Importance of Inference Space (as a concept)

I am not sure about you, but some responses my students would come up with include things like:

• It goes up and down.

• August temperatures [everywhere] are between 70-80.

• August temperatures in Indianapolis go up and down.

• Yearly temperatures in Indianapolis are between 70-80.

• August temperatures in Indianapolis are increasing because of climate change.

Ok, so there are a whole host of things going on in these sample responses from students…

The “goes up and down” is evidence that those students are not sure what aspects of the data to pay attention to when looking for a pattern and instead are focused on surface attributes of the data. This is an issue in and of itself, but we are not tackling it here.

The “are between 70-80”, in combination with the other aspects of each of those claims, is an over limitation to the data at hand. This indicates a struggle students have to understand these data in a broader context and that those are the range of observed average values, which again is an issue in and of itself but not for this conversation.

So, that leaves the other aspects of the claims. And those are indications of students not understanding the inference space of the data. What we can say from our data is dependent on what data we have. In other words, there is a boundary on what we can include in our claims from the data. This boundary is the inference space.

For this example, the we have data on the average monthly air temperatures from August, in Indianapolis, Indiana, over 14 years. In other words, this is our “inference space” from the data. Through these data, students can develop a better sense of what is typical air temperature (weather) for August in this Indianapolis, and start to build an understanding of a local climate pattern (common August air temperature in this location over time). This is what we can connect from or relate the data to in terms of broader concepts. But that is the boundary of what we can claim from the available evidence in these data.

Claims about August temperatures everywhere, all August or yearly temperatures in Indianapolis, and/or attributions to climate change all extend beyond the inference space of these data. A good claim within the inference space of the data could be something like: Indianapolis August air temperatures were typically between 70 and 80F from 2004-2018 with a slight positive trend over this timeframe.

Inference space is not a term we need or should teach our learners, but it is a concept that they definitely should build an understanding of over time.

NOTE ABOUT WHAT LEVEL OF CLAIM ASKING FOR

Much of our curricular emphasis at the moment with Claims, Evidence, and Reasoning is on asking students to reason only about data they have available on the page. This is what Pratt, Johnson-Wilder, Ainley, and Mason (2008) call a “Game 1” claim. With this kind of a claim, having an understanding of what your inference space is from the data at hand is extremely important. If we are only asking students about the data they have, then we need to make sure they are only making claims about the data they have. Ensuring alignment between our expectations of the students and their outputs is critical for teaching good data literacy practices and skills.

If instead, we are asking students to use the available data to reason about a larger, unknown population (aka from which the sample of data came and from which one could collect more data in the future) then this is a bit different. Asking students to talk about the larger population is what Pratt et al. (2008) call a “Game 2” claim. With this kind of a claim, knowing your inference space of the data is important BUT we also need to make sure we understand the broader context of the data and appropriate language to use (that accounts for uncertainty) in making a claim that “goes beyond the data at hand” (Rossman, 2008).

As a note, this “Game 2” kind of claim is a critical aspect of making informal and formal statistical inferences from data. And this is where we want/need students to be able to get to with data to be data literate citizens in the 21st century (but we will explore inference in a later post).

Resources

Looking for some more information for example strategies to help students build their conceptual understanding of inference space? Check out: our February 2020. Data Literacy 101: What can we actually claim from our data? Science Scope 43(6): 20-26 article for more.

References

Pratt, D., Johnson-Wilder, P., Ainley, J., & Mason, J. (2008). Local and global thinking in statistical inference. Statistics Education Research Journal, 7(2), 107–129.

Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view. Statistics Education Research Journal, 7(2), 5–19.