Fig 1.
Pie chart representing survey of methods used to analyze PBR study data.
Methods represented in shades of blue are variations of traditional ANOVA.
Fig 2.
Eight functions that share an overall mean of 70 across their domain.
Table 1.
Sums of squares and degrees of freedom for repeated measures ANOVA.
Table 2.
Distributions for random variation in amplitude, period, and phase for each level of the factor.
Table 3.
Average amplitude, period, and phase for the mean swim pattern functions.
Fig 3.
The left side shows swim speed over time of twenty fish simulated under level 1 of the factor (top), level 2 of the factor (middle), and level 3 of the factor (bottom), with the true average function overlaid in black. These are treated as the observed data. The right side shows the corresponding smoothed functions of swim speed.
Fig 4.
Boxplots of the averages of the functions simulated under three levels of a factor.
Table 4.
Univariate ANOVA results.
Table 5.
Repeated measures ANOVA results.
Fig 5.
One-way FANOVA Fobs(t) statistic based on the smoothed dataset.
The red dashed line indicates the 95% pointwise percentile calculated from the permutations.
Fig 6.
Estimated overall mean effect (top) and factor effect (bottom). Dashed lines are 95% pointwise confidence intervals formed using 1000 bootstrap replicates.
Fig 7.
Functional post hoc contrasts for the levels.
The dashed line is the pointwise 98.33% confidence interval using 1000 bootstrap replicates. The asterisk on the right indicates significance of the FFT test for the factor effect.
Fig 8.
Pointwise observations of swim speed by concentration of 1-heptanol.
The color of the background denotes the acclimation period (dark gray) and the alternating light (white) and dark (light gray) ten-minute periods.
Fig 9.
Boxplots of the averages of the functions for each concentration.
Circles outside of the fences of the boxplots represent potential outliers.
Table 6.
Univariate ANOVA results.
Table 7.
Repeated measures ANOVA results.
Fig 10.
Raw observations of swim speed (top), smoothed observations of swim speed (center), and the functional averages of the smoothed swim speed curves for each concentration level (bottom).
Fig 11.
Estimated overall mean effect (top) and concentration effect (bottom). Dashed lines are 95% pointwise confidence intervals formed using 1000 bootstrap replicates.
Fig 12.
One-way FANOVA Fobs(t) statistic applied to the smoothed dataset.
The red dashed line indicates the 95% pointwise percentile calculated from the permutations.
Fig 13.
Histogram of 10,000 FFT permutations.
The red dashed line indicates the 95th percentile of the permutations.
Fig 14.
Functional post hoc contrasts for the concentration levels.
The dashed line is the pointwise 95% confidence interval using 1000 bootstrap replicates. The asterisks on the right of the plots indicate significance of the FFT test for the concentration effect across the entire domain, and the asterisks inside the plots indicate significance within the corresponding brightness period.
Table 8.
The FFT test results for the main effects and post hoc tests for the entire domain and each of the light/dark regions.
For each region name, the letter refers to the brightness condition (light/dark), and the number corresponds to whether the region is the first or second light/dark period. In the “Decision” column, FTR means “fail to reject.”
Fig 15.
The first derivative of the smoothed swim speed curves (top), and the functional averages of the first derivative of the smoothed swim speed curves for each concentration level (bottom).
Fig 16.
Functional Fobs(t) statistic of the acceleration curves, where the red dashed line indicates the 95% pointwise percentile calculated from the permutations.
Regions of interest for the startle response are represented in light pink shading for dark to light transitions and dark pink shading for light to dark transitions.
Fig 17.
Functional post hoc contrasts for the acceleration curves for the concentration levels.
The dashed line is the pointwise 98.75% confidence interval using 1000 bootstrap replicates. Regions of interest for the startle response are represented in light pink shading for dark to light transitions and dark pink shading for light to dark transitions. The asterisks indicate significance of the FFT test for the concentration effect in the corresponding region.
Table 9.
The FFT test results for the main effects and post hoc tests for the acceleration curves across the entire domain and the first three minutes of each of the light/dark regions.
In the “Decision” column, FTR means “fail to reject.”