Quantitative Data

You already know about (non-numerical or categorical) qualitative data. But when you do have numbers, you have got quantitative data.

Quantitative Data (“numerical”)

Within quantitative data, there exists a sub-level of data types: discrete data or continuous data.

Discrete data is a whole number (integer) and it can’t be subdivided into smaller and smaller parts. Such as the number of eggs, number of wins, number of dogs (you can not have 3.2 dogs).

Continuous data continues on and on and on. These are data that can be broken into smaller and smaller units. The height of a person can be infinitely measured using precision equipment and does not have to stop at 1.82 meters. Usain Bolt’s 100m time is another example of continuous data, because it could be measured to the nanosecond and beyond.

Continuous data can be further categorized into a couple of types: interval and ratio.

Intervall

Interval scales are numeric scales in which we know both the order and the exact differences between the values. The classic example of an interval scale is Celsius temperature because the difference between each value is the same. For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.

Interval scales are nice because the realm of statistical analysis on these data sets opens up. For example, central tendency can be measured by mode, median or mean; standard deviation can also be calculated.

Here’s the problem with interval scales: they don’t have a “true zero.” For example, there is no such thing as “no temperature,” at least not with Celsius. Another example is the Gregorian calendar, which is commonly used for measuring dates. The intervals between consecutive dates are equal (one day), but there is no true “zero” date.

In the case of interval scales, zero does not mean the absence of value, but is actually another number used on the scale, like 0 degrees Celsius. Negative numbers also have meaning. Without a true zero, it is impossible to compute ratios. With interval data, we can add and subtract, but cannot multiply or divide.

Interval data allows for more parametric tests like t-tests and ANOVA. Histograms, box plots, and line charts are useful for interval data, showing distribution and trends

Ratio

Ratio scales are the ultimate nirvana when it comes to data measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero – which allows for a wide range of both descriptive and inferential statistics to be applied. At the risk of repeating the topic, everything before mentioned about interval data applies to ratio scales: plus ratio scales have a clear definition of zero. Good examples of ratio variables include height, weight, speed, duration and temperature in Kelvin.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided (ratios). Central tendency can be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales. This allows for the full range of statistical analysis, including parametric tests, and ratio statistics like rates or proportions. Similar to interval data, ratio data can be effectively visualized with histograms, box plots, line charts, and scatter plots.

Test what you have learned so far:

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