups. Successful rejection of the null hypothesis would indicate that there is at least one significant difference among the means. However, it does not imply that every mean is significantly different from all others; it merely indicates that at least one group’s mean differs from at least one other group’s mean. To identify which specific groups differ, post-hoc tests (e.g., Tukey’s HSD) would need to be conducted following the ANOVA.

Sample Size Determination

To decide on an adequate sample size that provides adequate statistical power (commonly set at 0.80), several factors must be considered:

1. Effect Size: Estimation of the expected effect size (e.g., small, medium, or large). Cohen’s f can be used, where small = 0.10, medium = 0.25, and large = 0.40.

2. Alpha Level: The significance level, typically set at 0.05.

3. Power Analysis: A power analysis can be conducted using software like G*Power or statistical tools available in R or Python. For instance, if a medium effect size is anticipated (Cohen’s f = 0.25), and using an alpha level of 0.05 with three groups, a power analysis might indicate that at least 60 participants (20 per group) are needed to detect significant differences among the groups.

4. Practical Considerations: Availability of participants and resources may also impact the final decision on sample size.

Conclusion

In summary, this hypothetical study utilizing a one-way between-subjects ANOVA aims to investigate how different study environments affect student performance on a mathematics test. The results from this analysis would provide insights into which study conditions lead to better academic outcomes, and understanding the statistical power and sample size considerations would ensure the reliability of the findings.