FRAMEWORKS FOR SCIENTIFIC RESEARCH

Frameworks for Scientific Research

Frameworks for Scientific Research

Question 1

In order to statistically test the weights in pounds for players in five American football teams obtained by random sampling, Analysis of Variance (ANOVA) test has been used. The analysis of variance (ANOVA) of a factor used to compare several groups in a quantitative variable. It is a generalization of the two-sample independent t-test in case when independent variable has more than two categories (Triebold, 2007). Categorical variable (either nominal or ordinal) defines the groups of independent variable that should be compared to the dependent variable. Analysis of Variance effectively defines the homogeneity with respect to dependent variable for particular variable categories (Corbin, 2008). ANOVA helps in predicting the relation between variable groups towards the dependent variable based on coherent properties of the independent variable. Thus, ANOVA statistical measurement method can be performed on each group and find out whether there are differences between them (Bernard, 2006).

The hypothesis tested in the one-way ANOVA is that the population means are equal. If the population means are equal, this means that the groups do not differ in their properties; consequently, factor is independent of defined variables (Creswell, 2009). In order to conduct the Analysis of Variance (One-way ANOVA) for the proposed research question, “Football Team” is used as an independent variable and the “Weight in pounds for players” is used as dependent variable. Football Team has been taken as a nominal variable and the “Weights in pounds for players” has been taken as a continuous variable measuring the weights of every player on Likert scale. Weight in pounds for players is categorized in five segments that are included in the analysis. These include San Francisco 49ers, Denver Broncos, Dallas Cowboys, Green Bay Packers, and Miami Dolphins.

Null hypothesis:

There is no statistically significant difference between average weight of players belonging to San Francisco 49ers, Denver Broncos, Dallas Cowboys, Green Bay Packers, and Miami Dolphins football teams.

Alternate hypothesis:

There is statistically significant difference between average weight of players belonging to San Francisco 49ers, Denver Broncos, Dallas Cowboys, Green Bay Packers, and Miami Dolphins football teams.

Analysis of Results

Descriptive statistics of the ANOVA are presented in the below table. Main notable thing to note is that sum of squares for the data is higher for the within groups as compare to between groups. Between Groups represent the 1713.77 sum of squares out of 23475.17; whereas, Within Groups constitute 21761.41 sum of square value in total proportion of variance. F-value stood at 1.575, which appears insignificant at 0.05 confidence interval level. This shows that ANOVA test for the two selected variables result in rejecting the null hypothesis and accepting the alternate hypothesis, which states that average weight of all team players is equal (Creswell, 2009).

ONEWAY Weight BY Team

  /STATISTICS DESCRIPTIVES

  /PLOT MEANS

  /MISSING ANALYSIS

  /POSTHOC=TUKEY ALPHA(0.05)

ANOVA

Weight (in Pounds)

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

1713.765

4

428.441

1.575

.189

Within Groups

21761.412

80

272.018

Total

23475.176

84

The output shows that the average weight of San Francisco 49ers players stood at 247pounds with standard deviation of 15.33pounds. Similarly, average weight of team players stood at 251, 254, 249, and 240 pounds for Denver Broncos, ...