Hypothesis Test for Laboratories

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Worked example from Tutorial 8

8.3Three laboratories, A, B, and C, are used by food manufacturing companies for making nutrition analyses of their products. The following data are the fat contents (in grams) of the same weight of three similar types of peanut butter.

| |Laboratory | |Peanut Butter |A |B |C |D | |Brand 1 |16.6 |17.7 |16.0 |16.3 | |Brand 2 |16.0 |15.5 |15.6 |15.9 | |Brand 3 |16.4 |16.3 |15.9 |16.2 |

Analyse the data at 5% significance by (a) carrying out a one-way ANOVA to see if there is a difference between the fat content of the three brands; (b) performing a two-way ANOVA to see if there is any difference between the Brands using the laboratories as blocks. (c) Do you think there is any evidence that the results were not reasonably consistent between the four laboratories?

a)One-way ANOVA
| |Laboratory | | |Peanut Butter |A |B |C |D |Mean | |Brand 1 | 16.6 |17.7 |16.0 |16.3 |16.65 | |Brand 2 |16.0 |15.5 |15.6 |15.9 |15.75 | |Brand 3 |16.4 |16.3 |15.9 |16.2 |16.20 | |Mean |16.33 |16.50 |15.83 |16.13 |16.20 |

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