In a report of a study of participants' speed of texting, the researchers say they found a difference between three means, with faster speed as a function of increased age. No difference, however, was found between the means as a function of gender. Assuming that the above data reflect a highly skewed interval variable, what conclusion about the study could be drawn and about the population participating in this experiment?
In statistics, the mean is the value calculated by adding all data together and dividing by the total number of data entries (1+5+16/3=mean). It is the arithmetic mean and it yields a value that may or may not actually be in the data set. The mean is useful for determining overall numerical value on a related set of data points but is meaningless in determining worth, substance, value or meaningfulness of the objects, persons, groups contributing the data points in the data set. Mode is the preferred statistical operations when determining worth, substance, value or meaningfulness. Median is the measure of the exact mid-point of the data. Mode is the measure of what value occurs most often. To illustrate, intelligence tests of an ethnic group may produce a mode (most often occurring measure) of 136 while the median (exact mid-point may be 120 and the mean may be 110 because of more extreme low data points than extreme high data points. The statistic that gives the most relevant information about worth, substance, value or meaningfulness relating to the intelligence of the ethnic group is mode, that which occurs most often.
An interval variable is a study variable that resembles an ordinal variable but with the distinction that the gaps between data points are meaningful and can therefore be used interpretively. The most commonly used illustration of meaningful and interpretive variable intervals is temperature variables. The difference between 10 and 20 degrees carries the magnitude as the difference between 75 and 85 degrees and can be used interpretively to say that the intervals have the same importance throughout the scale. Conversely, data ranked ordinally does not have meaningfulness between data points and cannot be used interpretively because, for example, the ordinal data points of coming in 3rd and 4th in a race bear no relation on magnitude between coming in 16th and 17th (there may a 2 minute difference between 3rd and 4th while there may be a 27 minute difference between 16th and 17th).
Skewed distributions are asymmetrical distributions. Symmetrical distributions have equal data spreads above and below the middle data point of the sample. Asymmetrical distributions are those in which there is a difference between the spread of data points with more distributed above or below. When the distribution of data points produces a difference between mean, median and mode values, with mean less than median and median less that mode (mean < median < mode), then the interval variable distribution is negatively skewed to the left. Conversely, when mean is greater than median and median is greater than mode (mean > median > mode), then the interval variable distribution is positively skewed to the right [left and right refer to the visual representation of the data on a graph].
If, for the sake of discussion, the sample discussed in speed texting is highly negatively skewed leftward with mean < median < mode, then, without any data at hand and with knowing only that increased speed in texting correlates directly to a function of increased age, though there is no correlation to a function of gender difference, and with the distribution graph highly negatively skewed to the left with the arithmetic mean being less than the mid-point of the data (median) and with the mid-point being less than the most frequently occurring data points, or mode, it might be possible to conclude that the random selection of ages yielded more young people than older ones and that the random selection of genders yielded an approximately equal number of males and females.
"Types of Variables." United Nations Educational, Scientific and Cultural Organization, UNESCO.