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One Way ANOVA between Subjects - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

English and Foreign Languages UniversityStatistics for Psychologists

One Way Anova between Subjects, Independent Samples, Test Hypothesis, Independent Variable, Anova Summary Table, Equal Variance, Logic of Anova, Within Group Variance are learning points of this lecture.

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Basic Statistics for
The Behavioral Sciences
LECTURE NOTES
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Download One Way ANOVA between Subjects - Basic Statistics for Behavioral Sciences - Lecture Notes and more Study notes Statistics for Psychologists in PDF only on Docsity!

Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

Ch. 13. One-way ANOVA (between-subjects) I. Situation A. Two or more independent samples. B. Test hypothesis about the equality of group means. C. One independent variable (one-way).

II. Procedure

A. H 0 : ฮผ 1 = ฮผ 2 = โ‹… โ‹… โ‹… = ฮผa. H 1 : H 0 is not true (at least two ฮผ's are significantly different from each other). B. ฮฑ: .05 or .01, Fcrit, dfnum=a-1 and dfden=N-a. C. TS: Fobs D. Decision: If Fobsโ‰ฅFcrit, reject H 0.

III. Fobs = MSB/MSW MSB = SSB/dfB = SSB/a- MSW = SSW/dfW = SSW/N-a SSB=

SSW=

A. ANOVA Summary Table Source df SS MS F Treatment a-1 SSB MSB MSB/MSW Error N-a SSW MSW โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€ Total N-1 SST B. Example

C. Assumptions

  1. Normality.
  2. Equal variance.
  3. Independence.

IV. F-distribution A. has two parameters, dfnum and dfden if H 0 is true. B. Positively skewed. C. Range: 0 - โˆž.

are different from each other.

  1. Why not multiple t-tests?---> Type I error. B. Procedure (Tukey's HSD)
  2. Put all means in order from the smallest to the largest.
  3. Make an axa mean-difference (MD) matrix only for the upper diagonal side.
  4. Compute a critical difference (CD). CD=q MSW / n , where q=the q-critical value.
  5. Compare CD to each of the mean-difference (MD), if MDโ‰ฅCD, reject H 0 (two groups are different). C. Example