The Problem of Finding the Best Strategy for Progress Computation in
Adaptive Web Surveys
Thomas M. Prinz, Jan Pl
otner and Anja Vetterlein
Course Evaluation Service, Friedrich Schiller University Jena, Am Steiger 3 Haus 1, Jena, Germany
Progress Indicator, Prediction Strategy, Fit Measure, Web Survey, Interaction.
Web surveys are typical web information systems. As part of the interface of a survey, progress indicators inform
the participants about their state of completion. Different studies suggest that the progress indicator in web
surveys has an impact on the dropout and answer behaviour of the participants. Therefore, researchers should
invest some time in finding the right indicator for their surveys. But the calculation of the progress is sometimes
more difficult than expected, especially, in surveys with a lot of branches. Current related work explains the
progress computation in such cases based on different prediction strategies. However, the performance of these
strategies varies for different surveys. In this position paper, we explain how to compare those strategies. The
chosen Root Mean Square Error measure allows to select the best strategy. But experiments with two large
real-world surveys show that there is no single best strategy for all of them. It highly depends on the structure of
the surveys and sometimes even the best known strategy produces bad predictions. Dedicated research should
find solutions for these cases.
Web surveys present items (questions) in a paper-like
format with various input fields. The survey itself
interacts with a server application and transfers the
inserted answers of the participants to it. In other
words, web surveys are web information systems.
The interface of a web survey is intuitive and
straight-forward in the common case. Besides the
input fields for answers, web surveys consist usually
of buttons to precede and sometimes also to recede in
the survey. Headers inform the participant about the
context of the survey and usually Progress Indicators
(PIs) inform the participants about the state of com-
pletion. This paper focuses on the PIs as part of the
Typically, the PI displays the progress in percent-
age between
. Unlike PIs of usual tasks in
general software, participants of web surveys have to
focus on the task (the survey), can influence the PI, and
do not necessarily have an interest on the result (Villar
et al., 2013). Therefore, PIs in web surveys are differ-
ent from those of other software (Villar et al., 2013),
e. g., for machine learning (Luo, 2017) and database
queries (Li et al., 2012).
Participants in web surveys prefer to have a PI
(Myers, 1983; Villar et al., 2013) to be aware of their
progress. However, the computation of the progress
can be difficult in case of surveys with adaptivity
(branches). (Prinz et al., 2019) propose an equation to
compute the progress in adaptive surveys. The equa-
tion is based on the number of remaining items (ques-
tions) at each point of time. This number of remaining
items depends on a chosen prediction strategy. Such
a strategy tries to predict the number of remaining
items for each page since the participants may take
different paths in the survey with different numbers of
remaining items. For example, two known prediction
strategies are: 1) take the minimum or 2) maximum
number of remaining items (Kaczmirek, 2009). How-
ever, (Prinz et al., 2019) suspects that it depends on
the structure of the survey which prediction strategy is
the best. Furthermore, the comparison of the quality
of the strategies seems to be not trivial.
One goal of this paper is to have a measure to
select that prediction strategy, which guesses the true
number of remaining items and, therefore, the true
progress as well as possible. We support the idea of
displaying the true progress since research in Human-
Computer Interaction (HCI) reveals high probable side-
effects of PIs on the answer and dropout behaviour
of participants (Villar et al., 2013). Especially the
progress speed (the rate in which the PI increases)
seems to influence the decision whether a participant
Prinz, T., Plötner, J. and Vetterlein, A.
The Problem of Finding the Best Strategy for Progress Computation in Adaptive Web Surveys.
DOI: 10.5220/0008345403070313
In Proceedings of the 15th International Conference on Web Information Systems and Technologies (WEBIST 2019), pages 307-313
ISBN: 978-989-758-386-5
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
finishes a long survey (Myers, 1985; Villar et al., 2013).
PIs increasing faster at the start and slower at the end
seem to encourage the participant to finish the survey.
