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Notes on Topic 13:
One-Way Analysis of Variance

    Demonstration of One-Way ANOVA
    (Independent-Measures)

    Example:

    This is hypothetical data from an experiment examining learning performance under three temperature conditions. There are three separate samples, with n=5 in each sample. These samples are from three different populations of learning under the three different temperatures. The dependent variable is the number of problems solved correctly.

    Independent Variable:
    Temperature (Farenheit)
    Treatment 1
    50-F
    Treatment 2
    70-F
    Treatment 3
    90-F
    0
    1
    3
    1
    0
    4
    3
    6
    3
    4
    1
    2
    2
    0
    0
    Mean=1 Mean=4 Mean=1

    This is a one-way, independent-measures design. It is called "one-way" ("single-factor") because "Temperature" is the only one independent (classification) variable. It is called "independent-measures" because the measures that form the data (the observed values on the number of problems solved correctly) are all independent of each other --- they are obtained from seperate subjects.

    Hypotheses:

    In ANOVA we wish to determine whether the classification (independent) variable affects what we observe on the response (dependent) variable. In the example, we wish to determine whether Temperature affects Learning.

    Demonstration:

    We demonstrate the logic of ANOVA by using this set of data. Here they are again, this time shown as a ViSta datasheet:

    The most obvious thing about the data is that they are not all the same: The scores are different; they are variable.

    Here are ViSta's summary statistics. Note, in particular, the means and standard deviations.

    Here are two plots of the data.

    • The first is a histogram of the data. The three groups are colored Red for T1, Green for T2 and Blue for T3. (See the WorkMap for rearanging the data to produce the histogram and do the ANOVA.)
    • The second is the diamond plot produced by the ANOVA that we do later on.
    Histogram
    Diamonds

    Are the groups different? This is what ANOVA trys to answer. What do you think?