In our previous class, we flew the paper airplanes of specific designs and recorded the distance they flew. The data file “PaperAirplane.xls” on the OnCourse website contains two variables:
Design:
1: Nick’s Paper Airplane
2: Origami Paper Airplane 3
3: Floating Paper Airplane
4: Worst Ever Paper Airplane
Distance: distance flown in inches
1. (1 point) Use SPSS to make a side-by-side boxplot of the four designs, and describe what you find. Remember to discuss whether there are outliers, the amount of overlap between the boxes, and the general trends present.
2. (1 point) Use SPSS to find the sample size, sample mean, and sample standard deviation of each design group.
3. (1 point) Is it reasonable to pool the variances for one-way ANOVA? Why or why not?
4. (1 point) Use SPSS to create a means plot. Discuss the results and how this compares to the side-by-side boxplot in #1.
5. (1 point) State your hypotheses for a one-way ANOVA test for this story.
6. (1 point) Run the one-way ANOVA in SPSS, regardless of your answer to #3. Report the F test statistic and the P-value.
F = ___________ P-value = ______________
7. (1 point) What are your conclusions in terms of the airplane story (using a significance level of 0.05)?
8. (1 points) Report the R-squared and the pooled estimate of the standard deviation.
R2 = _________
%_____
s = _______________
9. (1 point) Is it necessary to do the Bonferroni’s multiple comparison procedure? Give your reason why or why not.
10. (2 points) Regardless of your answer to #9, run the Bonferroni procedure using SPSS and report your results in terms of the story.
Phosphorus is an important element to our life. In a research study, 164 patients of age 65 or older took blood tests to find their serum inorganic phosphorus levels. The data file “phosphorus.xls” on the OnCourse website contains three variables:
Phosphorus: Serum inorganic phosphorus level (in mmol/L)
Age: 1=65-69; 2=70-74; 3=75-79
Gender: 1=Male, 2=Female
The researchers want to find out if age, gender and/or their interaction make a difference to the mean serum inorganic phosphorus level.
11. (1 point) Using SPSS, find the sample size, sample mean, and sample standard deviation for each of the age-by-gender combinations.
12. (1 point) Is it reasonable to pool the variances? Why or why not?
13. (1 point) Why is it important to check that it is reasonable to pool the variances?
14. (1 point) Using SPSS make a plot of the means of the combinations (with age on the x-axis). Describe what the plot tells you about each of the main effects and their interaction and how the plot tells you this.
15. (1.5 points) State the hypotheses (including variable names) for the two-way ANOVA tests.
16. (1.5 points) Using SPSS (regardless of your answer to #12), run the ANOVA tests. Report the F test statistics and P-values.
17. (2 points) State your conclusion to the hypothesis tests in terms of the story.
SPSS Instructions for Lab 7
1. Side-by-side Boxplot
Graphs Legacy dialogs Boxplot (Default ones: Simple, Summaries for groups of cases) Define Move “distance” into “Variable” box and move “design” into “Category Axis” box. OK
2. Plot of Means, one-way ANOVA and Bonferroni’s multiple comparisons
Analyze Compare Means One-Way ANOVA
Move “distance” into “Dependent List” box
Move “design” into “Factor” box
Click on “Post Hoc” Check “Bonferroni” box “Continue”.
Click on “Options” Check “Means plot” box “Continue” “OK”.
3. Table of means and standard deviations and checking equal variances
Analyze Compare Means Means
Move “distance” into “Dependent List” box.
Move “design” into “Independent List” box OK.
Two-way ANOVA
Analyze General Linear Model Univariate
Move “phosphorus level” into the “Dependent Variable” box and
Move both “gender” and “age” into the “Fixed Factor(s)” box
Click on “Plots.” Move “age” to the horizontal axis box and “gender” to the separate lines box. Click the “Add” button to move that combination to the bottom box. Click “Continue.”
Click on “Options.” Move “gender” and “age” into “Display Means for” box and check “Descriptive statistics” box. Click “Continue.”
OK
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