It contains all the knowledge related to the above topics in detail. The above topics has been presented very attractively made easy to understand

1. FACTORIAL, SAMPLING,
CENSUS AND
QUESTIONNAIRE
1
Presented by: TheCamouflage (BSc.CSIT 2nd Sem)
Rabin BK
Gagan Puri
Bikram Bhurtel

2.  Factorial experiment
 Types of Factorial experiment
 Sampling and Census
 Questionnaire
 Reference
Contents
2

3.  Refers to two or more set of related treatments
 It is more efficient than ordinary design because:
• Conclusion can be drawn, even if the factor is not replicated
• Two or more than two level of factors can be studied in the same design
• Interaction effect can be estimated but in ordinary design it is assumed
to be zero
 Types:
• 22 factorial experiment
• 23 factorial experiment
 Example:
• Using different level of Nitrogen for cultivation
• Dosage of medication
Factor
3

4. 22 factorial experiment
It has two independent factors to study: a, b
Each treatment is measured at low(0) and high(1) level
The treatment combination for this factorial experiment is:
A
B 0(𝑎0) 1(𝑎1)
0(𝑏0) 𝑎0 𝑏0=(1) 𝑎1 𝑏0=(a)
1(𝑏1) 𝑎0 𝑏1(b) 𝑎1 𝑏1=(ab)
4
a is at higher level and b is at
lower level
Both a and b are at higher
level
Both a and b are at lower
level
b is at higher level and a is at
lower level

5. 22 factorial experiment
Simple Effect (S.E)
• It is the difference between
the effect if higher and lower level
Main Effect (M.E)
• Average of simple effect of that factor
Interaction Effect (I.E)
• Combining effect of both A and B
5
S.E of A = (a)-1 [for b in lower level]
S.E of A = (ab)-(b) [for b in higher
level]
S.E of B = (b)-1 [for a in lower level]
S.E of B = (ab)-(a) [for a in higher
level]
M.E of A = average of S.E of A
1
2
×[(a)-(1)+(ab)-(b)]
M.E of B = average of S.E of B
1
2
×[(b)-(1)+(ab)-(a)]
I.E of AB =
1
2
×[(ab)+(1)-(a)-(b)]

6. 22 factorial experiment
For ‘r’ number of replications:
Sum of square of A:
Sum of square of B:
Sum of square of AB:
6
1
4𝑟
×[(a)−(1)+(ab)−(b)]
2
1
4𝑟
×[(ab)−(1)+(b)−(a)]
2
1
4𝑟
×[(ab)+(1)−(b)−(a)]
2

7. 23 factorial experiment
It has three independent factors to study: a, b, c
There are eight treatments combination
• M.E of A =
1
4𝑟
× [(abc)−(bc)+(ac)−(c)+(ab)−(b)+(a)−(1)]
• M.E of B =
1
4𝑟
× [(abc)+(bc)−(ac)−(c)+(ab)+(b)−(a)−(1)]
• M.E of C =
1
4𝑟
× [(abc)+(bc)+(ac)+(c)−(ab)−(b)−(a)−(1)]
• I.E of AB =
1
4𝑟
× [(abc)−(bc)−(ac)+(c)+(ab)−(b)−(a)+(1)]
• I.E of BC =
1
4𝑟
× [(abc)+(bc)−(ac)−(c)−(ab)−(b)+(a)+(1)]
• I.E of AC =
1
4𝑟
× [(abc)−(bc)+(ac)−(c)−(ab)+(b)−(a)+(1)]
• I.E of ABC =
1
4𝑟
× [(abc)−(bc)−(ac)−(ab)+(c)+(b)+(a)+(1)]
7
Main Effect (M.E)
Interaction Effect (I.E) For ‘r’
replications

