Dr. Tajuddeen A. Williams

ANOVA Study: The Alpha Shoe Company

· Personal Essays

My null hypothesis states that there is no significant affect on jump height based on the type of shoe a player wears. My alternate hypothesis states that there is a significant affect on the jump height based on the type of shoe a player wears. The independent variable is the type of shoe a player wears since it is the variable that can be manipulated. The dependent variable is the jump height because it’s the variable that we are measuring. We have five levels in our factor: Pluto, Omega II, Beta Super, Delta, and Gamma.

$a = 5$ $N = 25$ $n = 5$

We are able to determine the ${df}_{between}$ by subtracting the number of levels of the factor minus 1.

${df}_{between} = a - 1 = 5 - 1 = 4$

We can determine the ${df}_{within}$ by subtracting the total number of people in the experiment from the levels of factor

${df}_{within} = N - a = 25 - 5 = 20$

We can determine the total simply by adding ${df}_{between}$ and ${df}_{within}$ or by subtracting the total number of people in the experiment minus 1.

${df}_{total} = N - 1 = 25 - 1 = 24$

I need to look up my critical factor on an f-table. This will help me to determine whether my results are statistically significant. In order to do that, I need my ${df}_{between}$ and my ${df}_{within}$. These numbers are 4 and 20. This gives me:

(4,20) = \ 2.8661

If F is greater than my critical factor, we reject the null hypothesis. In this case, my F value of 7.820 > 2.8661. My p value is equal to 0.001. F(4,20) = 7.820, p < 0.05.

It is apparent that there is a significant difference on jumping height between the shoes. A post hoc test should be conducted because the results are significant. If they were not significant, we would not need to do so (Welkowitz, Cohen, & Lea, 2012). From the previous results, we know that there is significance, but we do not know what there is significance between.

The results of the post hoc test show that:

  • There was a significant difference between players who wore Pluto and Delta, and Pluto and Gamma, but no significant difference between Pluto and other shoes

  • There was not a significant difference between players who wore Omega II and other shoes.

  • There was a significant difference between players who wore Beta Super and Gamma, but no significant difference between Beta Super and other shoes.

  • There was a significant difference between players who wore Delta and Pluto, but no significant difference between Delta and other shoes.

  • There was a significant difference between players who wore Gamma and Pluto, and Gamma and Beta Super, but no significant difference between Gamma and other shoes.

We can conclude that the type of shoe worn does indeed affect the jumping height of each player and players who wore Pluto jumped higher than those of wearers of other shoes.

References

  • Welkowitz, J., Cohen, B. H., & Lea, R. B. (2012). Introductory Statistics for the Behavioral Sciences (7 ed.). John Wiley & Sons, Inc. ↩

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