To illustrate how these measures differ, Figure 3 plots the density distributions of the various indicators of Share of Time Teaching (Panel A), and Share of Time Teaching and Learning (Panel B). To help isolate differences, the third panel (Panel C) plots the densities of the difference between the two, namely the time lost due to students being off-task.<sup>33</sup> These distributions, while consistent with the averages (Table 4) and correlations (Table 10) for these variables, nevertheless provide additional insights. SDI, which records time in a minute-by-minute fashion, has the right-most distribution for Share of Time Teaching—meaning it assigns a greater share of time to be classified as teaching. In addition, the adjustment for learning based on the share of time with no more than 6 students off-task (which is recorded during snapshots at 5-minute intervals) has the left-most distribution. Stallings, where time on teaching is recorded during a snapshot every 10 minutes, has the left-most distribution for Share of Time Teaching—meaning that it assigns the least time as being classified as teaching. The distribution of time lost due to students being off-task is the right-most of the three tools—meaning that it is most likely to record an observation as being a non-learning one. Last, the _Teach_ instrument, which measures the time teaching in 3 snapshots during the first 15 minutes of a video clip, has an overall distribution of Share of Time Teaching time that is similar to that from Stallings. At the same time, however, the adjustment in _Teach_ has a distribution that is somewhere between that of SDI and Stallings—with few high-values for share of time lost.

On net, Stallings and _Teach_ have similar distributions in terms of Share of Time Teaching—and both are different from SDI. But patterns change after adjusting for off-task students. The adjustment has different effects for Stallings versus Teach, and the distributions are no longer similar. On the other hand, the distributions for SDI and _Teach_ become similar after adjusting.

Teaching and learning time from the various sources is generally positively associated with all four dimensions measured in CLASS. While the magnitudes of the coefficients are not generally large (typically around 0.2 to almost 0.5), and they are consistently statistically significantly different from zero. The correlation coefficient is highest in the case of the “Classroom Organization” variable in CLASS (where it reaches 0.55 for the correlation with Share of Time Teaching from SDI, Panel B). Share of Time Teaching and Share of Time Teaching and Learning are modestly (albeit statistically significantly) correlated with the Instruction variable from _Teach_ (Panels C and E).

The correlations between the high-inference variables in CLASS and _Teach_ do not suggest a close mapping between any of these (Panel F). The variables are all positively correlated with one another (with coefficients that are statistically significantly different from zero), but small: the highest correlation

> 33 Figure 3 shows the distributions using all observations for each instrument.  Restricting the sample to observations for all three instruments yields very similar results (see Appendix 1 Figure 1).

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