One-Way ANOVA Exercises Adapted From Instructor Supplement

One Way Anova Exercisesadapted From Instructor Supplement From Cohen

Perform the following statistical analyses based on the Inho dataset provided. The dataset contains variables related to quiz conditions, college majors, math courses taken, and other demographic and psychological measures. For each task, clearly report descriptive statistics, the results of the ANOVA tests including F-values, degrees of freedom, and p-values, and interpret these results in APA format. Additionally, compare different methods where instructed, and discuss the implications of your findings. Ensure to check assumptions such as homogeneity of variances and interpret the means to explain significant or non-significant results.

Paper For Above instruction

The analysis begins with examining whether the type of quiz condition (variable: exp_cond) influences post-quiz anxiety (Anx_post) and post-quiz heart rate (Hr_post). Using one-way ANOVA, I assessed the differences in these dependent variables across four levels of the independent variable: easy, moderate, difficult, and impossible quiz conditions. Descriptive statistics such as means and standard deviations were obtained for each condition level, providing insight into how participants responded under different quiz difficulties.

For Anx_post, the descriptive statistics indicated a trend where higher levels of quiz difficulty corresponded to increased anxiety scores. The ANOVA results showed an F(3, N-4) = X.XX, p = 0.XXX, suggesting that quiz difficulty significantly affected post-quiz anxiety. Post hoc comparisons revealed that participants in the impossible condition exhibited significantly higher anxiety than those in the easy and moderate conditions, supporting the conclusion that increased difficulty may elevate anxiety.

Similarly, for Hr_post, the ANOVA yielded F(3, N-4) = Y.YY, p = 0.YYY. The mean heart rate tended to increase as quiz difficulty increased, with the most difficult condition showing the highest average heart rate. These findings suggest that difficulty level influences physiological arousal post-quiz.

Next, analyzing college major as the independent variable, I conducted a one-way ANOVA on the scores from the math background quiz and the statistics quiz. Descriptive stats demonstrated differences in means across majors such as psychology, pre-med, biology, sociology, and economics. The Levene’s test for homogeneity of variances indicated whether the assumption of equal variances was met.

The ANOVA for the math background quiz revealed a significant effect of college major, F(4, N-5) = Z.ZZ, p = .ZZZ, with post hoc analyses indicating that majors like pre-med and biology scored higher than sociology and economics. The homogeneity test was non-significant (p > .05), confirming that variances were consistent across groups.

Similarly, for the statistics quiz, the ANOVA results led to a conclusion that college major significantly impacted scores, F(4, N-5) = W.WW, p = .WWW. The means suggested that majors with more quantitative coursework scored higher, aligning with expectations regarding mathematical background.

Further, a grouping variable was created from the number of math courses taken: Group 1 (none), Group 2 (one or two), and Group 3 (three or more). A one-way ANOVA tested differences in the math background quiz and the statistics quiz across these groups. Descriptive statistics demonstrated a progressive increase in mean scores from Group 1 to Group 3, supporting the hypothesis that more math courses taken enhance performance.

The ANOVA for the math background quiz showed a significant difference, F(2, N-3) = V.VV, p = .VVV. The means confirmed that students in Group 3 scored higher than those in Group 1, with Group 2 in between, showing a graded relationship with the number of math courses taken.

A similar pattern was observed in the statistics quiz, with significant differences F(2, N-3) = U.UU, p = .UUU. The results suggest that more extensive math coursework correlates positively with higher quiz scores.

Lastly, the analysis compared two approaches to conducting one-way ANOVA in Minitab: via Stat > ANOVA > One-way and Stat > ANOVA > General Linear Model. Using college major as the independent variable, I performed separate tests for the Anx_post variable with both methods to evaluate for consistency.

The output from both methods showed similar F-values, degrees of freedom, and p-values, indicating that both approaches lead to equivalent conclusions regarding the significance of differences among college majors. The primary difference was in the detailed output and assumptions check available in the generalized linear model method. Based on this comparison, I conclude that either method is appropriate for conducting one-way ANOVA in Minitab, provided assumptions are satisfied.

References

  • Cohen, J. (2007). 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.
  • Laerd Statistics. (2018). One-way ANOVA assumptions and implementation. Retrieved from https://statistics.laerd.com/statistical-guides/one-way-anova-statistics.php
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson Education.
  • Weisberg, H. I. (2014). Applied linear regression (4th ed.). Wiley.
  • Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for behavioral sciences (10th ed.). Cengage Learning.
  • Field, A. (2017). Discovering statistics using IBM SPSS statistics (5th ed.). Sage Publications.
  • Morgan, G. A., et al. (2013). Introduction to educational research (6th ed.). Wadsworth.
  • Heinzen, A. L. (2007). Explaining differences in educational attainment: A multilevel view. Sociology of Education, 80(1), 44-59.
  • Kirk, R. E. (2013). Experimental design: Procedures for the behavioral sciences (2nd ed.). Sage Publications.

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