math no need to show work
Spring 2021 Unit 4 | Take-home One-way between-subjects ANOVA: Jon is examining the impact of types of sunscreen on how many minutes it takes for people to sunburn. He asks groups of 10 people each to wear one of three sunscreens: 15 SPF, 30 SPF, and 50 SPF. The mean number of minutes before participants sunburned and SSbn, SSwn, and SStotal are reported below. Mean number of minutes before sunburn: 15 SPF 30 SPF 50 SPF 35 36 61 Source SS df MS F Between 85.12 _______ _______ _______ Within 76.14 _______ _______ Total 161.26 _______ **For Tukey HSD, use q = 3.44. For the one-way between-subjects ANOVA, identify: 1. The number of levels in the factor of interest (k) and total number of participants (N) (4 pts.): k = _______, N = _______ 2. Complete the ANOVA table above a. dfbn, dfwn, dftotal (6 pts.) b. MSbn, MSwn (4 pts.) c. F statistic (2 pts.) 3. The critical F value (2 pts.) critical F = ___________ 4. Should you reject or retain H0? (2 pts.) ____________________ Spring 2021 Unit 4 | Take-home 5. Calculate the Tukey HSD value (2 pts.) and determine whether the comparisons of each pair of levels is significantly different (6 pts.). Tukey HSD = __________ 15 SPF vs. 30 SPF: (circle one) Significantly different | Not significantly different 15 SPF vs. 50 SPF: (circle one) Significantly different | Not significantly different 30 SPF vs. 50 SPF: (circle one) Significantly different | Not significantly different Two-way ANOVA: For the problem below, use the ANOVA table to determine whether the main effects and interaction were significant. Use the table of means and effect sizes to interpret the significant effects. Reginald is interested in the how students’ memory for different topics is impacted by study method. He examines how flashcards versus study guides impact students’ memory of physics versus history. The mean performance memory scores, ANOVA table, and effect sizes are reported below. Mean memory scores: (Higher score = better memory) Flashcards Study guides Physics 12 9 History 29 32 ANOVA table: Source SS df MS F Between Studying method 15.23 1 15.23 2.53 Topic 37.11 1 37.11 6.16* Interaction 16.17 1 12.17 2.68 Within 120.40 20 6.02 Total 188.91 23 *p < .05 eta-squared (?!): notetaking method = 0.03, topic = 0.22, interaction = 0.05 circle your answers. (2 pts. each) 1. was there a significant main effect of studying method? yes | no 2. was there a significant main effect of topic? yes | no 3. was there a significant interaction? yes | no spring 2021 unit 4 | take-home for the following statements, circle true or false based on the results and statistical interpretation of the anova analysis: (2 pts. each) 4. overall, students remembered more in history than in physics. true | false 5. overall, students remembered more after flashcards than after study guides. true | false 6. overall, studying method did not impact student memory. true | false 7. students remembered more in history regardless of studying method. true | false 8. flashcards led to better memory regardless of topic. true | false 9. students remembered more after flashcards in physics and more after study guides in history. true | false 10. the impact of study guides on memory was dependent on the topic. true | false circle your answer. (2 pts.) 11. which of the following had the greatest impact on variance in students’ memory? a. studying method b. topic c. interaction .05="" eta-squared="" (?!):="" notetaking="" method="0.03," topic="0.22," interaction="0.05" circle="" your="" answers.="" (2="" pts.="" each)="" 1.="" was="" there="" a="" significant="" main="" effect="" of="" studying="" method?="" yes="" |="" no="" 2.="" was="" there="" a="" significant="" main="" effect="" of="" topic?="" yes="" |="" no="" 3.="" was="" there="" a="" significant="" interaction?="" yes="" |="" no="" spring="" 2021="" unit="" 4="" |="" take-home="" for="" the="" following="" statements,="" circle="" true="" or="" false="" based="" on="" the="" results="" and="" statistical="" interpretation="" of="" the="" anova="" analysis:="" (2="" pts.="" each)="" 4.="" overall,="" students="" remembered="" more="" in="" history="" than="" in="" physics.="" true="" |="" false="" 5.="" overall,="" students="" remembered="" more="" after="" flashcards="" than="" after="" study="" guides.="" true="" |="" false="" 6.="" overall,="" studying="" method="" did="" not="" impact="" student="" memory.="" true="" |="" false="" 7.="" students="" remembered="" more="" in="" history="" regardless="" of="" studying="" method.="" true="" |="" false="" 8.="" flashcards="" led="" to="" better="" memory="" regardless="" of="" topic.="" true="" |="" false="" 9.="" students="" remembered="" more="" after="" flashcards="" in="" physics="" and="" more="" after="" study="" guides="" in="" history.="" true="" |="" false="" 10.="" the="" impact="" of="" study="" guides="" on="" memory="" was="" dependent="" on="" the="" topic.="" true="" |="" false="" circle="" your="" answer.="" (2="" pts.)="" 11.="" which="" of="" the="" following="" had="" the="" greatest="" impact="" on="" variance="" in="" students’="" memory?="" a.="" studying="" method="" b.="" topic="" c.="">