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Chapter 3: Experiments with a Single Factor: The Analysis of Variance

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What If There Are More Than Two Factor Levels?

The t-test does not directly apply

The analysis of variance (ANOVA) is the appropriate analysis "engine" for these types of experiments

An Example (page 56)

An engineer is interested in investing the relationship between the RF power setting and the etch rate for this tool. The between the RF power setting and the etch rate for this tool. The objective of an experiment like this is to model the relationship between etch rate and RF power, and to specify the power setting that will give a desired target etch rate.

The response variable is etch rate.

She is interested in a particular gas (C2F6) and gap (0.80 cm), and wants to test four levels of RF power: 160W, 180W 200W, and 220W. She decided to test five wafers at each level of RF power

The experimenter chooses 4 levels of RF power 160W, 180W, 200W, and 220W.

The experiment is replicated 5 times - runs made in random order

The Analysis of Variance

Total variability is measured by the total sum of squares: SS_Total = SS_Treatments + SS_Error

A large value of SS_Treatments reflects large differences in treatment means

A small value of SS_Treatments likely indicates no differences in treatment means

Formal statistical hypotheses are: H0: Mu_1 = Mu_2 = ...= Mu_a, H1: At least one mean is different

While sums of squares cannot be directly compared to test the hypothesis of equal means, mean squares can be compared.

A mean square is a sum of squares divided by its degrees of freedom: df_total = df_treatments + de_error. MS_Treatments = SS_Treatments / df_treatments, MS_Error = SS_Error / df_error

If the treatment means are equal, the treatment and error mean squares will be (theoretically) equal.

If treatment means differ, the treatment mean square will be larger than the error mean square

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