Unit :V Biostatistics And Research Methodology

Design and Analysis of experiments:

Factorial Design: 

• It is an experimental design which involves two or more independent variables and one dependent variables.
• It is designed in such a way that all possible combinations of the selected value of each variable are used. e.g. 2² & 3³ factorial design

Terms:-

1) Factor: these are those variable which involves in any experiments. e.g. Concentration, Temperature, Drug Treatment, Diet etc. Can be qualitative & quantitively.

2)Levels: These are the value or designation associated with the factors. e.g. 50C Temperature, Drug treatment.

3) Effects: These are the variation due to the variation due to the variation of factors.

4) Interactions: These are the responses due to the additively of factor effects.

Factorial Design:

   z^k Here  k=Factor & z=Level

 1)  For 2² Factorial design:- 

There are two factors all at two levels.

 Here,  2² - Level-2 & factors-2

so, total possible combination treatments are:-  2² = 2×2=4

Here, total 4 cases, where 2-Negative &2-Posetive

Design:-

Also represnted as:-

Order	A	B	C	D
1	-	-	+	1
2	+	-	-	2
3	-	+	-	2
4	+	+	+	1

 (+) = 1

 (-) = 2

2) For 2³ factorial Design:-

There are two level and there factors 2³ =2×2×2=8 total 8 treatment combination 

two level- +ve and -ve

Now, for 2³ factorial D. We have to take there factors A,B and C and assigned combination into only two blocks.

Factorial Effects

Order (Sum of replicates)	A	B	C	AB	BC	AC	ABC	Block
1 (1)	-	-	+	+	+	+	-	2
2  a	+	-	-	+	-	-	+	1
3   b	-	+	-	-	-	+	+	1
4   ab	+	+	+	-	+	-	-	2
5   c	+	-	-	-	+	-	+	1
6   ac	+	-	+	-	-	+	-	2
7   bc	+	+	-	+	-	-	-	2
8  abc	+	+	+	+	+	+	+	1

(+)=1, (-)=2

2³ design in two blocks with ABC confirmed.

Advantages of Factorial Design:

• factorial design are economical as they save time as well as materials combination.
• Helps in Simultaneous study of two or more factors.
• Provide efficient and adequate relative information.
• Help in predicting the consequences when two or more factor are combined.