Statistical Methods for Economists – Week 8

                                       (Questions and Tasks)

The topic: Full factorial experimental plans

1.) In the framework of full factorial experimental plans, what do we mean by a “factor”?

2.) What is the main idea or aim of a full factorial experimental plan?

3.) Describe the experimental procedure.

4.) Read the Problem 1 (Spring) from [1]: Tosenovsky, F. (2014). Statistical methods for
economists, pages 108-115. Apply the method for the following problem.

5.) The Problem: Consider a local vendor who wants to increase her income from her bakery shop via
advertising. She tried three means of advertisement: social media (SM), billboards (B) and TV ads
(TV).

Factors and their (two) levels are given as follows in Table 1:

Table 1.

                                              Factor

                                              Symbol

                                            lower level

                                            upper level



                                                 -

                                                 +

                                           social media

                                                SM

                                             facebook

                                     facebook+Instagram+TikTok

                                            billboards

                                                 B

                                          small billboard

                                          large billboard

                                              TV ads

                                                TV

                                             20 sec ad

                                             40 sec ad


Then, the vendor designed and carried out the experimental plan, see the following Table 2. Output
1 and 2 are her earnings in USD (during 1 day).

Your task:

a) Evaluate factor effects (see Table 49 in [1]),

b) Evaluate statistical significance of factors’ effects (see Table 50 in [1]),

c) Provide graphical evaluation of factors’ significance (see Figure 12 in [1]).

d) Write down the regression model of the experiment (see page 115[1]).


Table 2.

                                                Run

                                           factor 1 (SM)

                                           factor 2 (B)

                                           factor 3 (TV)

                                             Output 1

                                             Output 2

                                              Average

                                                 1

                                                 -

                                                 -

                                                 -

                                                700

                                                840


                                                 2

                                                 +

                                                 -

                                                 -

                                                650

                                                690


                                                 3

                                                 -

                                                 +

                                                 -

                                                720

                                                820


                                                 4

                                                 -

                                                 -

                                                 +

                                                660

                                                740


                                                 5

                                                 +

                                                 +

                                                 -

                                                800

                                                830


                                                 6

                                                 +

                                                 -

                                                 +

                                                860

                                                850


                                                 7

                                                 -

                                                 +

                                                 +

                                                900

                                                960


                                                 8

                                                 +

                                                 +

                                                 +

                                                980

                                                940