Tim ran a \( \mathbf{3 x 2} \) between-subjects factorial ANOVA using an alpha of \( 5 \%, \mathrm{~N}=48 \) and \( \mathrm{n}=8 \). Fill in the missing spots in this ANOVA answer table below: \begin{tabular}{|r|c|c|c|c|c|} \hline Source & SS & DF & MS & F & Eta \\ \hline A(IV 1) & 100 & & & & \\ \hline B (IV 2) & 20 & & & & \\ \hline AxB & 15 & & & & \\ \hline Within & 200 & & & X & X \\ \hline Total & & & X & X & X \\ \hline \end{tabular} Use the ANOVA table from question \#1 above to answer the following questions: a. What is the f-critical value for the first main effect (A)? \( \qquad \) Significant \( (\mathrm{y} / \mathrm{n}) \) ? \( \qquad \)
Added by Jennifer P.
Close
Step 1
- For A (IV 1): \( \text{DF}_A = \text{levels of A} - 1 = 3 - 1 = 2 \) - For B (IV 2): \( \text{DF}_B = \text{levels of B} - 1 = 2 - 1 = 1 \) - For AxB interaction: \( \text{DF}_{AxB} = \text{DF}_A \times \text{DF}_B = 2 \times 1 = 2 \) - For Within: \( Show more…
Show all steps
Your feedback will help us improve your experience
Lien Le and 83 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with 2 levels of factor A, 3 levels of factor B, and n = 6 participants in each treatment condition. A. Fill in all missing values in the table. Show your work (i.e., all computational steps for finding the missing values). Hint: start with the df values. B. Do these data indicate any significant effects (assume p < .05 for hypothesis testing of all three effects)? Note: in order to receive full credit, your answer for each effect should include: the null hypothesis H0 & the alternative hypothesis H1, the critical F value used for the decision about H0, if the difference is statistically significant, the computed effect size, η2, and the conclusion in APA style format. Source SS df MS Between Treatments 75 2 37.5 Factor A 75 1 75 FA = 75 Factor B 45 2 22.5 FB = 22.5 A x B 6 2 3 FAxB = 6.00 Within Treatments 84 15 5.6 Total 165 22
Lien L.
5. With 3 df in the numerator and 60 in the denominator, i.e., F(3,60): a. What is the critical value of F at α = .05? b. What is the critical value of F at α = .01? c. How many groups are in the study? d. How many total participants are in the study? 6. The following summary table presents the results from an ANOVA comparing five treatment conditions with n = 30 participants in each treatment. a) Complete all the missing values (Hint: start with the df column). Source | SS | df | MS | F Between Groups | | | 40 | Within Groups | | | | Total | 800 | | b) What is the critical value of F at α = .01? (Use the closest tabled value for the degrees of freedom for the denominator) c) Is this F ratio significant at α = .01? d) Would your decision be to reject or fail to reject Ho?
Adi S.
4. The following table gives data for a 2 x 2 factorial experiment with two observations per factor-level combination. Factor B Level 1 2 Factor A 1 29.6, 35.2 47.3, 42.1 2 12.9, 17.6 28.4, 22.7 a. Calculate the two-way ANOVA summary table by hand. (Hint: there are two observations per treatment separated by a comma. Each level of each factor has 4 observations.) b. Test to determine whether the treatment means differ at α = 0.05 level of significance. c. Does the result of the test in b warrant a test for interaction between the two factors? If so, perform it using α = 0.05. i. Is a test for the main effects of factors A and B warranted? d. Regardless of you answer to part c, create the ANOVA table for the additive model. i. Test for main effects of factor A and factor B using α = 0.05. e. Given the results of your tests, which pairs of means, if any, should be compared?
Rakesh S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD