BIOM 121 1nd Edition Lecture 19 Outline of Last Lecture I. Analysis of Variancea. Why do we need a new test?b. Conceptual rationale for ANOVAc. Sources of variabilityOutline of Current Lecture I. Between-Subjects ANOVAa. Criteriab. Examplei. Fobsii. Hypothesis Testing StepsCurrent LectureI. Between-Subjects ANOVAa. Criteriai. More than 2 Tx groups (you can use as many as you want)ii. Different Ps in each group (independent samples, between-subjects)b. Ex) Informational interventions and attitude change about the MMR vaccinei. See handoutii. Basic formula for F:1. F= (Between-groups variance)/(Within-groups variance)a. F = MS Between/MS withini. MS = Means Squared = Variance2. Used to calculate Fobsc. Variancei. Total (s2) >> Partitioning Variance (dividing):1. Between-groups variance (s2 – normal formula; SS/df = MS)2. Within-groups variance (s2)d. Hypothesis Testingi. Ex) Start at Step 3 (Fobs)ii. See Handout (Description of Terms):These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.1. For each of the three pieces of variance2. T = Σx (for individual condition/group)3. Grand sum of x squared = Σx2a. Square every value, then add4. Grand totala. Grand sum of x (or sum of 4 T values)5. Total number of participants = N (n=in individual groups)iii. Calculate Values1. SSa. SStotal = Σx2 – G2/N = 2679 – (235)2/24b. SSwithin = Σ SS for each level = 23.5+21.5+45.5+131.33 = 221.83i. Add all individual SSc. SSbetween = Σ (T2/n) – G2/Ni. As many fractions as you have levelsii. 342/6 + 452/6 + 632/6 + 822/6 – 2352/24 = 156.13iii. OR SSbetween = SStotal - SSwithin2. dfa. dftotal = N – 1i. 24 – 1 = 23b. dfbetween = k – 1 i. 4 – 1 = 3c. dfwithin = N – k i. 24 – 4 = 201. Additive! (20 + 3 = 23)3. MS (Variance)a. MSbetween = SSb/dfbi. 156.13/3 = 52.04b. MSwithin = SSw/dfwi. 221.83/20 = 11.094. Fobs = 52.04/11.09 = 4.695. Tipsa. Label!b. Calculate everything as pre-work FIRST!c. Learn SPSS!iv. ANOVA Source TableSource SS df MS FobsFcritBetween 156.13 3 52.04 4.69 ?Within 221.83 20 11.09Total 377.96 231. Good way to organize data, helps to show relationships between numbersv. Finish Hypothesis testing steps1. Hypothesesa. Always two-tailed!i. H0: μ1 = μ2 = μ3 = μ4ii. H1: not H02. Critical value of Fa. Table (read instructions)i. .05 – lightii. .01 – darkb. dfi. Numerator: df used in numerator of F ratio: dfbetweenii. Denominator: dfwithinc. Fcrit(3,20) = 3.10i. Always positive, even though two-tailed (dealing with squared values!)ii. F = t23. Fobs = 4.694. Make decision about H0a. Reject H0i. What does this mean for ANOVA results?1. Sample Hypothesis: Disease Images > Narrative Danger > Autism correction > Disease
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