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Oneway ANOVA comparing 3 or more means

Oneway ANOVA comparing 3 or more means. Overall Purpose. A Oneway ANOVA is used to compare three or more average scores. Used when there is one IV with 3 or more levels and one DV. Sample data are used to answer a question about population means. Examples.

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Oneway ANOVA comparing 3 or more means

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  1. Oneway ANOVA comparing 3 or more means

  2. Overall Purpose • A Oneway ANOVA is used to compare three or more average scores. • Used when there is one IV with 3 or more levels and one DV. • Sample data are used to answer a question about population means.

  3. Examples • Does a new instructional method lead to more favorable student outcomes when compared to two types of traditional instruction comparison groups?

  4. Examples • Do low-income preschool children who live in the following situations differ in school readiness? • father present in the home • see father regularly • no contact with their father

  5. The F statistic • The F statistic is a ratio. • The denominator is within group variance. •  The numerator is between group + within group variance. • t2=F for the two group case.

  6. The F statistic • If the IV has no relationship to the population means, the F statistic will equal 1. • If F=1, there is no between group variance. 

  7. The F statistic • The F statistic examines whether sample means are varying more than they would be expected to vary due to sampling error alone.

  8. Assumptions • Normality • Homogeneity of Variance • Independence of Observations • Random Sampling

  9. Statistical Significance • How do you know when there is a statistically significant difference between the average scores you are comparing?

  10. Statistical Significance • When the F statistic is greater than 1 by enough to be beyond sampling error. • We know this because the p value is less than alpha, usually set at .05.

  11. Statistical Significance • A small p value tells us that there is a low probability that the variability in the means is due to sampling error alone. • We conclude there is more variability between the group means than would be expected by sampling error alone.

  12. Hypotheses • Hypotheses for the Oneway ANOVA: Null Hypothesis: • m1 = m2 = m3 ... mk Alternative Hypothesis: • mi =/= mj for at least one pair. • At least two of the population means are different. Where: • k = the number of population means

  13. Additional Considerations • There is a unique critical F value for each degrees of freedom condition. • A statistically significant F statistic does not tell us where the difference lies. • Confidence intervals and effect sizes can be very helpful in interpreting the results.

  14. Example • Our research design:

  15. The Research Question • Are classroom structural characteristic (class size, number of ELL children, etc.) different across the three stress groups?

  16. Writing About Results • Use APA format for reporting test statistics and p values: • t(29) = 7.345, p=.005 • F(1,123) = 2.446, p = .122 • Recognize the distinction between a statistically significant finding and an important finding.

  17. Writing About Results • Remember to review the writing guidelines in the handout on the website.

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