Sampling & Additional Results
Are you interested in the sampling process? In this page, I will walk through our process and provide opportunities for you to try it out yourself!
1) Picking the survey type.
Simple Random Sample
Imagine putting slips of numbers into a hat. Every number has an equal chance of being included in the sample.
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Pros: They are pretty representative and efficient
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Cons: If you have a large number of people, this might be an expensive, time-consuming option. Also, may not be possible/realistic.
Stratified Random Sample
First separate your population into groups (based on demographics, etc.). You then select members from each group randomly.
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Pros: members from each group will be represented in the sample
Cluster Random Sample
First separate your population into groups. The sample contains members from different groups. Randomly select a group.
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Pros: fast and efficient sampling method
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Cons: May not be possible
Systematic Random Sample
Using a list where members of the population are ordered. Select every nth member.
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Pros: very quick sampling
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Cons: it might not be possible to list all members of the population; also, could not be representative
So which survey did we pick?
We went with the Stratified Random Sample as we felt that the school population could be stratified into genders and grades. Furthermore, all genders and grades are likely to be represented in our sample especially if we're randomly choosing members from each of the "layers" we created.
2) Using the Class Roster, we assigned numbers to all students.
We used a class roster and assigned numbers for each student to create our pool. We removed all newspaper contributors from possible selection.
Freshman Girls: #621-719
Freshman Boys: #720-810
Sophomore Girls: #2-99
Sophomore Boys: #100-213
Junior Girls: #214-309
Junior Boys: #310-416
Senior Girls: #418-516
Senior Boys: #517-620
Some questions for you to consider:
1) Why did we divide our roster into grades and genders?
2) Why did we remove newspaper contributors from our sampling pool?
2) Why did we remove newspaper contributors from our sampling pool?
Newspaper contributors would also lead to bias in our results. We assume that they are more likely to read the newspaper as they would like to see their own and the team's contribution to the newspaper.
1) Why did we divide our roster into grades and genders?
We chose to use the Stratified Random Sampling, so we had to divide the students into groups based on similar demographics. We stratified by genders and grade levels, We focused on these specific variables as we felt they could impact our results the most. By "blocking" we have an equal representation in our sample and therefore reducing some of that bias.
3) We selected 10 students for each gender and grade using a random number generator.
For each grade-gender group (ex: Freshman Girls), we used a calculator to generate a random number.
We used the "RandIntNoRep" function in the Math > Probability section of the calculator (note: you can use any type of random generator) We want to input the lower bound and the upper bound of our population.
In this case, the lower bound = 621 and the upper bound = 719.
We repeated this and generated 10 numbers for each gender and grade.
Some questions for you to consider:
3) Why is randomness so important?
4) Why did we select 10 students?
3) Why is randomness so important?
Randomness reduces bias. An example of non-random sampling is voluntary sampling such that participants volunteer for the study. These people don't represent the population. Think about Rate My Professor, a site where students who are generally either very passionate or dispassionate about the class give ratings. These ratings don't represent all the students who take the class, but only a subset of students.
4) Why did we select 10 students?
A good sample size is approximately 10% of the population. We had estimated that they are about 100 students of each grade and gender (ex: freshman boys). Therefore, 10% of that population is about 10 students.
4) After creating our sample, we sent out emails and Instagram DMed our sample.
We send emails specifically to the students chosen by our sampling process. Think of them as "lottery" winners. Their "prize" is to take our survey.
If they did not respond to the first email, we emailed them again.
We wanted at least 50% of responses of all demographics, so we repeated the sampling process for the students who did not respond in each demographic. This time, in a simpler fashion. We only assigned numbers to each students who didn't respond and used a calculator to randomly select a number. We also sought their Instagram and DMed the student whose number corresponded to the generated number.
Some questions for you to consider:
5) What is the best way to reach out to these students?
6) What are some incentives for them to fill out the survey?
5) What do you think is the best way to reach out to high schoolers? Or if you are a high schooler, what is the best way to reach out to you?
6) What are possible incentives for students to fill out the survey? What might incentivize you to reply to the survey?
More About the Results
What is Independence?
Statistical independence means that one event's occurrence will not affect another event's occurrence. For example, flipping a coin is independent because each flip has a probability of 50% heads. One flip doesn't affect the other's probability.
We wanted to see if grade level and gender affected the probability of reading the newspaper, so how do we do that?
We conducted further statistical analysis to see if there's an association between grade level, gender and reading the Crane Clarion. Using this organized chart, we could find out what percent of freshmen, sophomores, juniors, and seniors read or do not read the Crane Clarion. Similarly, we can see what percent of boys and girls read the Crane Clarion
For grade level to be independent to reading the newspaper, the probability of reading the newspaper for each individual grade should be equal to each other. That means a freshman would have the same probability as a sophomore when reading the newspaper.
Is that true from the data?
False.
The probability that a freshman reads the Crane (9/10) does not equal the probability that a sophomore reads the Crane (4/10). This means that the chance a freshman reads the Crane is not the same as the chance a sophomore reads the Crane. Therefore, grade levels affect the probability someone reads the Crane.
Is the probability of a male student reading the newspaper equal to the probability of a female student reading the newspaper?
Is that true from the data?
False.
The probability that a boy reads the Crane (13/21) does not equal the probability that a girl reads the Crane (17/24). This means that the chance a boy reads the Crane is not the same as the chance a girl reads the Crane. Therefore, gender affects the probability someone reads the Crane.