perature Data
A way for the data of individuals measured at 20 and 25◦C to be combined is described
in Section 5.3. Now we wish to analyze the slope structure within the cyan curves and also within the red curves for this combined data set, with the goal of increased statistical power. Also the question of how do the slope structures between the cyan and red curves relate is analyzed. These questions will be investigated using the t-tests described in Section 5.1 and the visualization tool described in Section 5.2.
The results of the analysis of the adjusted data set, with both temperatures included, are shown in Figure 5.8. The adjusted data along with the mean curves for the cyan and red curves are shown in the bottom left of the figure. The upper left matrix displays the results for the t-tests of sets of line segments within the cyan curves. The lower right matrix displays results of the t-tests for sets of line segments within the red curves. While the upper right matrix displays the results of the t-tests between the cyan and red curves’ sets of line segments.
In viewing the upper left matrix, it can be seen that within the cyan curves the second and third sets of line segments have similar mean slopes. It also suggests that the last set of line segments has a similar mean slope to the second set of line segments. But due to the fact that the solid and dashed curves had different mean slopes for the last set of line segments after adjustment, this result is questionable. All other line segments have differing mean slopes. The mean curve of the cyan curves, in the bottom left corner, appears to have slopes which are equal after the first line segment. The difference in
Non−Extra Stage Data
Non−Extra Stage Data
Pvalues for Differences Of Slopes
1 0 0 0 0 1 0.535 0.096 0 0.535 1 0.019 0 0.096 0.019 1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Extra Stage Data
Non−Extra Stage Data
Pvalues for Differences Of Slopes
0.009 0 0 0 0 0.001 0.026 0 0 0.78 0 0.068 0 0 0.346 0.009 0 0 0 0.14 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Extra Stage Data
Extra Stage Data
Pvalues for Differences Of Slopes
1 0 0 0 0 0 1 0.001 0.075 0.009 0 0.001 1 0.048 0 0 0.075 0.048 1 0 0 0.009 0 0 1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 10 20 30 40 0 2 4 6 8 10
Mass vs Time View of Curves
Time
log(mass)
Figure 5.8: Bottom left displays adjusted data of 20 and 25◦ along with mean curves of cyan and red curves added. Matrix in top left shows results of t-tests for within cyan group. Matrix in bottom right shows results of t-tests for within red group. Matrix in top right displays results of t-test between cyan and red groups.
slopes of the third and fourth line segment does not appear visually, but does appear in the results of the t-test.
This matrix is similar to the separate 20 and 25◦ analysis in that the second and third
set of line segments have slopes which are not significantly different. Also the first set of line segments has a mean slope significantly different than the rest. The rest of the tests for the combined data seems to compromise between the two separate temperature analyses. For instance the second and fourth set of line segments had significantly dif- ferent mean slopes for 20◦ but not for 25◦, while the combined data has a p-value which
indicates borderline significance. Similar tests with differing results for 20 and 25◦, yield
test test results for the combined data set which are a compromise of these 2 results. This is expected since they have about an equal number of cyan curves for both temperatures.
Temperature 20◦ has 8 cyan curves while 25◦ has 12 cyan curves.
The matrix in the bottom right analyzes the slope structure within the red curves. The second and fourth sets of line segments, as well as the third and fourth may have similar mean slopes. The p-values for these comparisons are close to the border for significance, and therefore it is hard to distinguish if the mean slopes are similar or not. But the other p-values are much lower and therefore these mean slopes are much more similar than the others. The mean curve of the red curves, in the bottom left corner, reinforces these results. The middle three line segment slopes are visually much more similar to each other, than to the first and last. The beginning and end of this mean curve has a mean slope steeper than in the middle.
The combined data has mean slopes which are borderline significantly different for the third and fourth set of line segments. While the separate temperature analyses yield means slopes which were not significantly different for the third and fourth set of line segments. The rest of the matrix yields test results much similar to results of 20◦ than
25◦. This is expected since the 20◦ has 17 red curves while the 25◦ has only 11 red curves.
How the slope structures between groups relate is investigated by viewing the matrix in the upper right. This matrix suggests that the second, third and fourth line segments of the cyan curves have similar mean slopes to the last line segments of the red curves. But again due to the fact that the adjustment did not cause the last set of line segments of the solid and dashed lines to have equal mean slopes, this result is questionable. Also the mean slopes of the second and third sets of line segments of the cyan curves could be similar to the mean slope of the second set of line segments of the red curves. Although these p-values are borderline to be considered to have significantly differing slopes, the p-values are much larger than the rest of the p-values, except for the ones mentioned earlier. Again the slope structures of the mean curves can be investigated visually in the bottom left corner. The second line segment for the mean curve on the right appears to be parallel to the second and third line segments of the mean on the left.
For the between color analysis the statistical power seems to increase with the com- bined data set over the separate temperature analyses. Overall the p-values are lower except for the last column. Also the first sets of line segments have significantly different mean slopes for the combined data set, which was not true for either of the separate temperature analyses. Also the combined data results matrix has more p-values close to 0 than either of the other separate temperature analyses.