Cross Sectional & Longitudinal Studies
A cross-sectional study focuses on a wide range of individuals and is carried out during a specific
timeframe. They are usually quicker, easier and more suitable for certain situations such as, the observation
of a population or a representative of a subset.
Ex. Questionnaire was done in March of 1999 on how parents felt about Internet filtering. This is an
example of a cross-sectional study because it has a specific timeframe and broad range of individuals
involved.
A longitudinal study is carried out over an extended period of time and focuses on a small group of
individuals. This is the method of choice for psychological and medical studies however, they are difficult to
undertake and are usually expensive.
Types of longitudinal Studies:
Panel Study: Involves sampling a cross-section of individuals.
Cohort Study: Involves selecting a group based on a specific event such as birth, geographic location or
historical experience.
Retrospective Study: Involves looking to the past by looking at historical information such as medical
records.
Ex. Census was done in England and Wale’s recording information such as births, deaths and cancer
registrations. The data was collected in 1971, 1981, 1991 and 2001 and only one percent of the population
was included in the research. Therefore, it was a longitudinal study of a small group of individuals over a
long period of time.
Simple Random Samples & Voluntary Response Samples
Simple Random Samples - a method for drawing a sample from a population, such that all samples of a
given size have equal probability of being drawn.
Voluntary Response Samples - a sample that involves only those who want to participate.
Simple Random Samples:
Example 1: We have a list of 40 heads of households. Each has a unique number, 1 through 40. We want to
select 10 households randomly from this list. Using a random number table, we select consecutive 2-digit
numbers starting from the upper left. If a random number matches a household's number, that household
is added to the list of selected households. If a random number does not match a household's number (for
example, if it is greater than 40), then it does not select a household. After each random number is used, it
is crossed out so that it is never used again. We continue to select households until we have 10.
.
Voluntary Random Samples:
Example 1: “All students who enjoy Pepsi more than Coca-Cola raise your hand.” This is an example of a
voluntary random sample. It is the student’s choice whether or not they wish to participate.
Any sort of survey: mail, street, or on-line surveys are all examples of voluntary random samples.
Simple Random Samples and Voluntary Response Samples
In conclusion Simple Response Samples and Voluntary Response Sample are opposites in how they retrieve
data. The Simple Response Samples are based on a large group of participators all of whom give their
opinion and all who have an equal chance in getting picked. An example of Simple Response Samples is the
lottery because everyone has an equal chance to win and everyone is allowed to purchase a ticket. While
Voluntary Response Samples are based on a group of individuals who state their opinions because they
believe that theirs is the right one they have strong feelings for what they are saying. An example of a
Voluntary Response Sample would include call-ins whether for shows or radios, those who cast their
opinions on these voluntarily do so because they have strong feelings about the issue or who should win.
For Voluntary Response Samples those who are outspoken and believe highly in what they are saying,
usually pick themselves for these samples. While for Simple Response Samples everyone is picked to state
their opinion regardless of who believes more strongly on the issue.
Questionnaire Question Types
Closed Question:
Definition: Question requires the subject to select from a given list of responses or has an exact response, are
closed. Close-ended questions can be used for clarifying facts, verifying information already given or controlling
a conversation. They are also an example of collecting data in a primary form. This type of question makes it
easy to gather the information collected to be analyzed.
i.e: What is your gender?
Male
Female
This would give easy statisics, also if a class was asked about their favourite colour and four choices were given.
Open Question:
Define: Question that is answered in subject’s own words is open ended. Meaning the respondent is not
restricted by a fixed set of responses, and answer is broad based. This type of question includes the subject’s
feelings and/or opinions towards the given topic.
i.e: How do you feel about labradoodles?
What is your favorite food?
Questionnaire Question Types
Leading Question: a question that attempts to guide the subjects answer, it is phrased in such a way to
suggest the desired answer of the surveyor.
Example: Experts have proven that the unhealthy lunches served in school cafeterias are cause for obesity
in children. Do you encourage your children buy lunch at school?
