Thread: a completely randomized experimental design and regression

1. a completely randomized experimental design and regression

A company studied the effects of three different methods of promotions on sales of its crackers (labeled as Treatment 1 to 3). Fifteen stores were selected for the study and a completely randomized experimental design was utilized. Each store was randomly assigned one of the promotion types, with five stores assigned to each type of promotion. Other relevant conditions under the control of the company, such as price and advertisement, were kept the same for all stores in the study. Part of the data on the number of cases of the product sold during the promotional period, denoted by Y, are presented in the table below, as are also data on the sales of the product in the preceding period, denoted by X.
In the following , let cX be the centered value of X.
I1 = 1, if treatment =1, 0 if treatment =2; -1 if treatment = 3
I2 = 0 if treatment = 1; 1 if treatment =2; -1 if treatment = 3

Outputs of Model 1:

lm(formula = Y~ cX + I1+I2+ cX:I1 + cX:I2, data =cracker)

Coefficients:

Estimate Std. Error T value Pr > |t|

Intercept 33.83085 0.53577 63.144 3.162-13***

cX 0.91795 0.11542 7.953 2.32e-05***

I1 6.23582 0.78472 7.947 2.34e-05***

I2 0.64923 0.75076 0.865 0.410

cX:I1 0.08205 0.18588 0.441 0.669

cX:I2 0.07330 0.15035 0.488 0.638

Assuming that the model assumptions have been met, I would like to use a 1% significance level to test whether or not the regression lines of Y in terms of X for the three treatments have equal slopes. Are the following hypotheses right?

Null Hypothesis: The regression lines of Y in terms of X for the three treatments have equal slopes.
Alternative Hypothesis: The regression lines of Y in terms of X for the three treatments have different slopes

The p-value for I1 is less than .01. Thus, I think that the regression lines of Y in terms of Y for the three treatments have different slopes. But The p-value for I2 is greater than .01. Thus, I am not sure if the regression lines of Y in terms of Y for the three treatments have different slopes.

Does it make sense to test whether there is a difference in mean sales during the promotional period between the three treatments?

2. Re: a completely randomized experimental design and regression

hi,
wouldn't it be easier if you used indicator variables I1 =1 if treatment 1 0 otherwise and I2=1 if treatment 2 and 0 otherwise?

regards

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