We identify the measurement levels, nominal, ordinal, interval, and ratio. In this video I'll look at how you can interpret variables with different measurement levels. I'll also discuss other ways to classify variables according to their measurement characteristics. Categorical variables distinguish either unordered or ordered categories. A special type of categorical variable is a binary or a dichotomous variable. This type of variable has exactly two categories, such as male or female, smoker or non-smoker, furry or hairless. The categories can be natural like the male-female dichotomy, or created by the researcher, such as under 20 years of age and 20 or older. Categorical variables with more than two categories are sometimes called polytomous. For categorical variables differences between values are uninterpretable. Of course nominal and ordinal variables are both categorical. So how can we interpret numerical results from categorical variables? Well suppose I measure animal preference in a group of my friends by assigning the numbers 1, 2, and 3 respectively to friends who prefer dogs, cats, or hamsters. It doesn't make sense to look at the mean animal preference of say 1.2, and say that my friends have a low preference for animals. I could have assigned the numbers in a, the reverse order resulting in a high mean of 2.8. For a nominal variable like animal preference it only makes sense to look at frequencies, how many people there are in each category. What about a math test with ten questions that measures math ability at the ordinal level. Suppose I administer the test to my friends and find a mean score of 6.2. Is this mean interpretable? Well, not if the scores only reflect ordering. Because I can reassign the person with the highest score the number 15. The ordering is still the same, so the relations are preserved. Of course if I did this, the average test score would be suddenly much higher. The value is arbitrary and not informative of real differences between people on the property of interest. So if you have an ordinal variable, you should stick to frequencies and statistics like the mode and the median. Categorical variables can be contrasted with quantitative variables. Quantitative variables allow us to determine not only that people differ on a certain property, but also to what extent they differ. Interval and ratio variables are quantitative. For quantitative variables like temperature, weight and length, it does make sense to calculate a mean, and for example to compare means of groups. This is because the mean is influenced by the distance between numbers. For quantitative variables the distance between numbers actually corresponds to the distance between people on the property of interest. For example, if I measure the weight of friends who own a cat and the weight of my friends who own a dog. I can compare their mean weight to see if cat people are heavier, because they don't get the extra exercise from walking their pet. A final distinction that you should be able to make is between discrete and continuous variables. For continuous variables it's always possible, in theory anyway, to find a value between any other two values. Consider body weight. If one person weighs 65 kilograms and another 66 kilograms, we can easily imagine finding someone who weighs 65.5 or 65.72 or a 65.268334. As long as our measurement instrument is precise enough, any value between the minimum and the maximum on the scale should be possible. Discreet variables, on the other hand, can only take on a limited set of values. Nominal and ordinal variables are, by their nature, discreet. But quantitative variables can also be discreet. Check the number of pets someone has owned. This is a ratio variable, because differences can be compared. The difference between two and four pets is the same as between one and three pets. And because ratios can be compared, someone with four pets owns twice as many pets as someone with two pets. The set of possible values is very limited, however. We start at zero, and then the values one, two, three and four. But 1.3 pets or 4.7 pets are not valid values. So here we have an example of a discrete ratio variable. The distinction between continuous and discrete variables is less relevant because it's not associated with how you can interpret the measurement results, unlike the distinction between categorical and quantitative variables.
