Problem or The Investigative Question

1. Problem • or • The Investigative Question

2. Lesson Objective To learn how to write an Investigative Question Lesson Success Criteria • Can identify the aspects that make a suitable question • Can successfully write an investigative question

3. Problem This is where you decide what you would like more information about. This stage involves defining the problem of interest, and posing a question. Consideration of variables (the characteristics of interest that are being measured) need to be carefully defined and understood. We will be only working with comparison questions within this standard. The question would normally be written “I wonder if …” or “Do …” or “Does …” You should provide some thought or comment, as to what answer you would predict to the question you ask. NOTE: The question needs to written in a very specific way.

4. Problem/purpose/question Start with something that you are interested in finding out “I wonder if boys feet are bigger than girls?’ The problem section is about what data to collect and who to collect it from and why it’s important.

5. Your question must compare two sets of data. “Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls?”

6. Include the population you are sampling from. “Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ ? If our population was the data from the 2013 Census at Schools database, we would then write: “Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls in the 2013 Census at Schools database?”

7. What is wrong with this question? Are 13 year-old NZ boys bigger than 13 year-old NZ girls? It gives no indication as to what we need to specifically find out about in order to answer the question i.e. are we wanting to know about heights or weights or muscle size or ???

8. What is wrong with this question? Do 13 year-old NZ boys have bigger right feet than 13 year-old NZ girls? Ambiguous. Is it asking if all boys have bigger right feet than all girls?

9. What is wrong with this question? Does the typical/average 13 year-old NZ boy have a bigger right foot than the typical/average 13 year-old NZ girl? The word ‘average’ is not referring to the foot size but to the boy or girl being ‘average’.

10. What is wrong with this question? “Do 13 year-old NZ boys tend to have bigger right foot lengths than 13 year-old girls?” This has a focus on the units rather than the measure and it is not clear what we need to do to be able to answer the question. A possible interpretation could be if we take any 13 year-old boy and any 13 year old girl, then do we expect the boy to have a bigger right foot length than the girl?

11. What is wrong with this question? Is the average right foot length for 13 year old boys bigger than the average right foot length for 13 year-old girls? Focus is on the measure and compares locations of the centres of the two distributions. No image of distributions and their associated variability.

12. Good question Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls?

13. Why Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls? The question is structured with the key element, right foot lengths, at the very front of the question.

14. Why Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls? This sentence structure helps to give an image of two distributions of right foot length measures, one for 13 year-old NZ boys and one for 13 year-old NZ girls, both drawn against the same scale which presumably would be in centimetres.

15. Why Do right foot lengths for 13 year-old NZ boys tend to be bigger than right foot lengths for 13 year-old NZ girls? The word ‘tend’ means that in a plot of the two populations focus is on the measure and their two distributions. The word ‘tend’ means that in a plot of the two population distributions the boys‟ right foot lengths are shifted further up the scale than the girls.

16. An even better question!! Do right foot lengths (in cm’s) for 13 year-old NZ boys tend to be bigger than right foot lengths (in cm’s) for 13 year-old NZ girls? Notice that the variable’s measure is now included. This is a perfect example of what I would expect to be written for any statistical comparison investigation. (Just remember to include the additional Population information i.e. Census at Schools – if this is what we are using)

17. Reflection What vocabulary have we used today?

18. Homework Chapter 7: page 232-233 Exercise A: Statistical variables and questions