Statistics

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Compute a one-way ANOVA - Give the source table, test null hypothesis at .05 level. Please explain the steps to solving this.

Group 1: 26, 34, 46, 48, 42, 49, 74, 61, 51, 53
EX 1 : 484
Ex 1^2 : 25,024
n = 10

Group 2: 51, 50, 33, 28, 47, 50, 48, 60, 71, 42
EX 2 : 480
EX 2^2 : 24,392
n = 10

Group 3: 52, 64, 39, 54, 58, 53, 77, 56, 63, 59
EX 3 : 575
EX 3^2 : 33,925
n = 10

Group 4: 41, 49, 56, 64, 72, 65, 63, 87, 77, 62
EX 4 : 636
EX 4^2: 42,034
n = 10

  • Statistics -

    Let's use an example, and perhaps you can use this as a guideline for similar ANOVA problems.

    Suppose we wish to establish if a difference exists between three different levels of something (it doesn't matter what it is...this is just for purposes of illustration).
    
    Here are the values for each level:
    Level 1: 0, 1, 1, 2, 2
    Level 2: 1, 2, 1, 3, 3
    Level 3: 3, 3, 2, 4, 3

    Totals for each level are:
    Level 1: 6 -->add each value in the level for a total.
    Level 2: 10
    Level 3: 15

    Total of squared values for each level are:
    Level 1: 10 -->square each value in the level, then add for total.
    Level 2: 24
    Level 3: 47

    To calculate SS within for the ANOVA table, take (sum of total squared values) minus (sum of totals divided by number of values per level). It would look like this:

    (10 + 24 + 47) - [(6^2 + 10^2 + 15^2)/5] = 8.8
    
    SS between would be calculated this way:
    (6^2 + 10^2 + 15^2)/5 - (6 + 10 + 15)^2/15 = 8.13
    Note: 15 = total number of values in all levels.

    SS total = SS between + SS within = 16.93

    To calculate df between:
    k - 1 = 3 - 1 = 2
    Note: k = number of levels.
    
    To calculate df within:
    N - k = 15 - 3 = 12
    Note: N = total number of values in all levels.

    df total = df between + df within = 14

    To calculate MS between:
    SS between/df between = 8.13/2 = 4.065

    To calculate MS within:
    SS within/df within = 8.8/12 = 0.73

    To calculate F-ratio:
    MS between/MS within = 4.065/0.73 = 5.57

    Therefore, the ANOVA table would look like this:

    Source......SS......df....MS......F
    Between....8.13......2....4.065...5.57
    Within.....8.8......12....0.73
    Totals....16.93.....14


    I hope this example will help. It looks like you already have the values needed to do the calculations for each of your 4 groups. Remember to check the appropriate table for your critical value to compare to your F-ratio. Once you do the comparison, you will either fail to reject the null or you will reject the null. You can then form your conclusions.

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