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Bio2244 Lecture 23, 24 and 25.docx

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Biology 2244A/B
Angela White

Lecture 23, 24, 25 ANOVA - What is it? o Method for testing equality of three or more populations by studying sample variances o Better than using two samples at a time because doing this multiple times will reduce the confidence level (CL^trials)  Assumes independent tests  Increases risk of TYPE I ERROR F Distribution - Properties o F distribution NOT SYMMETRIC; RIGHT SKEWED o Values for F greater or equal to 0 o There is different F distribution for each pair of DF for numerator and denominator - One-way distribution o Because sample data separated into groups according to one characteristic o Ex. Each treatment group is separated based on treatment One-Way ANOVA - Things to consider o Small P-value will reject null hypothesis o Know sum of squares and mean square and their role in F statistic - Method: one-way analysis of variance o Also called treatment (NOT FACTOR)  Factor is the explanatory variable being studied - Requirements o Populations normally distributed (loose) o Populations have same variance or SD (loose) o Samples are SRS o Samples independent (ie. Not a matched pair) o Different samples from each population categorized in one way - to test o find P-value o if P-value < alpha, reject null - rational o Large F test statistic is located far to the right of the graph, meaning a smaller P value - Variation o Two ways to estimate common value of variance  Variance between samples (variance b/c of treatment)  Estimate of common population variance based on variation among sample means  Variance within samples (variance b/c of error)  estimate of common population variance based on sample variances o NOTE***  If there are only 2 samples, a two-tailed independent sample pooled t-test for means is equal to one-way ANOVA F test  F statistic value in this case is t statistic value squared - Calculations with Equal Sample Sizes n o Change in the F test statistic and P-value is only attributable to change in sample mean o An increase in difference b/w sample means will increase F and decrease P-value o Degrees of freedom  K is the number of samples, n is the sample size  Numerator DF = k – 1  Denominator DF = k(n – 1) - Calculation with Unequal Sample Sizes o With unequal sample sizes, we must use weighted measures to determine F statistic o SS(total) = SS(treatments) + SS(Error)  Using this we can get mean squares (MS) o To get mean squares, you divide the sum of squares by their respective DF  MS(total) = SS(total) / (N-1)
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