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Experimental Designs ( Tutorials)

I. To test effect of 2 factors, pack design & price on sales of a toilet soap brand.a sampleof 18 retail outlets was selected. They were exposed to three levels of pack designs blue,

green and red and 3 price levels Rs8, Rs11 & Rs 14. The data collected is shown in

Table 1

Table 1 Input Data for Experimental Design

S.No. Sales Pack design Price

1 500 1 1

2 440 2 1

3 360 3 1

4 300 1 2

5 280 2 2

6 250 3 2

7 200 1 3

8 150 2 3

9 250 3 3

10 600 1 1

11 450 2 1

12 510 3 1

13 400 1 2

14 350 2 2

15 300 3 2

16 250 1 3

17 275 2 3

18 220 3 3

The output of SPSS is shown in Table 2

Table 2

Source of Variation Sum of Squares DF Mean Square F Sig of F

Main effects 209305.556 4 52326.389 13.645 .001

Pack design 12536.11 2 6238.056 1.635 .248

Price 196769.444 2 98384.722 25.656 .000

2 Way interactions 9838.889 4 2459.722 .641 .646

Pack Designx price 9838.889 4 2459.722 .641 .646

Residual 34512.500 9 3834.722

Total 253656.944 17 14920.997

Q1 Identify dependent and independent variables

Q2 Identify the type of Design

Q3 Formulate appropriate hypothesis

Q4 Interpret the results?

Solution

Ans 1

1. Dependent variable = Sales

2. Independent variables = prices , pack designs

Ans 2

Factorial Design

Ans 3

Hypothesis 1: The mean level of sales remains the same for all three levels of pack design (main effect 1)

Hypothesis 2: The mean level of sales remain the same for all 3 levels of prices (main effect 2)

Hypothesis 3: The mean level of sales remain the same for all combination of pack designs and price (interaction effect)

Ans 4

We find significance of F values (P values) are as follows

Pack design = .248 > 0.05,

Price = .000 < .05Pack design by price = .646 >.05

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Accordingly price effect is statistically significant at 95% confidence level. Since P value is < .05, this means hypothesis No. 2 is

rejected

2. Hypothesis 1 & 3 cannot be rejected as corresponding p values are greater than .05

3. We conclude that price alone has an impact as sales. Neither pack design nor combination of pack design with price has any

significant impact on sales

II. The Taj group hotel chain wants to test preference of the target customer (high incomegroup) for 4 non vegetarian dishes. 28 customers were asked to give their opinion about

the taste of the 4 common non veg dishes served to them on 10 point rating scale.

The dishes were coded as follows

CODE DISH NAME

1 CHICKEN PLATTER

2 HONEY CHICKEN

3 CHICKEN SPINACH

4 TANDOORI CHICKEN

The data on rating given by 28 respondents is shown in Table 1

S. No. Dish Type Rating

1 1 6.00

2 1 7.003 1 8.00

4 1 5.00

5 1 9.00

6 1 8.00

7 1 7.00

8 2 8.00

9 2 8.00

10 2 9.00

11 2 8.00

12 2 7.00

13 2 9.00

14 2 8.00

15 3 7.00

16 3 6.00

17 3 6.00

18 3 5.0019 3 7.00

20 3 7.00

21 3 5.00

22 4 6.00

23 4 6.00

24 4 7.00

25 4 6.00

26 4 8.00

27 4 7.00

28 4 6.00

The output of SPSS is shown in Table 2

Source of Variation Sum of Squares DF Mean Square F Sig of F

Dish Type 15.714 3 5.238 5.641 .005

Error 22.286 24 .929Total 38.000 27 1.407

Q1 Identify dependent and independent variable

Q2 Describe the type of DesignQ3 Formulate the hypothesis

Q4 Interpret the results

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III.

In the above example the location of the Taj Group Hotel was considered as an extraneous variable. Seven locations were used and coded as

follows

CODE LOCATION

1 CHENNAI

2 BANGALORE3 MUMBAI

4 NEW DELHI

5 GOA

6 KODAIKANAL

7 JAIPUR

The data on rating, dishes & cities is given in Table 1

S.No Dish Type Rating Location

1 1 6.00 1

2 1 7.00 2

3 1 8.00 3

4 1 5.00 4

5 1 9.00 5

6 1 8.00 6

7 1 7.00 7

8 2 8.00 1

9 2 8.00 2

10 2 9.00 3

11 2 8.00 4

12 2 7.00 5

13 2 9.00 6

14 2 8.00 7

15 3 7.00 1

16 3 6.00 2

17 3 6.00 3

18 3 5.00 4

19 3 7.00 5

20 3 7.00 6

21 3 5.00 7

22 4 6.00 1

23 4 6.00 2

24 4 7.00 3

25 4 6.00 4

26 4 8.00 5

27 4 7.00 6

28 4 6.00 7

The output of SPSS is given in Table 3

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Table 3

Source of Variation SS DF MS F Sig

Dish Type 15.71 3 5.24 8.35 .001

Location 11.00 6 1.83 2.92 .036

Error 11.29 18 .63

(Total) 38.00 27 1.41

Q1 Identify the dependent, independent & extraneous variable

Q2 Identify the type of designQ3 Formulate the hypothesisQ4 Interpret the results

Ans 1

Dependent variable = rating , Independent variable = dish type, extraneous variable = location of the hotel

Ans 2

Type of design randomized block design

Ans 3

Hypothesis no 1 = The mean rating of the dish type is same for all 4 dishesHypothesis no 2 = The mean rating of the dish type is same for all 7 blocks

Ans4

Since P values of dish type(.001) as well as location(.036) are both less than0.05, we reject both the hypotheses & Conclude that

i) Mean ratings given to 4 types of dishes are significantly different.i i) The locations have an impact on ratings.

IV) Analyse and interpret the following data concerning output of wheat for four varieties A, B, C & D obtained as a result of experiment

conducted using a latin square design. Columns indicate four levels of moisture contents. Rows indicate four levels of soil fertility

C 25 B 23 A 20 D 20

A 19 D 19 C 21 B 18

B 19 A 14 D 17 C 20

D 17 C 20 B 21 A 15

The output of SPSS is shown in Table 1

Table 1

Source of Variation Sum of Squares DF Mean Square F Table

value of F

at 5%

Between Columns 7.5 3 2.50 1.43 4.76

Between Rows 46.5 3 15.50 8.85 4.76

Between Varieties 48.5 3 16.17 9.24 4.76

Residual or Error 10.5 6 1.75

Total 113.0 15

Q1 Identify the dependent, independent & extraneous variable

Q2 Identify the type of design

Q3 Formulate the hypothesis

Q4 Interpret the results

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