Analysis: Levene's Test For Equality Of Means

Register to read the introduction… Deviation |Std. Error Mean |
|Pair 1 |
| |N |Correlation |Sig. |
|Pair 1 |Before & After |20 |.193 |.415 |

|Paired Samples Test |
| |Paired Differences |
|9 |4 |
|3 |7 | |1 |6 | |6 |8 | |5 |7 | |7 |7 | |8 |8 | |3 |6 | |10 |7 | |3 |8 | |5 |9 | |2 |8 | |9 |7 | |6 |3 | |2 |6 | |5 |7 | |8 |6 | |1 |5 | |6 |5 | |3 |6 | A dependent t-test showed that there was no difference in the mean preference for Nibbles or Wribbles, t (19) = -2.01, 0.1 > p > 0.05. We fail to reject the null. 5. Using the following table, provide three examples of a simple one-way ANOVA, two examples of a two-factor ANOVA, and one example of a three-factor ANOVA. Complete the table for the missing examples. Identify the grouping and the test variable. |Design |Grouping variable(s) |Test variable | |Simple ANOVA |Four levels of hours of training—2, 4, 6, and 8 hours |Typing accuracy | |Simple |Three levels of ‘Number of Hours Studied’ – Less than |Test Scores | | |2, 2-4, More than 5 hours | | |Simple |Four Levels of BMI – underweight, average, overweight |Diabetes | | |and obese | | |Simple |Three levels of ‘Shoe Type’ – flats, short heels, |Number or ankle pains per week | | |Stilettoes | | |Two-factor ANOVA |Two levels of training and gender (two-way design) |Typing accuracy | |Two |Three levels of ‘Education’ – No college, |Job Salary | | |Undergraduate, Graduate – and Gender | | |Two |Four Levels of Favorite Snack – Dairy, Fruit, Chips, |Weight | | |Other – and Gender | | |Three-factor ANOVA |Two levels of training, two of gender, and three of |Voting attitudes | | |income | | |Three |Gender, BMI category, and Education |Income | 6. The data set for this problem can be found through the Sage Materials in the Student Textbook Resource Access link, listed under Academic Resources. Using the data in Ch. 13 Data Set 2 and the IBM® SPSS® software, compute the F ratio for a comparison between the three levels representing the average amount of time that swimmers practice weekly (< 15, 15–25, and > 25 hours) with the outcome variable being their time for the 100-yard freestyle. Does practice time make a difference? Use the Options feature to obtain the means for the groups. Copy and paste the output from IBM® SPSS® into this worksheet. |Descriptives | |Time | | | |Test of Homogeneity of Variances | |Time | |Levene Statistic |df1 |df2 |Sig. | |.306 |2 |33 |.739 | |ANOVA | |Time | | | |Dependent Variable:Time | | | | |Practice |N |Subset for alpha = 0.05| | | | |1 | |Tukey HSDa,,b |15-25 hours |13 |57.962 | | |25 hours |13 |59.031 | | |Sig. …show more content…
| |.875 |

The one-way ANOVA showed no significant difference between practice time (< 15 hours, 15 – 25 hours, > 25 hours) and the time to complete a 100-yard freestyle, F (2, 33) = 0.160, p = 0.853. Because of this, the post-hoc test was not needed. We fail to reject the null. The practice time is not associated with time to complete 100-yard free-style in this sample.

7. When would you use a factorial ANOVA rather than a simple ANOVA to test the significance of the difference between the averages of two or more groups?
A factorial ANOVA is used when you have two or more nominal variables as independent variables and a continuous variable as a dependent variable. One or more of the nominal variables can have more than two levels. A one-way ANOVA only has one independent nominal variable with more than two levels. 8. Create a drawing or plan for a 2 × 3 experimental design that would lend itself to a factorial ANOVA. Identify the independent and dependent variables. |Variable |Education – Diploma |Undergraduate |Graduate | |Gender – Male |Job Salary |Job Salary |Job Salary | |Gender – Female |Job Salary |Job Salary |Job Salary | From Salkind (2011). Copyright © 2012 SAGE. All Rights Reserved. Adapted with