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One-Way Dependent Groups ANOVA


Research Question

Experimental Design

Statistical Hypothesis

    Are the mean settings of the two groups sampled from the same population or different populations? Is µ1 = µ2?

Hypothesis Testing Model

    Ho: µ1 = µ2

    Ha: µ1 <> µ2

The Test Statistic

    The test statistic is the F-statistic (aka "variance ratio")

The Sampling Distribution

    If the Ho is true then the F value from the experiment will be drawn from the sampling distribution of F with n1 = 1 and n2 = 55 degrees of freedom.

Type-I Error rate

    We'll use a 5% Type-I error rate.

Decision Rule

  • The Critical Value of the test statistic is .95F1,55 = 4.016. Note: Your table doesn't have this entry. The rule is to use the nearest tabled value with fewer DF. In this instance that would be F with 1 and 40 DF or 4.08.
  • Reject Ho if F > 4.016

    Data

    Descriptive Statistics

    Subject Letter Span Digit Span
    1 xx xx
    2 xx xx
    3 xx xx
    ... ... ..
    56 xx xx

    Letter

    Digit

    Diff

    56

    56

    56

    Count

    6.28

    7.34

    -1.06

    Mean

    0.9905.

    1.1643.

    1.0228.

    est Sigma

    0.1324.

    0.1556.

    0.1367.

    SEM

    0.4760.

    Slope

    2.7829.

    y-intercept

    0.5596.

    corr

ANOVA Source Table

Concerning the Dependent Groups ANOVA Table:

ANOVA Summary Table

Source

SS

df

MS

F

Subjects

In Excel this row is labeled "Rows"

Numerator of F

99.7477679

55

1.81359578

3.46760301

This F "tells" whether or not some subjects had memory spans different from other subjects. Irrelvant or trivial in this instance.

Treatment

In Excel this row is labeled "Columns"

Numerator of F

31.609375

1

31.609375

60.4372624

This F "tells" whether or not the independent variable had an effect on the value of the dependent variable.

Error

Denominator of F

28.765625

55

0.5230

Total

160.122768

111

MSs do not Total

Statistical Decision

Interpretation


Calculations for ANOVA (optional)

The Dependent Groups ANOVA Source table is calculated using Excel. I do not know of an intuitive calculation scheme for the Dependent Groups ANOVA.

© 2006 by Burrton Woodruff. All rights reserved. Modified Tue, Sep 26, 2006