On the contrary, if a PI is slow at the beginning and gets
faster at the end seems to discourage and causes higher
dropout rates (Conrad et al., 2003; Matzat et al., 2009;
Conrad et al., 2010). A meta-analysis of PI speeds by
(Villar et al., 2013) supports these observations.
The long-term effects of different PI speeds are not
researched. Even though more participants complete
a survey by using a fast-to-slow increase of the PI, if
the participants become aware of the varying PI speed,
it might decrease their willingness to participate in
future surveys by the survey provider. Instead, PIs
which try to display the true progress are honest to the
participants and should reduce side-effects of PIs.
In this position paper, we argue that the Root Mean
Square Error (RMSE) is a useful measure to describe
the quality of prediction strategies for progress com-
putation. This measure allows to compare uses of
strategies and to choose the “best” one. Researchers
conducting surveys can use the RMSE to determine
the best known strategy for their surveys and can give
the participant a PI, which represents the true progress
as well as possible. Furthermore, this paper shows
that the yet known trivial prediction strategies lead to
bad predictions in some cases. Further research should
find solutions for these cases.
The paper has the following structure: At first, it
explains in Section 2 how we can compute the progress
in adaptive surveys and how we can apply the predic-
tion strategies. Based on this computation, the pa-
per presents four measures for the determination of
the quality of a prediction strategy in Section 3 and
shows their application in Section 4. Section 4 argues
further which measure is most suitable and explains
some disadvantages with current prediction strategies.
Section 5 ends the paper with a brief discussion and
Although a lot of studies consider the differences in PI
speeds, the computation of an accurate progress in web
surveys (especially in surveys with high adaptivity) is
not in the research focus. The thesis of (Kaczmirek,
2009) and the work of (Prinz et al., 2019) based on
it are the only available work to the best knowledge
of the authors, which try to answer how to calculate
the progress in web surveys with adaptivity. The lack
of knowledge about the “path” a participant takes in a
survey, is the main problem in progress computations.
Prinz et al. propose an algorithm, which supports
Figure 1: A simple questionnaire graph.
different prediction strategies. By applying one of
several strategies it is possible to approximate the true
progress as well as possible.
The approach with different prediction strategies
is based on an abstract survey model called the ques-
tionnaire graph (in short Q-graph). The Q-graph de-
scribes the structure of questionnaires. It is an acyclic,
connected digraph
Q = (P, E)
with a set of pages
P = P(Q)
and a set of edges
E = E(Q)
, which con-
nect the pages. The Q-graph
has exactly one page
without any incoming edge (the start page) and exact
one page without any outgoing edge (the end page).
A page
P P(Q)
is a finite set
of items
,. ..
. For this reason,
is the number of items
on page
. For reasons of simplicity, each item is
assumed to be unique. Figure 1 illustrates a simple
The edges build paths throughout the Q-graph. A
path is a sequence
W = (P
,. .. ,P
m 0
, of pages,
,. .. ,P
. For this sequence, there is an edge
for each two pages appearing consecutively:
0 i <
m: (P
) E(Q).
(Prinz et al., 2019) propose a general equation to
compute the progress for arbitrary Q-graphs. The equa-
tion is recursive and returns values between
(i. e., 0 and 100%):
ρ(P) = ρ(P
) + |P|
1 ρ(P
The equation contains the following parts:
scribes the progress at the current page
. The com-
putation of the current progress needs the progress
of the previous page
. If the current page
is the first page of the Q-graph, then it is assumed
. The equation adds the impact on
the progress of the current page,
, to the
progress of the previous page.
is the number of
items on the current page. The impact of a single item
on the progress on the current page is
. It
contains the remaining progress (
1 ρ(P
) and the
number of remaining items (
). The usage of the
remaining progress in the equation allows the progress
to adopt to the number of remaining items. For exam-
ple, if a participant follows a branch, which reduces
the number of remaining items, then the impact of
each item increases, accelerating the growth of the PI.
WEBIST 2019 - 15th International Conference on Web Information Systems and Technologies
Input: A Q-graph Q and a selection operator t.
