A Researcher Is Interested In Whether Participating In Sport

5 A Researcher Is Interested In Whether Participatingin Sports Positi

A researcher is interested in whether participating in sports positively influences self-esteem in young girls. She identifies a group of girls who have not played sports before but are now planning to begin participating in organized sports. She gives them a 50-item self-esteem inventory before they begin playing sports and administers it again after six months of playing sports. The self-esteem inventory is measured on an interval scale, with higher numbers indicating higher self-esteem. In addition, scores on the inventory are normally distributed. The scores appear below. Before After a. What statistical test should be used to analyze these data? b. Identify H0 and Ha for this study. c. Conduct the appropriate analysis. d. Should H0 be rejected? What should the researcher conclude? e. If significant, compute the effect size and interpret. f. If significant, draw a graph representing the data.

Paper For Above instruction

The research question examines whether participation in sports has a positive effect on self-esteem among young girls. The study employs a repeated-measures design, where the same participants are assessed before and after engaging in sports. This design is suitable for analyzing differences in self-esteem scores over two time points within subjects, aiming to determine whether a significant change occurs post-intervention.

The appropriate statistical test for this scenario is the paired samples t-test, which compares the means of two related groups—in this case, the self-esteem scores before and after participating in sports. The assumption of normality of the differences and interval scale measurement are key considerations that justify the use of this test (Field, 2013).

The hypotheses for this study are as follows:

- Null hypothesis (H0): There is no difference in self-esteem scores before and after participating in sports (μ_before = μ_after).

- Alternative hypothesis (Ha): There is a difference in self-esteem scores before and after participating in sports (μ_before ≠ μ_after).

To conduct the paired samples t-test, the researcher would compute the differences between each participant’s pre- and post-scores, calculate the mean and standard deviation of these differences, and then use the t-formula to determine if the observed mean difference is statistically significant.

Suppose the analysis yields a p-value less than the significance level (commonly α = 0.05). In that case, H0 should be rejected, indicating that sports participation has a statistically significant effect on self-esteem. Conversely, if the p-value exceeds 0.05, H0 cannot be rejected, and the researcher concludes that there is no statistically significant change in self-esteem after participation.

If the results are significant, calculating the effect size provides insight into the magnitude of the change. Cohen’s d for paired samples is calculated by dividing the mean difference by the standard deviation of the differences (Cohen, 1988). An effect size of 0.2 is considered small, 0.5 medium, and 0.8 large. Interpreting this helps understand whether the statistically significant change is also practically meaningful.

Finally, visual representation of the data can be achieved through a bar graph depicting pre- and post-scores or a line graph illustrating mean self-esteem scores at both time points. Such visual aids facilitate easier interpretation of the data trends and the magnitude of change over time.

In conclusion, the paired samples t-test is an appropriate method for testing whether sports participation influences self-esteem in young girls in this study. The researcher should base findings on the statistical significance and effect size, and graphically illustrate the differences to effectively communicate results to both academic and practical audiences.

References

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
  • Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Sage Publications.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
  • Howell, D. C. (2012). Statistical methods for psychology (8th ed.). Wadsworth.
  • Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher's handbook (4th ed.). Pearson.
  • Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2019). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.
  • Heard, R. W. (2002). Research methods for students, educators, and researchers. Routledge.
  • Field, A. (2018). An adventure in statistics: The reality enigma. Sage Publications.
  • Chapman, S. P., & Carter, P. M. (2014). Practical statistics for the behavioral sciences. Routledge.

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