Research Methods - Chapter 8: Sampling

1. Population: The group we wish to generalize about. Also known as Universe. 

ex. individuals, political parties, municipal goernments etc.

2. Sampling: The process of drawing a sample of cases from a larger population

Clearly identify the population to be studied

1, The unit of analysis (individuals, political parties, municipal govs. etc)

2. The geographic location

3. The reference time period

1. Population parameter: population characteristic or variable expressed in numeric terms (when the responses of each member of the population are measured)

• ex. The mean income of all families in a city
• ex. The age distribution of the city's population

2. Statistic: A numeric estimate of a variable in a sample, used to estimate a population parameter

a sample that accurately represents the larger population from which it was taken.

Ex. if the pop. has 30% Asians, 60% Caucasians and 10% Africans, then the sample should reflect a similar racial distribution

1. The accuracy of the sampling frame

2. The sample selection method

3. The sample size

A list of all the units in the target population. 

Ex. If our target population is students at Canadian universities during 2014-15, the sampling frame would list all registered students.

Who is included and who is excluded.

ex. Telephone list may not include the poor and homeless.

Some other lists may not account for changes in the population caused by birth, death or migration

Quantitative Typically uses probability sampling 

Qualitative: non-probability sampling more common

1a. Sampling based on probability theory that allows us to estimate the likelihood that our sample provides a representative picture of the population. 

1b. It is the random selection of a sample where each unit of the population has an equal opportunity to be selected for the sample.

2. It helps us to minimize conscious and unconscious sampling bias

Divide the number of possible favourable outcomes by the total number of possible outcomes. 

Ex. We have 10 students, and 6 are female. our probability of selecting a female studen is 6 divided by 10, or 60%. 

6 is the number of favourable outcomes, and 10 is the total number of possible outcomes.

Part 1: P(A) = r/n

P: is the probability of event A

r: is the number of favourable outcomes

n: is the number of total outcomes.

Part 2: P(AB) = P(A) P(B/A)

P(AB): is the probability of the joint occurence of events A and B

P(A): is the probability of event A

P(B/A): is the probability of event B after event A. 

Part 3: P(B/A) = P(B)

see page 159

the process where every case in the population is listed and the sample is selected randomly from the list

it distributes sample statistics around the population parameter in a normal bell shaped distribution

add the individual scores, and divide it by the total number of cases. 

ex. Between 6 people, they had 12 pets total. Divide 12 (pets) by 6 (people) and you get a mean of 2.

So, 2 would be the mean (or peak of the bell curve) of the total sample distribution.

So in other words, the probability of randomly selecting a mean of 2 is greater than any higher or lower number

Confidence interval: The range of values within which the population parameter is likely to fall

Confidence level: The estimated probability that a population parameter lies within a given confidence interval

Sampling error: The difference between the sample statistic (the estimated value) and the population parameter (the actual value). 

ex. A large sampling error indicates that the sample statistic deviates greatly from the population parameter.

• 1. The homogeneity of the sample
• How similar a population is with respect to variables

2. The number of variables under study

3. The desired degree of accuracy

• What is the margin of error you are willing to accept?
• Knowing the margin of error allows researchers to state their sample statistics as a confience interval

The law of diminishing returns.

ex. a sample size with a of 383 represents a population of 100,000 with a 5% margin of error, where as adding onlye one more to 384 will allow you to represent a population of 500,000 at the same margin of error

If the survey found that 40 per cent of the sample intended to vote for party X, we could assume that within the population of all voters, there was a 95% chance that between 37% and 43% would vote for party X. There is also a 5% chance that party X would get either less than 37% of the vote or more than 43% of the vote.

A sampling method based on the sample size needed. If we want 5 percent of the population to be included in the sample, we select one out of every 20 cases by using a selection interval of 20. 

Pro: Systematic sampling can be more practical and efficient than simple random sampling

• Con: It is less random and thus less accurate.
• A list that is ordered alphabetically will elicit biased results, so the frame also needs to be randomized.

Breaking the population into mutually exclusive subgroups, and then randomly sampling each group. Afterwards, we would combine the subsamples to construct our larger sample. 

Advantage: It allows us to focus on small subgroups so that we can understand how these small groups compare with the larger population

Disproportionate stratified sampling: If the population of subgroup A is way smaller than subgroup B, such as Saskatchewan and Ontario, we can use it to increase the number of responders from Sask and decrease form Ontario. But you would need to assign weights to responders to get a representative sample of the overall Canadian population.

Especially useful when we have sub-groups like race, gender or nationality

The process of dividing the population into a number of subgroups (clusters), and then randomly selecting clusters within which to randomly sample. 

Good when we can't get a full population sampling frame, such as the whole population of Canada.

ex. If you were conducting door to door interviews across Canada, this would avoid random cases spread out across the whole country and save on travel costs. 

How its done: divide the country into clusters. randomly select 2 of them. Further break down those clusters into similar population size, such as city blocks. Randomly select 10 city blocks to conduct interviews in. 

Problem: You could randomly draw two consituencies form northern Ontario, which would appear biased.

Advantages: Can pursue more in-depth descriptive informaiton

Disadvantages: Cannot identify margins of error or confidence intervals

• Accidental sample: convienitence sample where research gathers data from an "accidental" encounter, such as a "person on the street"
• It is quite biased, as a person on the street in a downtown area is likely an office worker, and not a homemaker or a retired person.

Purposive sampling: Involves researcher selection of specific cases where the researcher uses their judgement in the selection process. 

Can select for specific criteria, and ensure that some diversity is included.

Snowball sampling: begins by identifying a few cases, from which the researcher gets referrals and interviews others and so on.

Quota sampling: When accidental or purposeful sampling is combined with stratification. The researcher identifies a number of target groups, and then sets a quota. You have to know the characteristics of your population ahead of time, and you try to mirror the larger population with quotas. 

They are non-probabilistic, and so we must be careful when generalizing back to a larger population.

ex. need 15 men and 15 women. How they meet the quota can vary.

The bigger our samples, the more it clusters around the true mean. A sample of 3, 4, 5 and 6. This is what happens in probability sampling. We are getting closer mean, so the margin of error is reduced.