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UH KIN 4310 - Two-way ANOVA
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KIN 4310 1nd Edition Lecture 18Outline of Last Lecture I. ANOVA II. ANOVAIII. F StatisticIV. Calculating FOutline of Current Lecture I. Two-way ANOVAII. FactorsIII. Main EffectsIV. Interaction EffectsV. ExampleVI. Interaction Effect of FactorsVII. F StatisticVIII. ANOVAIX. ANOVA – SPSS OutputX. Example: Two-way ANOVAThese 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.Current LectureI. Two-way ANOVAa. Like one-way ANOVA, but there are two independent factorsb. Used when we want to learn about the main effects of each factor individually, but also want to understand how they interactc. AKA Factorial ANOVAd. Note: In one-way, you just have one factor that distinguishes the groups from oneanother. In two-way, you have two factors which is called the factorial ANOVA. We will not have to perform this in our assignment, we just have to know what it is.II. Factorsa. A FACTOR is a variable that separates data into groups.i. E.g.:1. Gender: Male or Female2. Diet: High-fat or Low-fat3. Treatment: Placebo, low dose, high does4. Age: Young, middle-aged, elderly5. Physical Activity Level: Sedentary, activeIII. Main Effectsa. When there is a significant difference between different levels of a factorb. E.g.i. There is a main effect of DIET on BMIii. There is a main effect of AGE o n BMIiii. There is a main effect of GENDER on STATUREc. Note: We look for main effects in a two-way ANOVA.IV. Interaction Effectsa. When the effect of one factor depends on another factorb. E.g.i. There is an interaction between IRRIGATION and FERTILIZER on TREE GROWTHc. Note: In a two way analysis, you look for main effects and interaction effects (how they work together)V. Examplea. What is the effect of message volume and gender on persuasiveness?b. Note: From the data, we want to know if it is statistically different and this is what ANOVA is asking. Is volume a factor in delivering advertising measurement?Is gender a factor in delivering advertising measurements?c.d. H1: There is a main effect of VOLUMEe. H2: There is a main effect of GENDERf. H3: There is an interaction between VOLUME and GENDERg. Note: For source of variation, we have the factors and then the bottom two are from the pervious ANOVA that we learned. MS is SS/df. F is the test statistic, for the first hypothesis test, F is high and is greater than the critical value so we reject the null hypothesis so there is a significant main effect of volume. There are different critical values because of the different degrees of freedom. The datashows that it is unlikely to happen by random chance if the null hypothesis is true. P-values are small which means that if it is less than alpha, then we have conclusive evidence and reject the null hypothesis.VI. Interaction Effect of Factorsa.b. Note: When you have different shapes like this, we have an interaction because the pattern of volume is different with males and femalesVII. F Statistica. F = MSb/MSwb. If there is a significant effect of treatment, then MSb will be large relative to MSwand F will be largec. If F > Fcrit, then there is an effect of treatment, and we can reject the null hypothesis.VIII. ANOVAa. When the variance within groups decreases, the variance between groups becomes more apparent.i. Note: when you reduce variance within groups, there is less overlap. The variance between groups stayed the same in this case. We just changed the denominator (smaller MSw), and made it smaller so F increased. Here, we can reject the null hypothesis.b. When the variance between groups decreases, the variance within groups becomes more apparent.i. Note: The bottom part is the same, we reduced MSb and the variance between group means got smaller and they overlapped and here, it is really hard to reject the null hypothesis because they are all jumbled and it is hard to see the difference between the two and F decreases. If you don’t have a lot of variances, it is harder to prove something.c. All ANOVA tests concern the right-tail of the F-distributiond. A large value of F represents a low probability that the data could have resulted ifHO is truee. Critical values of F are calculated based on degrees of freedom (size of dataset)f. Note: fewer df means you are more likely to make a type 2 error.IX. ANOVA – SPSS Outputa.b. Note: The top table is descriptive statistics. ANOVA is the inferential statistics which means we are testing a hypothesis. This one is the one-way analysis. Sig is the p-value. The table leads us to the result of rejecting the null which is a positive result. Numbers are unlikely to occur by random chance is the null is true which is just a 1% chance.X. Example: Two-way ANOVAa.b. Note: prob > f is the pvalue. There is a huge effect in the model. There is a significant difference between the models. There is a main effect of factory. Thereis evidence that there is no reaction of model and factory. Small p = strong


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UH KIN 4310 - Two-way ANOVA

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