Caffeine and Tests: University researchers are interested in how much drinking c
ID: 3131560 • Letter: C
Question
Caffeine and Tests:
University researchers are interested in how much drinking caffeinated drinks before exams can change the outcome of a student’s test score. To do so they want to give students a cup of coffee before an upcoming chemistry exam. The researchers decide that they should give students coffee with one of four different caffeine amounts: 0mg, 50mg, 100mg, 150mg, one hour before the exam. Then after the exam, each students test score is recorded. There are six sections of the chemistry class and each is taught by a different Teaching Assistant. To control for variation of exam scores across different sections, the researchers select four students from each section in accordance with a block design with the class sections as the blocking factor. Each student within a section will receive a randomly selected caffeine dosage for their coffee. The test scores are summarized in the following table where each cell, unless otherwise indicated, shows the test score for a particular student. The row and column of that student indicate the students class section and caffeine dosage.
Caffeine
0mg 50mg 100mg 150mg
Section
001 73 73 78 74
002 72 76 78 72
003 68 72 81 73
004 74 77 86 80
005 73 79 88 81
006 74 75 81 81
Caffeine
Group 72.33 75.33 82.00 76.83
Means
Grand Mean = 76.625
(a)
Create a Block ANOVA table for this data. This means it must have a column for Source, Sum of Squares, Degrees of Freedom, and Mean Squares.
*Be careful: what kind of factor is the class section?*
The sums of squares are SST =294.12; SSB =160.37, SSTotal = 529.62. Makesure to include the Total source of variation row in your table
(b)
Is there significant evidence to conclude that at least one pair of caffeine levels have different mean test scores? (level of significance = 0.05)
(c)
Is there significant evidence to conclude at least one pair of sections have different mean test scores? (level of significance = 0.05)
(d)
Use the Tukey’s Pairwise Comparison procedure to assess which caffeine level has the highest mean test score. This requires six comparisons in total. Which groups differ? Is there a best caffeine level in terms of test scores? Explain why you can or cannot make this conclusion.(level of significance = 0.05)
(e)
In a few sentences, summarize your findings in a way that would explain the results of (b), (c), and (d) to someone without statistics knowledge.
Explanation / Answer
a)
b) There is a significant evidence to conclude that at least one pair of caffeine levels have different mean test scores because the F value is > the critical value i.e., 19.57571 > 3.287382
c) There is a significant evidence to conclude at least one pair of sections have different mean test scores because the F value is > the critical value i.e., 6.404326 > 2.901295
d) Using tukey's pairwise comparision The caffeine levels 100 has highest mean test score. the groups 0mg and 100 mg and 50 mg and 100 mg differ.
e) We can summarize there is a there is significant difference among the sections and also among the caffeine dosage levels at 0.05 level of significance.
ANOVA Source of Variation SS df MS F P-value F crit Rows 160.375 5 32.075 6.404326 0.002251 2.901295 Columns 294.125 3 98.04167 19.57571 1.91E-05 3.287382 Error 75.125 15 5.008333 Total 529.625 23