The Following Data Are From An Experiment Comparing Three Di
The Following Data Are From An Experiment Comparing Three Different Tr
The following data are from an experiment comparing three different treatment conditions: A, B, and C. The researcher has conducted the experiment using two different experimental designs: an independent measures design and a repeated measures design. The questions are as follows:
a. If the experiment uses an independent measures design, can the researcher conclude that the treatments are significantly different? Test at the .05 level of significance.
b. If the experiment is done with a repeated measures design, should the researcher conclude that the treatments are significantly different? Test with .05 alpha again.
c. Explain why the analyses in parts a and b lead to different conclusions.
Paper For Above instruction
The experiment comparing three different treatment conditions—A, B, and C—aims to determine whether different treatments have significantly different effects. The two proposed experimental designs, an independent measures design and a repeated measures design, offer different analytical frameworks, yielding potentially different conclusions about treatment effects. This paper explores whether the treatments are significantly different in each design, applying the appropriate statistical tests and explaining the reasons for any differing conclusions.
Understanding the Designs
An independent measures design involves assigning different participants to each treatment group, with no participant experiencing more than one treatment. This design emphasizes between-group differences. Conversely, a repeated measures design involves the same participants experiencing all treatments, allowing for within-subject comparisons, which control for individual variability.
Part A: Independent Measures Design Analysis
In the independent measures scenario, the researcher tests whether the differences among the treatments exceed what might be expected by chance. Typically, this involves conducting an Analysis of Variance (ANOVA) for independent groups.
Given the data are from three treatments, the null hypothesis (H0) is that all treatments have the same effect, and the alternative hypothesis (H1) suggests at least one differs. At a significance level of α = 0.05, the researcher calculates the F-statistic and compares it to the critical value from the F-distribution considering the appropriate degrees of freedom.
Hypothetical Data & Calculation: Suppose the means for treatments A, B, and C are 20, 25, and 30, with similar variances. An ANOVA would determine if observed differences are statistically significant. If the F-calculated exceeds the critical F-value, H0 is rejected, indicating significant differences among treatment effects.
Part B: Repeated Measures Design Analysis
In a repeated measures design, the same participants are exposed to each treatment. This design generally offers more sensitivity to detecting differences because variability due to individual differences is controlled.
The appropriate test here is a repeated measures ANOVA, which partitions the total variance into variance due to treatments, subjects, and error. The null hypothesis remains that the treatments have equal effects. The test statistic is again compared against critical values at α = 0.05.
Suppose the analysis yields an F-value that exceeds the critical threshold, leading to rejection of H0, implying treatments differ significantly. If not, the conclusion is that treatments do not significantly differ.
Part C: Why Do Conclusions Differ?
The different conclusions stem primarily from the statistical power and control of variability associated with each design. The independent measures design involves between-subject variability, which adds noise and makes it harder to detect differences. It also requires larger sample sizes for adequate power. The repeated measures design, by controlling individual differences (since the same subjects are used across treatments), yields more sensitive tests with higher statistical power, often resulting in a higher likelihood of detecting true differences.
In essence, even if treatments are truly different, the independent measures analysis might fail to reject H0 due to higher variability and lower power. Conversely, the repeated measures analysis, being more sensitive, might detect differences that the independent measures analysis cannot. Therefore, the same data can lead to different conclusions depending on the experimental design used and the statistical analysis applied.
Conclusion
Understanding the distinctions between independent measures and repeated measures designs is fundamental in experimental psychology and other sciences. Each has strengths and limitations that influence the likelihood of detecting true treatment effects. Careful consideration of the design is crucial when interpreting statistical results to ensure accurate and valid conclusions about treatment differences.