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Homework - Analysis of Variance - One-Way

DIRECTIONS: Be sure to show the necessary calculations to back up your answers and show all work neatly. Use the six step procedure shown in class for any hypothesis tests. Attach Minitab output where appropriate and mark it up to clearly indicate what is relevant and that it agrees with your hand calculations.

Definition/Essay (10 points each)

  1. List three reasons why it is not a good idea to use a bunch of t-tests to analyze an experiment with more than two groups.

  2. Assuming we have four groups and do a one-way ANOVA, list all simple comparisons that are possible?

  3. When doing a one-way ANOVA, the final calculations are placed into an ANOVA summary table. In this table, two quantities must add up to a total in two cases. What are the quantities and what are the two cases?

  4. One multiple comparison procedure is called the protected t test. Why is it called "protected"?

  5. The F statistic is a ratio. Please describe this ratio.

Multiple Choice (5 points each)

  1. The term error variance is equivalent to the
    a. total variance.
    b. variance between the groups.
    c. variance within the groups.
    d. range divided by the mean.

  2. In a one-way ANOVA, the assumption of homogeneity of variance applies to
    a. the variance within the groups.
    b. the variance of the means associated with the treatment groups.
    c. the total variance.
    d. nothing, since the assumption is irrelevant to the ANOVA.

Problems (40 points consisting of 30 for hand calculations and 10 for MTB)

  1. Suppose you are interested in the use of technology in the classroom. We do an experiment in which we teach each of three sections of a Psychological Statistics class in a different way. One section of six students receives the standard lecture format (blackboard & discussion), a second section of six students receives the same lectures but presented with Microsoft Powerpoint, and for the third section, the lectures are available on the web. The dependent variable is performance on a standardized (final) exam. The data for the three groups follow. Do an analysis by hand (including a graph of the means) as well as using Minitab. If the omnibus F is significant, you should conduct post hoc comparisons.

    SUBJECT
    GROUP
    Lecture
    PowerPoint
    Web
    1
    65
    85
    92
    2
    72
    74
    80
    3
    64
    64
    78
    4
    85
    85
    96
    5
    59
    65
    85
    6
    78
    81
    82

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