Section 4: Interpreting the Data
Contents
Section 4: Interpreting the Data¶
You should now have generated two values, one showing the duration of the exposition in the format used by Bowen and the other showing the average BPM of the secondary theme. We now need to compare them to Bowen’s results.
A note on linear regression models.¶
Although he doesn’t mention this in the article, the graphs contained in Bowen’s fig. 19.1 are examples of linear regression models. This is too broad of a topic to cover here, but the idea behind such a model is to use the relationships between two or more variables (here, the year of a recording and the duration or BPM of the exposition/second theme) to predict the relationship between these variables for observations that we didn’t analyse.
Regression models allow us to make predictions in two ways. Prediction within the range of values in the dataset is known as interpolation; prediction outside the range of values is known as extrapolation. Generally, there are more statistical problems associated with extrapolation than interpolation. However, in this case we are not using extrapolation to make formal predictions: we have already gathered our data, and all we are doing is using extrapolation to check it against Bowen’s model.
Comparing your data to Bowen’s.¶
We won’t be going into the maths required for formal extrapolation now. Instead, all you need to know is that the values Bowen’s model predicts are:
Year |
Exp. Duration |
2nd Them. BPM |
|---|---|---|
2010 |
1.43 |
185 BPM |
2020 |
1.40 |
188 BPM |
Take a look at these values and compare them to your own. How close are they to your data?
If the model does seem to explain the data you gathered, why do you think this is - and does this mean Bowen’s model is still valid? If not, what might have happened in the intervening twenty years to cause a change in performance practice? Finally, if only one of Bowen’s values comes close to your own, what might this suggest about the other sections of the exposition as well as the second theme?
Try and think about these issues when answering the questions on the following page!