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Anova steps and notation total

Review Sheet Analysis of Variance ANOVA ANOVA Steps and Notation Given the following hypothetical data from an experiment examining learning performance under three temperature conditions Temperature Conditions T SS n X T T SS SS n n X X ?X G N k The letter k identi ?es the number of treatment conditions the number of levels of the factor The number of scores in each treatment is identi ?ed by a lowercase letter n The total number of scores in the entire study is speci ?ed by a capital letter N The total ?X for each treatment condition is identi ?ed by the capital letter T The sum of all the scores in the research study the grand total is identi ?ed by G You can compute G by adding up all of the N scores or by adding up the treatment totals G ?T The ?nal calculation for ANOVA is the F-ratio which is composed of two variances F variance between treatments variance within treatments sample variance s SS df Recall that SS ?X ?? ?X N Total Sum of Squares SStotal SStotal ?X ?? G N In our example we have SStotal ?? CWithin-Treatments Sum of Squares SSwithin SS ?SS within inside each treatment SSwithin Between-Treatments Sum of Squares SSbetween SSbetween ? T n ?? G N SSbetween - ?? ?? To verify our analysis check to see that the two components add up to the total SStotal SSbetween SSwithin Total Degrees of Freedom dftotal dftotal N ?? dftotal ?? Within-Treatments Degrees of Freedom dfwithin dfwithin ? n ?? ?d ?n each treatment dfwithin N ?? k dfwithin ?? Between-Treatments Degrees of Freedom dfbetween dfbetween k ?? dfbetween ?? The two parts we obtained from this analysis of degrees of freedom add up to equal the total degrees of freedom dftotal dfwithin dfbetween CMS variance s SS df MSbetween s between SSbetween dfbetween MSwithin s within SSwithin dfwithin F MSbetween MSwithin F Then it is useful to organize the results in a table called ANOVA summary table Source SS df MS Between treatments F Within treatments Total CHypothesis testing with ANOVA Given the data Placebo T SS Drug A T SS Drug B T SS Drug C T SS N G ?X H ? ? ? ? Ha At least one of the treatment means is di ?erent We will use a Analyze the SS to obtain SSbetween and SSwithin b Use the SS values and the df values to calculate the two variances MSbetween and MSwithin c Finally use the two MS values variances to compute the F-ratio The F-ratio for these data have df Note that an F-ratio larger than rejects the null in this problem C