sampling and statistical theory

population

any complete group of interest

census

investigation of all the individual elements making yp the population a total enumeration rather than a sample

sample

subset of some larger population that is measured or observed in some way to infer what the entire population is like

statistic

to sample as parameter is to population

why we need a sample

• cuts costs, reduces labor requirements, gathers vital info quickly

• more accurate than a census

• occurs in the process of the research project

• provides the case against a census

sampling frame

a list of elements from which the sample may be drawn

stages in selection of sample

• define target population

• select sampling frame

• determine if a probability or non-probability sampling will be used

• plan procedures for selecting sampling units

• determine sample size

• select actual sampling units

• conduct fieldwork

sampling frame examples

demographics (age, gender, income)

psychographics (attitudes towards a firm/brand, political affiliation)

geographic (city, state, country)

behavioral (purchase / online search behavior, social media usage)

random sampling error

statistical fluctuations that occur because of chance variations in the elements selected for the sample

systematic error

result from non sampling factors, primarily the nature of a study’s design and the correctness of execution

systematic error example

CNN conducted a poll on their website about electric vehicles. 68% preferred EVs over gas vehicles. They concluded that 68% of Americans preferred EVs over gas vehicles.

data processing error

made by administrator during data entry or coding or editing or tabulation or analysis stages

sample selection error

made by administrator in selecting sampling units

interviewer error

unintentionally made by administrator whle administering the interview / survey

interviewer cheating

deliberate manipulation by administrator while administering the interview / survey

measurement error

made by administration where he fails to communicate the scale of measurement (you are measuring satisfaction on a 7-point scale, but the respondent thinks you are using a 5-point scale)

acquiescence bias

aka agreement bias; when respondents tend to select a positive response option disproportionately

extremity bias

aka extreme response bias; the survey respondents answer questions with extreme views even if they don’t actually feel that way

social desirability bias

when respondents give answers to questions that they believe will make them look good to others, concealing their true opinions or experiences

probability sampling

every population element has a known, nonzero probability of selection

nonprobability sampling

probability of any member or the population being chosen is unknown

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a convenience sample?

a) ask the 10 students who are near to me
b) ask the students who scored in the top
quartile (top 25 percentile)
c) ask the 5 girls and 5 boys who come first to class
d) ask a student and then ask him to refer another of his friends. Continue till we get 10 responses.

a

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a judgemental sample?

a) ask the 10 students who are near to me
b) ask the students who scored in the top
quartile (top 25 percentile)
c) ask the 5 girls and 5 boys who come first to class
d) ask a student and then ask him to refer another of his friends. Continue till we get 10 responses.

b

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a quota sample?

a) ask the 10 students who are near to me
b) ask the students who scored in the top
quartile (top 25 percentile)
c) ask the 5 girls and 5 boys who come first to class
d) ask a student and then ask him to refer another of his friends. Continue till we get 10 responses.

c

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a snowball sample?

a) ask the 10 students who are near to me
b) ask the students who scored in the top
quartile (top 25 percentile)
c) ask the 5 girls and 5 boys who come first to class
d) ask a student and then ask him to refer another of his friends. Continue till we get 10 responses.

d

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a simple random sample?

a) assign each student a number from 1-40.
Randomly select 10 numbers between 1-40.
b) assign each student a number from 1-40. After selecting the first number randomly select numbers at equal intervals till we reach a sample size of 10.
c) consider different groups. For example, male and female students. Select 5 female and 5 male respondents.
d) consider different groups. For example, male and female students. Select one group for example, female and ask 10 female students.

a

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a systematic sample?

a) assign each student a number from 1-40.
Randomly select 10 numbers between 1-40.
b) assign each student a number from 1-40. After selecting the first number randomly select numbers at equal intervals till we reach a sample size of 10.
c) consider different groups. For example, male and female students. Select 5 female and 5 male respondents.
d) consider different groups. For example, male and female students. Select one group for example, female and ask 10 female students.

b

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a stratified sample?

a) assign each student a number from 1-40.
Randomly select 10 numbers between 1-40.
b) assign each student a number from 1-40. After selecting the first number randomly select numbers at equal intervals till we reach a sample size of 10.
c) consider different groups. For example, male and female students. Select 5 female and 5 male respondents.
d) consider different groups. For example, male and female students. Select one group for example, female and ask 10 female students.

c

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course. Which of the following represents a cluster sample?

a) assign each student a number from 1-40.
Randomly select 10 numbers between 1-40.
b) assign each student a number from 1-40. After selecting the first number randomly select numbers at equal intervals till we reach a sample size of 10.
c) consider different groups. For example, male and female students. Select 5 female and 5 male respondents.
d) consider different groups. For example, male and female students. Select one group for example, female and ask 10 female students.

d

proportional stratified sampling

the number of samples taken from each subgroup (stratum) reflects its actual size in the population, ensuring accurate representation

disproportional stratified sampling

sample sizes from each stratum are not in line with their population sizes, often oversampling smaller or more important subgroups to give them greater focus

multistage area sampling

a cluster sampling approach involving multiple steps with a combination of multiple probability techniques

a computation of sample size requires

• Required degree of precision

• Desired level of confidence

• Estimate of population variability

number of sample elements (sample size) required to achieve a given precision at a specified confidence is

N=Z² * S² / D²

z= confidence (90% ~1.6, 95% ~2, 99% ~2.6)

s= estimated population variance

d= precision

type 1 and type 2 errors