In this post, I will explain three core concepts to understand quantitative methodology in psychology. I want to stop here to describe more intuitive but essential ideas which are on the basis of more complex and notorious statistical reasoning, mainly in psychometrics. Firstly, I will describe how humans use the numbers in our daily life to establish quantity. Secondly, I am going to define the concept of variable and levels of measurement. And finally, I will introduce broadly the notion of validity in order to illustrate how to assign the number to abstract things. In other words, this post is thought mainly for undergraduate students, but also like an exercise of divulgation and teaching skills. Moreover, it is a training for me because English is not my first language as you can see in this blog, but I want to attract the more diverse public to here, for this reasons any feedback about language is welcome. No more word and here we go.
Numbers have been with us since ancient times. We can imagine a group of primitive humans collecting fruits and thinking about the food could be enough for everybody. Moreover, we can think in rivals tribes estimating how soldiers men or spears have the others because they need to know if they need more preparations or changing his strategy. Likewise, numbers and quantitative thinking begin when we are little children. For example, we need to know if we receive the same amount of ice-cream than our brother or we have all our toys. We learn to differentiate people older, bigger, stronger or friendly, but, of course, in an intuitive way.
In this sense, I can differentiate three main concepts. Three ideas that we need to remember very well, moreover, you should visualize these concepts in your mind. If you can see these things I believe you can improve your statistical thinking. These concepts are frequency, size, and distance.
Frequency is about counting objects, things or events. Maybe a prisoner doing mark in the wall to estimate how many days he needs to wait to get out there. Maybe a boy drawing above a calendar to calculate how many days he needs to wait for Christmas. Someone scoring each team in a football match or groups of friends playing D&D calculating the result of several dices to determinate if they defeated a monster.
Then, the size is about the thing are bigger or smaller than others. In this point, we can understand how important is measuring to establish differences and doing comparisons among things. For instance, two geeks are discussing King Kong or Godzilla is the biggest monster. Firstly, they are talking like fans, only with passion, but one of them use more <<sophistical>> reasoning and he decided to use objective reference in order to determinate the greatness of this favorite monster. He says that according to movies, Godzilla is on average bigger than King Kong because the giant lizard is clearly taller than the building than it destroys. Indeed, they could discuss not only about height but weight too (another concept that you can recognize in statistical jargon). How can they decide? may they calculate the mean between both?
Nevertheless, the conversation has become more obscure and foggy because the King Kong fan says the Giant Gorilla is more influential, more iconic… and How can they determinate measure to abstract concepts like influential or iconic? which could be the measure units? the scale? the reference? Maybe we are arriving in the dark land of psychological constructs…
Finally, we have the distance. A very useful concept. A messenger needed to give a letter a king from another kingdom, he asks about how far it was this place, and other servant said to him: 3 days with a horse. The messenger thought he needs at least one week to do this travel. Two warriors compete about who is the best, they have made hundreds of feats, but the proudest said: You can never reach me, you are definitely far from me.
In another place, two lovers confess their love for each other. One of them says that he loves her from here to the moon, but she responds that she loves him from here to the stars. Love measured in distance, a simple idea as effective. And we are one step to declare the love to the infinite.
In 1946, S.S. Stevens published “On the Theory of Scales of Measurement”. In this heroic paper, he saved psychology (or he extended its agony) of attacks from real sciences with real (objective) measures. The “enemies” argued that psychological variables do not accomplish all mathematical properties and, therefore, psychologists we cannot measure, thus psychology cannot be a science. However, Stevens did his movement and it was well played. He proposed different measurement levels, a set of categories to named different variables, thus we can do statistical analysis with psychological variables, but we need recognizing four types:
e.g. Variable Type of monster 1= mammal 2= reptile
e.g. Variable Size 1= Small 2= medium 3= Big
e.g. Variable Corpulence from 1 to 20 points
e.g. Variable height = Metters
Stevens (1946) define (paraphrasing to N.R. Campbell) measuring as the assignment of number numeral to objects or events according to rules. However, which are the rules? this is the real challenge. We want to assign numbers to our variables but before we need to define what is a variable.
Review the next images:
We can differentiate to Homer and Lisa (nominal level, perhaps it could be debated if intelligence is nominal is ordinal considering it has only two levels).
But we don’t know how much difference in intelligence they are.
Then, we can add to marge and Bart in order to show grades in intelligence (Ordinal level).
Moreover, we could get the IQ scores, and now we can say, for instance, that Lissa is 30 points more intelligent than Homer (Interval level) .
Intelligence is a variable here. A variable is simply a feature that varies among cases, objects or events in a determined population. If something does not show differences among the cases, then this is not a variable is constant. For example, monstrosity could be understood like a constant between King Kong and Godzilla, but they vary in one is a mammal and the other a reptile. Likewise, it is possible to define variable according to its function. They can be dependent or independent. For instance, if we based with the graphic with Simpsons family we could hypothesize a relationship between gender and intelligence, maybe we say intelligence depends on gender, specifically female gender is associated with an increase in intelligence.
Therefore, we can identify an attribute to measure, which is a variable, and it could be nominal, ordinal, interval or ratio. Now, we need an instrument to reveal what is the grade or level that someone or something has. This instrument, according to a Cronbach and Meehl (1955) should have construct validity. This concept could be defined as the property of an instrument, where it measures what it claims to measure. In other words, “X” scores in the test depend on the “X” construct that it is measuring.
Easy to write? easy to imagine? Sadly it is not easy to do. The main problem, is very likely other factors infiltrate in this equation. For example, we could propose more variables on the right side in the equation, maybe anxiety or self-esteem. Hence, we need to elucidate if our score shows only and wholly intelligence or/and other attributes of the people. How do these factors interact? how much do they weight in the total score?
To summarize, measuring in psychology is related to frequency because we likely count how many correct answers someone had in an intelligence. Counting is essential to assign numbers to things, a basic skill. Then in research comparing groups, we will want to estimate the size of the effect, or in more simple words, how much has a group in a variable in comparison with others. For example, how much effective is a treatment versus a placebo? Moreover, when you obtain your first regression models, you want to analyze if the residues in your model, in other words, the distance from the predicted values with the actual values. More simply, dispersion statistics like Standard Deviation is the average of the distance (or how much far) from every case respect to the mean (center).
Statistics is so abstract sometimes. Many students struggle with it because they can imagine the concepts. I was one of them, and for this reason, I try to teach in a more kindly way.