Output: For each P P(Q) the remaining items rem(P).
Set rem(P) = 0 for each P P(Q)
worklist queue
while worklist 6=
0 do
P dequeue(worklist)
directSucc {succ : (P, Succ) E(Q)}
if directSucc visited then
if directSucc =
0 then
rem(P) |P|
else if |directSucc|= |{Succ}| = 1 then
rem(P) |P|+ rem(Succ)
rem(P) |P|+
visited visited {P}
Figure 2: The general algorithm for computing the number
of remaining items for arbitrary prediction strategies (taken
from (Prinz et al., 2019)).
Otherwise, if the number of remaining items increases,
the impact with each item decreases, decelerating the
growth of the PI.
At the beginning of an adaptive survey, the path,
a participant takes, is unknown which makes it neces-
sary to predict the number of remaining items
But different prediction strategies are possible making
the computation of the progress a challenge. (Prinz
et al., 2019) defined a general algorithm for comput-
ing the number of remaining items
for each
page for arbitrary prediction strategies. A property of
the algorithm is the usage of a selection operator
representing these strategies. The algorithm receives
the selection operator as input making the algorithm
independent from the operator. Figure 2 shows the
algorithm. In this paper, we focus on the description
of the selection operator. For a more general overview,
see (Prinz et al., 2019).
There are exactly three situations during the com-
putation of the remaining items for a page
. Either
has 1) no successor, 2) exactly one direct successor,
or 3) more than one direct successor. The number
of remaining items for the first both situations is the
sum of the number of items on
, and the number
of remaining items
of the direct successor
in the case of situation 1)). In situation
3), different numbers of remaining items may reach
via the direct successors
.. .
n 2
The selection operator receives all those numbers as
),. .. ,rem(Succ
, and produces
a single prediction for
. The algorithm contains
these situations in the inner if-then-else-structure.
Typical examples of selection operators are the
minimum and maximum functions. Taking the mini-
mum, the number of remaining items is the smallest
number of items. The progress is fast at the beginning
and becomes slower if the participant takes a path con-
taining more items than the operator has detected. For
the maximum, it is vice versa. It represents the largest
number of items.
Different prediction strategies usually result in differ-
ent predicted progresses. Since a survey needs a single
strategy, which provides the best prediction, we need
a measure to compare the precision of such strategies.
A PI in a survey should commonly represent the
true progress as well as possible. The computation
of the true progress needs the exact number of re-
maining items. However, a survey engine knows this
exact number only after the participant is finished. In
other words, only after a participant completes a path
W = (P
,. .. ,P
n 1
, then the computation knows
the exact number of remaining items on each page
,. .. ,P
and can compute the true progress ρ
A strategy within a set of prediction strategies
,. .. ,t
n 1
, is the best one if it minimizes
the discrepancy between the predicted and the true
progress best. Many measures regarding prediction
accuracy are proposed in literature and a lot of recom-
mendations explain in which situations a specific mea-
sure should be used. (Hyndman and Koehler, 2006)
consider different measures of prediction accuracy in
detail and provide a good overview about them. All
the measures have in common that they are based on
the difference between the prediction and the actual
measured value (in our specific case, the true progress).
Our basic idea is that we set the true and pre-
dicted/displayed progress in relation. That means,
we have a value pair
of the true and
displayed progress for each page
on a path a par-
ticipant has visited. The pair
can be
read as “on page
the true progress was
the progress
was displayed”. If the predicted
progress differs from the true progress, it results in an
e(P) = ρ(P)ρ
. All the pairs
can be computed for a prediction strategy and it results
in a set
, which contains all of these pairs. For the
comparison of different strategies
.. .
n 2
there is such a set for each strategy: M
, .. ., M
Notice that
have percentage scales. That
means, measures based on percentage errors are ap-
plicable. (Hyndman and Koehler, 2006) mention four
typical measures of percentage errors:
1. Mean Absolute Error (MAE), |e|
The Problem of Finding the Best Strategy for Progress Computation in Adaptive Web Surveys
2. Median Absolute Error (MdAE), median(|e|)
3. Root Mean Square Error (RMSE),
Root Median Square Error (RMdSE),
Applying one of the measures produces a value
for each strategy
1 i n
. Since the true progress
is always the same for each strategy and all values are
on the percentage scale, statistics allows us to compare
the different values. The strategy with the lowest value
is the best one of the considered strategies.
