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ANOVA EXAMPLE

ANOVA EXAMPLE. PART I. Access read times in miliseconds. 8 files of each size: Small: 50,000 characters Medium: 75,000 Large: 100,000. One-way ANOVA Table. Failed to reject H 0 at 0.05 significance level. Conclusions. H 0 : H 1 : At least one of the means differs.

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ANOVA EXAMPLE

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  1. ANOVA EXAMPLE

  2. PART I • Access read times in miliseconds. • 8 files of each size: • Small: 50,000 characters • Medium: 75,000 • Large: 100,000

  3. One-way ANOVA Table Failed to reject H0 at 0.05 significance level

  4. Conclusions • H0: H1: At least one of the means differs. Decision rule: If F > 3.47, reject H0. Test statistic: F = 2.60 • Decision: do not reject H0. • There is insufficient evidence to conclude that the average read times differ depending on the file size. • The Tukey procedure should not be used since the null hypothesis above was not rejected. • There is inadequate evidence on which to form a conclusion about differences in average read times based on file size.

  5. PART II Buffer size: 20 kbytes 40 kbytes

  6. Two-way ANOVA Table Reject H0 of no interaction at 0.05 significance level Reject H0 of no buffer size effect at 0.05 significance level Reject H0 of no file size effect at 0.05 significance level

  7. Interaction • H0: There is no interaction between buffer size and data file size. • H1: There is an interaction between buffer size and data file size. Decision rule: If F > 3.55, reject H0. Test statistic: F = 4.0835 • Decision: Since Fcalc = 4.0835 is above the critical bound of 3.55, reject H0. • There is sufficient evidence to conclude there is an interaction between buffer size and data file size.

  8. Buffer Size • H0: μ20 = μ40 • H1: μ20 is not equal to μ40 Decision rule: If F > 4.41, reject H0. Test statistic: F = 131.8529 • Decision: Since Fcalc = 131.8529 is well above the critical bound of 4.41, reject H0. • There is sufficient evidence to conclude that average read time does differ between the two levels of buffer size.

  9. File Size H0: H1: At least one of the means differs. Decision rule: If F > 3.55, reject H0. Test statistic: F = 19.5403 Decision: Since Fcalc = 19.5403 is above the critical bound of 3.55, reject H0. There is sufficient evidence to conclude that the average read times differ depending on the file size.

  10. Interaction Effect

  11. Conclusions • Given the interaction effect was significant, some levels of file size work better with one of the buffer sizes than the other. • We cannot directly conclude that there is a significant difference in average read times due to buffer size or file size (main effects) because the average read times for different buffer sizes are different for different sizes of files.

  12. Conclusions Continued • Conclusions about the relative speed of the buffers or file sizes cannot be drawn because buffers and file sizes interact. • Because the two factors interact significantly, the completely randomized design is superior to the factorial design model because the presence of their interaction prohibits us from being able to look at the individual effects of each factor separately.

  13. New Format for one-way ANOVA

  14. One-way ANOVA result Statistical decision: Reject null at 0.05 significance level

  15. Tukey Kramer in PHStat We enter this value

  16. Pair wise comparisons

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