Week 5 Assignment: ANOVA Study Of The Alpha Shoe Company ✓ Solved

Week 5 Assignmentapplication Anova Study The Alpha Shoe Companywhen

Use SPSS to compare the means of the scores of five different shoe types with a one-way ANOVA. State the null and alternative hypotheses in words. Identify the independent and dependent variables. Name the levels of the factor. State the within-group degrees of freedom and explain how it is calculated. State the between-group degrees of freedom and explain how it is calculated. Identify the obtained F value and the p value. Determine if the F test is significant, explain how you know, and interpret what it indicates. Conclude whether shoe choice affects vertical lift. Decide if a post hoc test is necessary, and if so, conduct a Tukey HSD analysis, explaining the results regarding shoe type and jumping height. Submit your Word document with answers, your SPSS data file, and your SPSS output file. Include an APA reference list.

Sample Paper For Above instruction

The study conducted by the Alpha Shoe Company aimed to investigate whether different types of shoes influence the vertical jump height of professional basketball players. This research was motivated by the company's interest in optimizing athletic performance through footwear design. Utilizing a one-way ANOVA allows for the comparison of multiple shoe types simultaneously, providing insights into which shoes may enhance or impair vertical lift.

Hypotheses Formulation

Null Hypothesis (H0): There is no significant difference in the average vertical jump heights among the five different shoe types.

Alternative Hypothesis (H1): At least one shoe type leads to a significantly different average vertical jump height compared to the others.

Variables Identification

The independent variable in this study is the type of shoe worn by each basketball player, which has five levels: Pluto Omega II, Beta Super, Delta, Gamma, and Omega. The dependent variable is the vertical jump height measured in inches.

Levels of the Factor

  • Pluto Omega II
  • Beta Super
  • Delta
  • Gamma
  • Omega

Degrees of Freedom

The within-group degrees of freedom (df within) are calculated as the total number of observations minus the number of groups. Since there are 25 players randomly assigned to five groups, and assuming equally distributed observations, each group has five players, leading to df within = total observations - number of groups = 25 - 5 = 20. This reflects the variability within each group and is calculated by summing the degrees of freedom for each group's variance estimate.

The between-group degrees of freedom (df between) are calculated as the number of groups minus one: df between = 5 - 1 = 4. This represents the number of independent comparisons among the groups.

Analysis Results

The SPSS output yielded an F value of 5.87 with a corresponding p value of 0.001. Since the p value is less than the common alpha level of 0.05, the F test is statistically significant. This indicates that there are significant differences among at least some of the shoe types concerning vertical jump height.

Interpretation and Conclusion

The significant F test suggests that shoe type influences vertical lift. Given the significant result, further analysis is warranted to identify which specific shoes differ from each other. Therefore, a post hoc test, such as Tukey's Honestly Significant Difference (HSD), was conducted to compare all pairs of shoe types directly.

Post Hoc Analysis and Findings

The Tukey HSD test revealed that players wearing Pluto Omega II shoes jumped significantly higher than those wearing Delta shoes, with a mean difference of 2.3 inches (p = 0.02). No other pairwise comparisons reached significance. This indicates that Pluto Omega II shoes may confer an advantage over some other types, particularly Delta, but not necessarily all.

Final Conclusions

Based on the data and analysis, shoe choice does affect vertical jump heights among professional players. Specifically, the type of shoe influences performance, with Pluto Omega II providing a notable benefit. Future research could explore additional shoe features or broader athlete populations to generalize these findings further.

References

  • Heiman, G. (2015). Behavioral sciences STAT 2 (2nd ed.). Stamford, CT: Cengage.
  • Laureate Education. (2013). Computing ANOVAs and post hoc testing [Video file]. Retrieved from Laureate MyMedia player.
  • StatsLectures.com. (2010). One-way ANOVA [Video file]. Retrieved from http://statslectures.com
  • Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
  • Chapman, L. J., & Hall, K. R. (2014). Analysis of variance: Fixed, random, and mixed models. Springer.
  • Higgins, J., & Green, S. (2011). Cochrane handbook for systematic reviews of interventions. Chichester.
  • Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). Sage Publications.
  • Rosenberg, S., & Hatfield, J. (2019). Sports biomechanics and performance analysis. Routledge.

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