A value of
is perfect for all measures, it means
that the error between the true and predicted progress
is zero. The RMSE and RMdSE have the disadvan-
tage that they are infinite, undefined, or skewed if
all observed values are
or near to
(Hyndman and
Koehler, 2006). Since the true progress has values in
the range from
, this disadvantage does not
affect them.
The approach relies on the knowledge of the true
progress and, therefore, on empirical data. Unfortu-
nately, as with any empricial study, these data is usu-
ally not available before the survey starts. To overcome
this problem, data can be generated by pilot studies,
simulations, or path-explorations of the survey for ex-
ample. Pilot studies refer to conducting the survey
with a subset of the population, whereas in simulations
virtual participants answer the questionnaire. In a path-
exploration, an algorithm computes all (or most) paths
of the survey and computes sample progresses for each
path. But adaptive surveys may have a (exponential)
large number of such paths. Furthermore, all three
possibilities have in common that they should repre-
sent a “realistic” usage of the different paths. Different
weights exist for the paths and influence the measure.
The researcher should be aware of this.
In our department, we conduct large surveys with hun-
dreds of variables and items and many adaptive paths.
The survey engine, that we use, stores the paths on
which the participants “walk” through the surveys. For
each participant, it is possible to compute the true num-
ber of remaining items for each visited page. Besides
the true progress, we can also compute the predicted
progress for different prediction strategies in retrospect
with Equation 1 and the algorithm of Figure 2. As a
result, we get data sets with the true and displayed
progresses for each strategy for each participant. With
these it is possible to determine the most suitable mea-
sure and the best strategy.
4.1 Experimental Settings
We took two of our surveys, survey A and survey B.
Table 1 describes the structure of the surveys based
on empirical data. In the table,
refers to the
number of pages with branches,
is the number of
pages within a path, and
refers to the number of
items a participant has seen. Both surveys have similar
characteristics except for
. For
survey A we have more available data sets, whereas
survey B has much more branches.
For both surveys, we produced data sets for three
different prediction strategies: minimum (min), mean,
and maximum (max). If a page has more than two
direct successor pages, the minimum strategy takes the
smallest number of remaining items. The maximum
strategy takes the largest number of remaining items
in such a case, whereas the mean strategy computes
the mean number. At this place, it is important that the
mean represents not the empirical mean of items on
all empirical paths. It represents the selection operator
mean used in the general algorithm. The expected
remaining items on the start page vary for both surveys
(cf. Table 1,
) and are higher for survey
B except for the min approach, which is very small
with a value of
. The values in parentheses represent
adjustments on the surveys explained in the following.
4.2 Lessons Learned
Screening paths are paths at the start of a survey in
which a participant receives a few key questions to
determine if they are part of the specific target popu-
lation. Depending on their answers, the survey either
continues to the main part or ends quickly. Therefore,
there is an exit path to the end without many items.
The first lesson we learned was that the inclusion of
screening paths in the progress calculation usually pro-
duces bad predictions. By taking the min strategy, the
exit path has the fewest remaining items and, there-
fore, decreases the number of remaining items on all
paths at the beginning of the survey (cf.
Table 1). In survey B, this leads to progresses near
after passing the page where the screening path
ends. For the strategies mean and max, the screening
path does not have a great impact.
Adaptive page chains are subpaths with many adap-
tive pages, however, each participant only sees a small
number of them. In survey B, there are a lot of such
pages, which contain items about special topics. In
general, each participant has only seen one or two of
these approx. 30 pages. For min, such chains dis-
appear which skews the results as most participants
see at least one page. The max strategy includes each
WEBIST 2019 - 15th International Conference on Web Information Systems and Technologies
Table 1: Structure and important empirical properties of survey A and survey B.
