# Statistics Project Part 3

Running Head: Statistics Project Part 3 1

Statistics Project Part 3 3

Statistics Project Part 3

Nasser Y Miranda

University of Phoenix

August 18th, 2018

 Anova: Single Factor Anova: Single Factor SUMMARY SUMMARY Groups Groups Count Sum Average Variance Relationship Supervisor 50 125 2.5 1.030612 Happiness Happiness 50 370 7.4 2 ANOVA ANOVA Source of Variation Source of Variation SS df MS F P-value F crit Between Groups Between Groups 600.25 1 600.25 396.1246 3.34E-36 3.938111 Within Groups Within Groups 148.5 98 1.515306 Total Total 748.75 99 Tukey’s HSD Difference n (Relationship) n (Happiness) SE q statistic Relationship 4.9 50 50 1 4.9 Happiness 4.9 50 50 1 4.9

The Single factor one-way ANOVA is basically used to test whether the population means of observations of more than one treatment effects are equal (Brady, 2015). Since F > F crit the null hypothesis has to be rejected in this case. In this case, 396.1246 > 3.938111 thus we reject the null hypothesis in the sense that means for Happiness and Relationship are not equal. Post Hoc testing is useful in identifying the differences that are significant (Kuznetsova, Brockhoff, & Christensen, 2017). As opposed to the t-test, the ANOVA is useful in comparing means of more than two groups to test the hypothesis (Maurya, 2015). Moreover, since ANOVA goes to the extent of showing the statistical significance between the groups, it also reduces type I error (Keith, 2014).

References

Brady, S. M., Burow, M., Busch, W., Carlborg, Ö., Denby, K. J., Glazebrook, J., … & Springer, N. M. (2015). Reassess the t test: interact with all your data via ANOVA. The Plant Cell, tpc-15.

Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modeling. Routledge.

Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. B. (2017). lmerTest package: tests in linear mixed effects models. Journal of Statistical Software, 82(13).

Maurya, V. N., Jaggi, C. K., Vashist, S., Ogubazghi, G., Varshney, D. K., Maurya, A. K., & Arora, D. K. (2015). Impact of some significant factors for intern’s job satisfaction and performance using t-test and ANOVA method. American Journal of Biological and Environmental Statistics, Science Publishing Group, USA, 1(1), 19-26.