## Saturday 31 August 2013

### Two-factor (two-way) ANOVA

SciStatCalc Version 1.3 is capable of implementing two-factor ANOVA.

Consider the example reproduced from
http://www-stat.stanford.edu/~susan/courses/s141/exanova.pdf

Example Suppose you want to determine whether the brand of laundry detergent used and the temperature affects the amount of dirt removed from your laundry. To this end, you buy two different brand of detergent (“ Super” and “Best”) and choose three different temperature levels (“cold”, “warm”, and “hot”). Then you divide your laundry randomly into 6 × r piles of equal size and assign each r piles into the combination of (“Super” and “Best”) and (”cold”,”warm”, and “hot”). In this example, we are interested in testing Null Hypotheses
H0D : The amount of dirt removed does not depend on the type of detergent H0T : The amount of dirt removed does not depend on the temperature
One says the experiment has two factors (Factor Detergent, Factor Temperature) at a = 2(Super and Best) and b = 3(cold,warm and hot) levels. Thus there are ab = 3 × 2 = 6 different combinations of detergent and temperature. With each combination you wash r = 4 loads. r is called the number of replicates. This sums up to n = abr = 24 loads in total. The amounts Yijk of dirt removed when washing sub pile k (k = 1, 2, 3, 4) with detergent i (i = 1, 2) at temperature j (j = 1, 2, 3) are recorded in Table 1.

Table 1:
Cold               Warm            Hot

Super            4,5,6,5             7,9,8,12          10,12,11,9

Best              6,6,4,4           13,15,12,12       12,13,10,13

The above information can be stored in a CSV file, and this file can be sent as an email attachment. The contents of the file are as below:-

# 3 2 4
4,7,10
5,9,12
6,8,11
5,12,9
6,13,12
6,15,13
4,12,10
4,12,13

Note that the first comment line has three numbers - the first number is the number of first factor  (temperature level) categories (Cold,Warm,Hot), which is the number of dataset columns in table 1, while the second factor (brand of detergent) categories is the number of rows (Super, Best). The number of rows with data in the CSV file is (number of second factor categories * number of samples per dataset). In the example above, the number of samples per dataset is known as the number of replicates.

A video of carrying out the two-factor ANOVA using SciStatCalc is accessible at link http://www.youtube.com/watch?v=Tji0ZTTyTsQ.

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