Survey A Survey B Survey A Survey B
1041 193 N
11 38 min 4 6
|Path| mean 246.70 290.97
min 2 2 max 339 377
mean 16.34 18.49 rem(start)
max 25 23 t = min 46 (167) 7 (258)
Var 48.56 24.63 t = mean 115 (241) 254 (495)
t = max 345 (288) 706 (700)
number of participants,
number of branching pages in Q-graph,
|Path| =
empirical length of
empirical number of items seen,
rem(start) =
remaining items on the start page (values in parentheses
are adjustments explained in the text)
adaptive page resulting in a high number of remaining
items. The mean strategy smooths the high number
of remaining items, however, usually only by half. In
Table 1,
indicates long adaptive page chains
with a value of
in survey B instead of
in A. The
second lesson we learned was that such chains of adap-
tive pages produce bad predictions too.
As a consequence, we adjusted our experiments
with the surveys A and B by removing the screening
paths from the progress computation. Otherwise, it
is meaningless to compare the results of the different
strategies. The adjustments result in different numbers
of remaining items for each strategy (see
parentheses in Table 1). We left the chains of adaptive
pages as they contain important items.
4.3 Experimental Results
Figure 3 shows the results of our experiments. The
axis describes the true and the
axis the displayed
(predicted) progress for each strategy. The black line
illustrates a perfect prediction strategy and the true
progress, respectively. An observation is that the min
approach results in overestimations of the progress,
whereas the max approach results in underestimations.
For survey A, mean has values above and below the
true progress line. For survey B, the values of mean are
all below the line because of the mentioned adaptive
page chains.
Figure 3 contains the values for the four mea-
sures MAE, MdAE, RMSE, and RMdSE. Actually,
the MdAE and RMdSE result in nearly equivalent val-
ues. The Appendix explains why.
For survey A, the mean strategy has the lowest
MAE of
and RMSE of
, but the max strategy
has the lowest MdAE and RMdSE with both
The mean and max strategy seem to estimate the true
progress best. The min approach is the worst approach.
The distribution of the points supports the result.
For survey B, the strategies perform differently:
the min approach is the best and the max strategy is the
worst one for all four measures. However as a whole,
all strategies perform worse in survey B. There is no
strategy which predicts the true progress well. Even
though min is the best strategy of the three, a visual
inspection of the predicted values in Figure 3 shows
that for many participants the displayed progress is
even though they still have around
of the survey to go. A reason for this behaviour are
the adaptive page chains corresponding with a high
number of branching pages (cf. Table 1,
The poor fit is supported by higher values instead of
those for survey A. The worse fitting for survey B
could also be a result of the small number of available
In our application context, high errors should be
penalized more than smaller errors since higher errors
have a stronger impact on the overall progress calcu-
lation and can lead to noticeable deviations from the
true progress whereas small errors should be almost
invisible to the participant. The RMSE is, therefore, a
good choice, because it squares the error giving large
errors more weight. Like Figure 3 shows, the RMSE is
always the highest. Actually, the value of the RMdSE
is always close to the MdAE as mentioned before. The
squaring of the error in the RMdSE has not a great
effect on the resulting value, as also shown in the Ap-
For survey A, the mean (MAE and RMSE) as well
as the max strategy (MdAE and RMdSE) have small
values as mentioned before. Figure 3 shows that the
max strategy has more outliers for survey A than the
mean strategy. Following the above argumentation, the
mean strategy should be used since the outliers may
lead to noticeable deviations. This is supported by a
higher RMSE.
Altogether, we recommend to use the RMSE for
comparing different prediction strategies for PIs. It is
most sensitive to high deviations.
Figure 4 shows the error distribution for all strate-
gies in both surveys. For survey A, the mean and max
strategies result in errors near zero with less variance
The Problem of Finding the Best Strategy for Progress Computation in Adaptive Web Surveys