A researcher wishes to assess whether vitamin C is effective in the treatment of colds. To evaluate this hypothesis, the researcher decides to conduct a 2-year experimental study. The researcher obtains 30 volunteers from undergraduate classes to participate. The researcher randomly assigns an equal number of students to three groups: placebo group (group 1), low doses of vitamin C (group 2), and high doses of vitamin C (group 3).

In the first and second years of study, students in all three groups are monitored to assess the number of days that they have cold symptoms. During the first year, students do not take any pills. In the second year of the study, students take pills that contain one of the following: no active ingredients (placebo group 1), low doses of vitamin C (group 2), or high doses of vitamin C (group 3). The researcher’s SPSS data file includes 30 cases and two variables: a variable distinguishing among the three treatment groups and a dependent variable (i.e., the difference in number of days with cold symptoms in the first year versus the number of days with cold symptoms in the second year; year 2 sick days – year 1 sick days).

Use the following data set to answer questions below. Use an alpha of .05 when deciding about statistical significance (NOTE: the questions regarding the planned contrasts specify a direction).

DATA SET:

Group 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3

Diff 12 -2 9 3 3 0 3 2 4 1 -2 -3 3 -2 0 -4 -3 5 -9 -6 6 -7 -6 -6 -6 -4 -2 -6 6 5

When you use this procedure, please include planned contrasts that test the following:

• Does having any dose of Vitamin C significantly decrease number of cold symptoms compared to having a placebo?
• Does having high dose of Vitamin C significantly decrease number of cold symptoms compared to having a low dose?

*ANSWER ALL THE BLANKS FOUND IN THE FOLLOWING QUESTIONS*

Although not necessary because there is homogeneity of variance, what would we conclude about the effect of Vitamin C on change in cold symptoms if we were to use the results of a Welch Test?

• There _________ (WAS or WAS NOT) a significant effect of Vitamin C on change in the number of days with cold symptoms
  • F-test results to support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(No Decimals), ___________(round to 2 decimal places)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

Although not necessary because there is homogeneity of variance, what would we conclude about the effect of Vitamin C on change in cold symptoms if we were to use the results of a Brown-Forsythe Test?

• There _______________ (WAS or WAS NOT) a significant effect of Vitamin C on change in the number of days with cold symptoms
  • F-test results to support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(No Decimals), ___________(round to 2 decimal places)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

According to the SPSS output from a one-way independent ANOVA (main results), what would we conclude about the effect of Vitamin C on change in cold symptoms?

• There ________________ (WAS or WAS NOT) a significant effect of Vitamin C on change in the number of days with cold symptoms
  • F-test results to support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(no Decimals), ___________(no decimals)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

• There _______________ (WAS or WAS NOT) a significant linear trend indicating that as the dose of Vitamin C increased, change in the number of cold symptoms decreased proportionately.
  • F-test results to support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(no Decimals), ___________(no decimals)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

• There _______________ (WAS or WAS NOT) a significant quadratic trend.
  • F-test results to support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(no Decimals), ___________(no decimals)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

Using the "does not assume equal variances" results of the tests of the planned contrasts, complete the following statements?

• Planned contrasts revealed that having any dose of Vitamin C _______________ (DID or DID NOT) significantly decrease number of cold symptoms compared to having a placebo
  • t-test results that support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(round to 2 decimal places)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)

• Planned contrasts revealed that having high dose of Vitamin C _______________ (DID or DID NOT) significantly decrease number of cold symptoms compared to having a low dose.
  • t-test results that support your conclusion:
  • F=___________ (round answer to 3 decimals)
  • df=__________(round to 2 decimal places)
  • p=___________(round answer to 3 decimals)
  • Effect Size=__________(round answer to 2 decimals)