Conceptual self-assessment for: A deeper understanding of data, statistics, probability, and estimation

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The following are some recommended conceptual self-assessment questions for the lesson called A deeper understanding of data, statistics, probability, and estimation. They’re intended for you to work through to test your own understanding of the key concepts we covered there.

Question 1:

a) Why is is it so important to sample a population?

b) Provide three real life examples we didn’t discuss in class where taking sample is required for practical reasons.

c) Taking a full census isn’t usually possible. Provide an example where it would be.

Question 2:

a) Are people working in the field for geospatial applications likely more aligned with the discipline of probability or the discipline of inferential statistics? Explain.

b) Statisticians and geomatics engineers might look at the word estimation differently. Explain. What is each generally trying to estimate?

Question 3:

a) What are the different types of data and scales of measurement?

b) Provide an example of each scale of measurement that we didn’t see in class

c) We talked about how some scales of measurement are preferred over others in statistics. Which were they, and why?

d) Why wouldn’t we always use the preferred scales? Provide an example. (You might find this easier to answer after looking at the data for the applied problems related to this topic.)

Question 4:

When I was in a train station in France, I was leaving a public washroom and took the photo shown here of a quick survey (under the sign) that they wanted people to fill in before or after drying their hands in one of the two white hand dryers you can see in the picture. People are being asked to push one of the three colored buttons to indicate how satisfied they are with the cleanliness of the bathroom.

This struck me as a wonderful example to bring into our discussions about data types, measurement scales, populations, and samples.

a) What is the population in this case?

b) What type of data are they going to get? Use the categories we saw in class when answering this.

c) What scale of measurement applies here?

d) Could you take an arithmetic mean or calculate the standard deviation of the data they will collect? Either way, what does your intuition or prior knowledge tell you might be more useful for describing those data? (We’ll see more on this later. I’m just trying to point out how some descriptive measures can be less well suited to some data types and/or measurement scales.)

e) Data type and measurement scale aside, how ‘good’ a sample of the population do you think the train station managers will get in this situation? I can think of at least two good reasons why it very likely won’t be representative of the actual population. What are those reasons? And which one of them in particular is likely to very significantly bias the results of their experiment?

Question 5:

The following video shares a scenario of two approaches to sampling a population – one by a guy named Bobby and one by a guy named Billy.

Watch the video and use your knowledge of sampling and statistical inference to explain why Bobby’s results and approach to sampling might not be as trustworthy.

There are lots of levels to the discussion here (with the approach to sampling, and the reliability and validity of the instrument among them). But don’t go too deep. I’m just looking for your thoughts from the perspective of sampling a population.

That’s it for the conceptual questions for this topic!

If you’re one of my students, then you’re expected to answer these on your own and submit them according to the directions provided in class, i.e. you don’t  need to submit them through this website. Don’t forget that our TA and I are both here to help you in the associated lab (and/or tutorial) sessions.

Put your answers to the conceptual questions below into a single document. I don’t mind if you hand write it or type it out – do what works best for you.

But I want you to use the same document for all of the self-assessment questions you do before the due date, i.e. you will be asked to hand them all in together. This means you should keep things well organized with clear headings so you (and your TA) can figure out which solutions refer to which questions. Good self-assessment documents use headings and some even provide the links, e.g. the URL for this page. This helps you keep track and go back and forth quickly between the problems and solutions.

Also, keep in mind that you will be asked to submit them through D2L, so you’ll have to scan any handwritten documents.

You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.

The following schedules are for Alex’s in-class students:

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