Loaded Question: a question that suggest an answer desirable by the surveyor or are emotionally charged,
the surveyor uses these types of questions to obtain data and results that have a favourable outcome for
the
person
that
the
survey
is
being
done
for.
Example: Should people from other countries be allowed to go to Canadian Universities when it takes away
from Canadian high school students?
Cluster Sample (not handed in) Destructive Sampling
Destructive Sampling is a technique used by companies in which the selected element can no longer
be reintroduced to the population. Destructive Sampling allows the sampler to test the structural integrity
of the product. For example, earthquake engineering requires destructive sampling in order to ensure that
the materials used would hold up to the force of such a powerful natural disaster. There are times when
Destructive Sampling, sometimes referred to as “Destructive Testing” can be a good economical decision.
These tests are usually much easier to carry out than Non-Destructive testing, and it is often much easier to
interpret the results. When products are mass produced, the cost of destroying a small number of products
is worth the cost. For example, the cost of doing a few crash tests is less than the cost of a lawsuit after a
vehicle malfunction. It is rarely an economical decision to carry out Destructive testing when only one or a
few products are created (ex: in the case of a building).
Margin of Error Summary
The margin of error is a statistic that represents the amount of random sampling error in a survey’s
results. The theory behind this is that the larger the margin of error, the less faith people will have in this
survey’s results. With a larger margin of error, the truth behind the results will not be as strong and the
survey will not provide a strong, conclusive representation of the population.
Margin of error is created by one main issue in sampling. This issue comes from the number of
people sampled. If the sample size is small, the data will be less accurate. However, if a huge group is
sampled, the conclusive data about the population will be more accurate.
Margin of error can be calculated using different perspectives. The typical formula for margin of
error is the standard error formula.
Standard error =
p(1  p)
n
In this equation, p represents the percentage, n represents the sample size and the value of the
standard error calculation will represent how much higher or lower the sampled percentage actually could
go. For example, if the standard error value was 0.02, then the percentage from the sample could truthfully
have a value of anywhere up to 2% higher or lower of the given sample percentage.
E.g. A survey said that 58% of Americans drink coffee every day in the morning. The survey sample
size was 1000 people. Find the margin of error in this statistic.
Standard error =
p(1  p)
=
n
0.58(1  0.58)
= 0.0156 = 1.56%
1000
Margin of error is therefore equal to 1.56%.
Multi-Stage Sample & Convenience Sample
Multi-Stage Sampling: A method of sampling in which the total population is first divided into a large
“primary stage,” and then is divided into smaller and more specific “secondary” and “tertiary stages.” This is
done to provide a more accurate representation of the group being sampled. Example: Polling voters is
done this way. The primary stage would be something such as a large geographic area and the secondary
and tertiary stages could be smaller geographic areas.
Convenience Sampling: A method of sampling where the group being sampled is chosen based on ease of
access. Example: A survey being conducted in a mall. This is an example because the group being sampled is
quite small and most likely does not accurately represent the population.
Stratified Sample
Stratified Sampling is a method used to categorize the population into separate smaller groups, then
sampling from each subgroup. Stratification is the actual process of dividing the population group into
smaller subgroups to be independently sampled. Stratified Sampling is useful when there are similar
subgroups, if they are different in major ways then stratified sampling will not be useful. When data in
subgroups are not equal in size, but are equal in importance stratified sampling cannot be used, when this
happens is gives more importance to subgroups with greater data. Stratified sampling is just as good as
random samples but they need an advanced knowledge of the populations’ characteristics.
•
Example-A high school student who is studying year ten attitudes in the school uses registration
tuition classes as strata and studies a random selection of students from each of these classes.
Example 2- A study population is a high school with students in grades 9, 10 and 11. Researchers want
to know how much these students spend weekly for ice cream, on average and what percentage of
students spend at least $10 weekly for ice cream.
A sample of 40 students was elected. Grade 9 spends $5, 10 spends $15.4, 11 spends $10.1.
15% of grade 9 spend at least %10
100% of grade 10 spend at least $10
45.45% of grade 11 spend at least $10