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Types of Data and Measurement Scales
A dolls house
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Types of Data We often want to classify variables and data sets according to their type of data so that we can use an appropriate display or apply an appropriate statistical analysis to the data. The subtypes of data become increasingly orderable starting from having no order to a precise, multiplicative scale. Categorical Data (Qualitative Data) Categorical data and variables consider qualities. The qualities are worded descriptions that classify the data collected into categories. Categorical variables should list the categories it is using if possible (i., there is not an infinite, or near infinite set of possibilities). Categories can be written with a numerical shorthand such as 1 = Red; 3000 = Melbourne CBD; 5550 4485 = phone number or can group numbers into categories such as less than 250, 250–500, more than 500. Nominal Categorical Data Nominal, from the Latin nominalis, meaning "pertaining to a name or names". A nominal variable's categories have no unique way to be ordered or ranked. Personal opinions on the categories are not considered to be a unique order as it changes from person to person. Examples Favourite ___, type of ___, gender, race, eye colour, postcode, phone number, bank account number Ordinal Categorical Data Ordinal, from the Late Latin ordinalis, meaning "showing order, denoting an order of succession". An ordinal variable's categories have a unique, natural way to be ordered or ranked. That is, the categories are described with ordered language such as disagree/no opinion/agree, below ____/equal to/above ____, low/medium/high, dislike/neutral/like, 1st/2nd/3rd, unsatisfied/neutral/satisfied. Examples Socio economic status (low income, middle income, high income), education level (year 10 pass, VCE, TAFE certificate, bachelor, masters, doctorate), rating (despise, tolerate, neutral, enjoy, love) Numerical Data (Quantitative Data) Numerical data and variables consider quantities. The quantities are the number of a particular thing or given with the unit that variable is measured in. Discrete Numerical Data Discrete, from the Latin discretus, meaning "separate, distinct from others". A discrete variable uses discrete, indivisible units that can be counted. That is, we cannot further divide the units any more than what we define. While the values are generally whole numbers, they can be decimals/fractions if there is a specific set it can be such as halves or quarters. Examples Number of _______, shoe size, monetary values (costs, sales) Continuous Numerical Data Continuous, from the Latin continuus, meaning "joining; following on after another". A continuous variable uses continuous, infinitely divisible units that are measured along a scale. Examples Height, weight, length, capacity, temperature, rates
Types of Data and Measurement Scales
Types of Measurement Scales A continuous variable may be measured with an interval scale or a ratio scale. Interval Scale Interval, from the Latin intervallum, meaning "a space between". An interval scale can order and show the difference between values but cannot describe the number of times one value is greater or lesser than another. This is because zero on an interval scale does not mean the absence of what it is measuring, it is an arbitrary choice of zero. If there are different units that can measure the same thing but they do not share a common zero, they will be on an interval scale. Values on an interval scale can be meaningfully added and subtracted but not multiplied or divided. Example Temperature in Celsius or Fahrenheit: 30 °C is not three times as hot as 10 °C but it is 20 °C hotter. pH scale: a pH level of 3 is not twice as acidic (or half as basic) as a pH of 6. Ratio Scale Ratio, from the Latin ratio, meaning in a mathematical sense "relation between two similar magnitudes in respect to quantity, measured by the number of times one contains the other". A ratio scale can order and show the difference between values and describe the number of times one value is greater or lesser than another. This is because zero on a ratio scale is precisely defined as the absence of what is being measured. Values on a ratio scale can be meaningfully added, subtracted, multiplied, and divided. Examples Height, weight, length, capacity, temperature in Kelvins (0° K is the absence of heat), duration (elapsed time), rates Flow Chart for Types of Data and Measurement Scales
Types of Data and Measurement Scales
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