Introduction to Statistics Module 1

Question 1

Population of Interest define and give an example.

Answer 1

• The group you aim to draw conclusions about, defined by your research question.
• If you’re studying shopping habits in Toronto, your population of interest might be all residents of Toronto who shop at grocery stores.

Question 1

Statistical population

Answer 1

• The group from which you can actually sample, based on your study design. It’s the group to which your statistical conclusions are valid.
• If you send a survey to 100 email addresses of Toronto residents, the statistical population is all the people with active email accounts in Toronto.

Question 2

Sampling unit

Answer 2

• The individual units randomly selected to gather data
• In the email survey example, the sampling unit would be the email addresses of the respondents.

Question 3

Sample

Answer 3

• The actual group of sampling units from which you collected data.
• If 72 people respond to your email survey, the sample includes those 72 responses.

Question 4

Observation Unit

Answer 4

• The subject from which you collect the data, often the same as the sampling unit but sometimes different.
• If your survey is about grocery preferences, the observation unit would be the individual people responding.

Question 5

Measurement Variable

Answer 5

• What you want to measure about the observation units.
• You might measure the type of grocery store each person shops at (e.g., local stores vs. chains).

Question 6

Measurement Unit

Answer 6

• The scale on which the measurement variable is recorded.
• If measuring the age of shoppers, the measurement unit might be years.

Question 7

Explain the connection across the five hierarchical scales of a statistical study design

Answer 7

1) Sampling Unit: You start by selecting random sampling units (e.g., email addresses).

2) Sample: The collection of these sampling units that you actually observe (e.g., 72 email responses).

3) Observation Unit: The entities from which you directly collect data (e.g., the people responding).

4) Statistical Population: The total collection of all possible sampling units (e.g., all people with email accounts in Toronto).

5) Population of Interest: The broader group your research is focused on (e.g., all people who shop at grocery stores in Toronto).

Question 8

Describe the steps involved in a statistical study, and the role of descriptive statistics versus inferential statistics

Answer 8

Sampling: Designing your study and selecting your sample.
Example: Randomly selecting 100 people from Toronto to answer a survey about grocery shopping habits.

Measuring: Collecting data from your observation units.
Example: Asking each person which grocery store they prefer and how much they spend on groceries per week.

Descriptive Statistics: Characterizing the data from your sample. This involves summarizing data with averages, tables, or graphs.
Example: Finding that 40% of respondents prefer local stores, while 60% prefer large chains. This is a descriptive statistic.

Inferential Statistics: Using your sample data to make broader conclusions about the statistical population, including accounting for uncertainty.
Example: If 60% of your sample prefers large chains, you might infer that about 60% of the entire population of Toronto prefers large chains, though there is some uncertainty.

Question 9

Identify questions that can be answered using descriptive statistics versus inferential statistics

Answer 9

Descriptive Statistics: Answers questions about the sample itself.
Example: “What percentage of my sample prefers local stores?” (Answer: 40%)

Inferential Statistics: Answers broader questions about the population based on the sample.
Example: “What percentage of all shoppers in Toronto likely prefer local stores?” (You infer based on the sample data, considering possible sampling error.)

Question 10

Single population inference

Answer 10

Single Population Inference: Drawing conclusions about one population from your sample.
- Example: Using data from your Toronto sample to infer what the entire population of Toronto prefers in terms of grocery stores.

Question 11

Comparison Among Population

Answer 11

Comparing different groups within your statistical population.

Example: Comparing the preferences of people living in different neighborhoods or comparing people who shop at local stores versus large chains. Inferential statistics will help you determine if the differences are statistically significant.