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interpretation of this scale by a user is that the distances between all the data
points along the scale are equal. A question to ask yourself when deciding
whether you can treat some data like this as interval or not is whether a point
halfway between any two of the defined data points makes sense. If it does, then
it makes sense to analyze the data as interval data.
2.2.4 Ratio Data
Ratio data are the same as interval data but with the addition of an absolute
zero. This means that the zero value is not arbitrary, as with interval data, but has
some inherent meaning. With ratio data, differences between the measurements
are interpreted as a ratio. Examples of ratio data are age, height, and weight. In
each example, zero indicates the absence of age, height, or weight.
In user experience, the most obvious example of ratio data is time. Zero seconds
left to complete a task would mean no time or duration remaining. Ratio data let
you say something is twice as fast or half as slow as something else. For example, you
could say that one user is twice as fast as another user in completing a task.
There aren't many additional analyses you can do with ratio data compared
to interval data in usability. One exception is calculating a geometric mean,
which might be useful in measuring differences in time. Aside from that cal-
culation, there really aren't many differences between interval and ratio data in
terms of the available statistics.
2.3 DESCRIPTIVE STATISTICS
Descriptive statistics are essential for any interval or ratio-level data. Descriptive
statistics, as the name implies, describe the data, without saying anything about
the larger population. Inferential statistics let you draw some conclusions or
infer something about a larger population above and beyond your sample.
The most common types of descriptive statistics are measures of central ten-
dency (such as the mean), measures of variability (such as the standard devia-
tion), and confidence intervals, which pull the other two together. The following
sections use the sample data shown in Table 2.1 to illustrate these statistics.
These data represent the time, in seconds, that it took each of 12 participants in
a usability study to complete the same task.
2.3.1 Measures of Central Tendency
Measures of central tendency are simply a way of choosing a single number that
is in some way representative of a set of numbers. The three most common mea-
sures of central tendency are the mean, median, and mode.
The mean is what most people think of as the average: the sum of all values
divided by how many values there are. The mean of most user experience met-
rics is extremely useful and is probably the most common statistic cited in a
usability report. For the data in Table 2.1 , the mean is 35.1 seconds.
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