Example of a Completely Randomized Design

 

Refer to sections 14.2 and 14.3 of text (8th ed), 15.2 and 15.3 of 7th ed.

 

An experiment was conducted to compare 3 brands of gasoline. Each brand was used with 7 different cars of the same weight and engine size, under similar operating conditions. The data collected were the miles per gallon obtain for each of the cars.

 

 Brand A: 19 24 24 21 20 22 25

 Brand B: 25 26 34 25 24 24 23

 Brand C: 25 31 28 29 28 30 28

 

Do the data provide sufficient evidence to indicate a difference among the brands of gasoline?

 

First, some exploratory analysis. Start with some boxplots to compare mileages of the 3 brands.

Locations of the centre (average) of each distribution do not appear to be the same.

 

Compare means, etc. among the 3 brands.

 

Descriptive Statistics: Mileage by Brand

 

# Some output deleted

 

Variable   Brand             N       Mean     Median     TrMean      StDev

Mileage    A                 7     22.143     22.000     22.143      2.268

           B                 7     24.286     24.000     24.286      1.113

           C                 7     28.429     28.000     28.429      1.902

 

 

 

 

One-way ANOVA: Mileage versus Brand

 

Analysis of Variance for Mileage

Source     DF        SS        MS        F        P

Brand       2    142.95     71.48    21.44    0.000

Error      18     60.00      3.33

Total      20    202.95

                                   Individual 95% CIs For Mean

                                   Based on Pooled StDev

Level       N      Mean     StDev  --------+---------+---------+--------

A           7    22.143     2.268   (-----*----)

B           7    24.286     1.113           (-----*-----)

C           7    28.429     1.902                            (-----*-----)

                                   --------+---------+---------+--------

Pooled StDev =    1.826                 22.5      25.0      27.5

 

 

 

Test if there is a difference among the 3 brands: