KIN 4310 1nd Edition Lecture 18 Outline of Last Lecture I ANOVA II ANOVA III F Statistic IV Calculating F Outline of Current Lecture I Two way ANOVA II Factors III Main Effects IV Interaction Effects V Example VI Interaction Effect of Factors VII F Statistic VIII ANOVA IX ANOVA SPSS Output X Example Two way ANOVA 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 Current Lecture I Two way ANOVA a Like one way ANOVA but there are two independent factors b Used when we want to learn about the main effects of each factor individually but also want to understand how they interact c AKA Factorial ANOVA d Note In one way you just have one factor that distinguishes the groups from one another 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 Factors a A FACTOR is a variable that separates data into groups i E g 1 Gender Male or Female 2 Diet High fat or Low fat 3 Treatment Placebo low dose high does 4 Age Young middle aged elderly 5 Physical Activity Level Sedentary active III Main Effects a When there is a significant difference between different levels of a factor b E g i There is a main effect of DIET on BMI ii There is a main effect of AGE o n BMI iii There is a main effect of GENDER on STATURE c Note We look for main effects in a two way ANOVA IV Interaction Effects a When the effect of one factor depends on another factor b E g i There is an interaction between IRRIGATION and FERTILIZER on TREE GROWTH c Note In a two way analysis you look for main effects and interaction effects how they work together V Example a 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 e f g VI H1 There is a main effect of VOLUME H2 There is a main effect of GENDER H3 There is an interaction between VOLUME and GENDER 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 data shows 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 Interaction Effect of Factors a b Note When you have different shapes like this we have an interaction because the pattern of volume is different with males and females VII F Statistic a F MSb MSw b If there is a significant effect of treatment then MSb will be large relative to MSw and F will be large c If F Fcrit then there is an effect of treatment and we can reject the null hypothesis VIII IX ANOVA a 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 distribution d A large value of F represents a low probability that the data could have resulted if HO is true e 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 ANOVA SPSS Output a 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 ANOVA a 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 There is evidence that there is no reaction of model and factory Small p strong evidence