8. 23 factorial experiment contd…
8
For ANOVA table:
 SSA =
[(abc)−(bc)+(ac)−(c)+(ab)−(b)+(a)−(1)]
8𝑟
2
 SSB =
[(abc)+(bc)−(ac)−(c)+(ab)+(b)−(a)−(1)]
8𝑟
2
 SSC =
[(abc)+(bc)+(ac)+(c)−(ab)−(b)−(a)−(1)]
8𝑟
2
 SSAB =
[(abc)−(bc)−(ac)+(c)+(ab)−(b)−(a)+(1)]
8𝑟
2
 SSBC =
[(abc)+(bc)−(ac)−(c)−(ab)−(b)+(a)+(1)]
8𝑟
2
 SSAC =
[(abc)−(bc)+(ac)−(c)−(ab)+(b)−(a)+(1)]
8𝑟
2
 SSABC =
[(abc)−(bc)−(ac)−(ab)+(c)+(b)+(a)+(1)]
2
ANOVA Table
Source Of
Variation
df SUM OF
SQUARE
MEAN SUM
OF SQUARE
F-
RATIO
Treatment …
SSA 1 ……. ……. …….
SSB 1 ……. ……. …….
SSC 1 ……. ……. …….
SSAB 1 ……. ……. …….
SSBC 1 ……. ……. …….
SSAC 1 ……. ……. …….
SSABC 1 ……. ……. …….
Error … ……. ……. …….
Total … ……. ……. …….

9. Sampling
- process of selection of small no. of items that represent the entire
population under study
- information on outcome of fundamental issues such as birth rate, poverty
rate, employees rate etc. is obtained
Census
- measurement of every units in the population
- conducted by CBS in every ten years interval
- information on fundamental issues such as population size, land size, forest
size etc. are obtained
9

10. Every units in the target population have a known non-
existent selection probability
Probability techniques are used in every stage of
selection of the sampling units
Adequate sample size are allocated for the story
Conditions for sample designing
10

11. Programmatic reason:
- sampling cuts costs, reduces non power requirements and
gather vital information quickly
Accurate and reliable result:
Toxic tests
Life testing and Deteriorating product test
Reasons for conducting sample survey
11

12. Sampling error
- difference between the sample results and the true results
- reduced by increasing sample size
- taken from population estimates from different samples and population
values
- measured by Standard Error
- range of sampling error at a particular level of confidence is estimated
Sources of error
12

13. Non – Sampling errors :
a) Sampling selection error
- Frame error
- Respondent selection error
- Sample replacement error
b) Measurement error
- Interviewer error
- Response error
- non response error
- measurement instrument bias
- Processing error
13

14. • Objective of the survey
• Defining the population to be sampled
• The frame and sampling units
• Data to be collected
• The questionnaire or schedule
• Method of collecting information
• Non – respondents
• Selection of proper sampling design
• Organization of field work
• The pretest
• Summary and analysis of the data
• Information gained for future surveys
Principle steps in a sample survey
14

15. Types
Structural
- closed ended:
e.g. What is your ethnic group?
a)Dalit b)Janajati c)others
Unstructural
- opened ended:
e.g. What are your successes ?
Questionnaire design
15

16. Semi structural
- both closed and open ended:
e.g. 1) Do you like CSIT ?
a) yes b)no c)don’t know
2) If yes, why ?
3) If no, why ?
16

17. Structural Unstructural
Response are predefined Response are not predefined
Easy for field staff. Difficult for field staff to understand
and write response
Easy for coding Difficult for coding
Consumes less cost in coding and
analysis
Consumes more cost in coding and
analysis
Consumes more time in it Consumes less time in it
If respondent has different opinion than
options given, it can’t be included
Flexible to include different opinion
of respondent
Comparison between structural and unstructural questionnaire
17

18. • Title shall be clear
• Basic information such as location, respondent name, interviewers
name, date of interview should be included
• The words used need to be simple
• The word or sentence shall have no ambiguity
• Should be culture sensitive
• The options given shall be represented in members in coding
• The question shall be leading question
• Shall have clear instruction
Pre – requisite of a good questionnaire
18

19. Single purpose survey
- made of at least a sample (or full population in the case of a census),
- a method of data collection (e.g., a questionnaire) and individual questions or items that
become data that can be analyzed statistically
Multi purpose survey
- designed to provide statistics annually for a number of small, self contained topics,
including a number of labor related topics
Organization aspect of sample survey
19

20. Steps in single purpose survey
• Define purpose
• Identity prevalence rate ( Accurate rate ) of the study theme
• Obtain complementary rate ( non - prevalence rate )
q = 1 – p {(100 – p)% }
• Define confidence level (1 – a)
• Define degree of detection error ( standard error of estimate )
- denoted by ∂
• The minimum sample site is n = z2pq/∂2
- minimum sample size (n) is maximum at p = 0.5 , z = 1.96, d = 0.05, then n = 384
• Distribution of sample size based on sampling method
• Individual sample selection
• Non – sampling error
• Negotiation with cost
20

21. References
1. Statistics II, Vikash Raj Satyal, Bijaya Lal Pradhan
21

22. Queries
22