Time Intensity tests are designed to measure the temporal evolution of a single attribute.

Results are plotted as time-intensity curves and key parameters of the curves are calculated. Results can be averaged per panellist or per product.

- Time_Intensity.xlsx
- The dataset should have a single attribute (Intensity) with datatype TDS.
- Each row in the dataset has a start and a stop time, the intensity is constant between start and stop times.

Time - intensity (T-I) studies address the relationship between the onset, intensity, and duration of perception of a sensory attribute. In practice, the time and intensity are initially set at zero, subjects are exposed to a stimulus, and the perceived intensity is then recorded with the corresponding time coordinates until the intensity returns to zero again, or the allocated time for the assessment has ended. These relationships are commonly illustrated in the form of Time Intensity curves of perceived intensity versus time. [from Lui and MacFie paper]

The key parameters of the time-intensity curves are calculated in the analysis and are presented in the results.

The time-intensity curve can be divided into four distinct
phases. In practice a curve may not
conform strictly to these phases:

- Reaction phase: before the first positive value of the
perceived intensity is registered, this happens at T-start. This is the period
required for the panellist to perceive and react to the stimulus.
- Ascending phase: the perceived intensity increases from
zero to maximum. Time from T-start to T-max.
- Stationary phase:
maximum intensity maintained for some interval. In some cases, this phase
degenerates to a single point. Time from T-max to T-dec.
- Descending phase:
from maximum intensity to end of perception. The perceived intensity decreases
to zero. Time from T-dec to T-end.

When the curves are averaged, across the Panel or across Panellists, and the Standardize option is not selected, the raw curves are simply averaged - so the average curve is the average intensity taken at each time point.

Where the curves need to be averaged, and the __Standardize__ option is selected, the
method in the 1990 Liu and MacFie paper ‘Methods for averaging time-intensity
curves’ are followed.

The standardization method works as follows:

- The average values of the parameters I-max
(maximum intensity), T-start, T-max, T-dec and T-end, of all the individual
scores to be averaged, are first calculated. The average values are arithmetic
means.
- All curves are normalized in the intensity
direction, to have the same level of maximum intensity. The values of I for
each curve j are transformed to I’ = (I-max/I-max-j) * I
- Curves are normalized in the t direction to have
the same T-start, T-max, T-dec and T-end as follows:
- T’ = ((T-max – T-start)/(T-max-j
– T-start-j))*(T-T-start-j) + T-start when T-start-j <= T <= T-max-j
- T’ = (T-end – T-dec)/(T-end-j –T-dec-j)*(T-T-dec-j) + T-dec when T-dec-j
<= T <= T-end-j
- To average the values of I, the ascending and descending phases of each curve are both divided into equal time intervals, in this case for each integer value of T. For each T, the unique corresponding I is calculated.

If the __Correction__ option is selected, then outliers
and anomalies are recoded. And anomaly is defined as, for example, an increase
during the decreasing phase. If an intensity point detected at time (t+1) named as I_{t+1} is detected as larger
than I_{t} and *I _{t+1}* is larger than

**Results by****:**Should the curves by displayed by- Panel - giving one curve per product.
- Panellist - giving one curve per panellist per
product.
- Replicates - giving results for each replicate
for each panellist and each product (i.e. no averaging)
**Correction:**Where there is what the software assesses to be an anomaly in the curve e.g. a decrease during the increasing phase or vice versa, should the software correct this Yes/No.**Standardize:**Curves are averaged following the method in Lui and MacFie Yes/No.**Number of decimals:**Required number of decimals for values given in the results.

Results are returned in two tabs.

- A table of the intensity values per time point. This is returned for the by Panel and by Panellist options, and the tables are of the averaged values. If standardize = Yes and / or Correction = Yes, the table contains standardized and / or corrected data. If by Replicates is selected and Correction = Yes, then the table of corrected intensity values per time point is returned in the export, but not displayed in the results.
- Plots of the TI values in the table are displayed if by Panel or by Panellist is selected. If by Replicates is selected individual curves are not returned.

**Max. Intensity:**Maximum intensity over the duration of the measurements.**T****(First Max):**First time that the maximum intensity was reached.**T (Last Max):**Time that the maximum intensity ended.**Max. Duration:**Length of time that the intensity is at a maximum.**Area (Total):**The total area under the time intensity curve.**Area (Max):**The area under the time intensity curve for the portion of the curve when the intensity is at a maximum.**Area (90% Max):**The area under the time intensity curve for the portion of the curve when the intensity is at or above 90% of the maximum.**T (First 50% Max):**First time that 50% of the maximum intensity is reached.**T (Last 50% Max):**Last time that 50% of the maximum intensity is recorded.**T Start (90% Max):**First time that 90% of the maximum intensity is reached.**T Stop (90% Max):**Last time that 90% of the maximum intensity is recorded.**Duration (90% Max):**Length of time that the intensity is at or above 90% of the maximum.**Asc. Start:**Time the intensity curve starts to ascend.**Asc. Stop:**Time the intensity curve stops ascending (should be when the maximum is reached on a standard curve).**Asc. Duration:**Length of time that the intensity is increasing (difference between Asc. Stop and Asc. Start).**Asc. Area:**Area under the time intensity curve for the ascending portion of the curve.**Asc. Slope:**Slope of the ascending portion of the time intensity curve. This is calculated by fitting a linear model to the points in the ascending portion of the curve. If there are only 2 or fewer points in the ascending portion of the curve then the slope is not calculated (and NA is returned).**Desc. Start:**Time the intensity curve starts to descend.**Desc. Stop:**Time the intensity curve stops descending (should be the last time a non-zero intensity is recorded).**Desc. Duration:**Length of time that the intensity is decreasing (difference between Desc. Start and Desc. Stop).**Desc. Area:**Area under the time intensity curve for the descending portion of the curve.**Desc. Slope:**Slope of the descending portion of the time intensity curve. Calculated as for the ascending slope.

When the “By Replica” option is selected, users can also use the Results table to run ANOVA, for example, on the parameters. The Excel export file of the results table needs to be imported as a dataset in EyeOpenR to run an ANOVA. In order to make the table compatible with EyeOpenR Row 1 (with the table title) and Column A (with the row numbers) needs to be removed so that the Assessor column starts in cell A1.

- The time intensity code is written from scratch and does not use any R packages.

Y.H. Liu and H.J.H MacFie, methods for averaging time-intensity curves. Chemical Senses, Vol 15, pp471-484, 1990.

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