Self-Check Questions (ungraded)

One-way ANOVA

Aidong Adam Ding
Made using Slidify in R. (Click mouse then right arrow key for next slide.)

Question 1:

Suppose that we have random samples of \({Y_{1,1}},...,{Y_{n_1,1}},...,{Y_{1,10}},...,{Y_{n_{10},10}}\) from ten groups with total \(N = n_1 + ...+n_{10} = 127\) observations. From the data, we find SSB=21.6, SSW=107.8.

  1. Calculate the F-test statistic for ANOVA
  2. Find the p-value for the ANOVA F-test

1) 2.6048

The group numbers g=10, so the degrees of freedom are g-1=9 and N-g=127-10=117.

Hence, MSB=21.6/9=2.4 and MSW=107.8/117=0.921

So that F=MSB/MSW=2.6048

2) 0.0089

The p-value is found by R command:

1-pf(21.6/9/(107.8/117),df1=9,df2=117)

Find the degrees of freedom, and take the ratio MSB/MSW

Use R to find the p-value from the F-distribution.

Question 2:

We want to test if the gene expression values have same means in five groups. The gene expression values are stored in a vector g.expr and the corresponding group identifiers are stored in the vector gr.

What is the R command for getting the ANOVA table?

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