2  Variables

A variable is a characteristic or attribute that can vary or take on different values. These values can be measured, observed, or manipulated in a study. For example, we can measure someone’s depressive symptoms, observe a child’s aggressive behavior on the playground, or manipulate the type of learning intervention a highschooler gets. As researchers we use variables to examine relationships, make comparisons, and draw conclusions about the phenomena we are are studying.

We will review four major classifications of variable that are often called the NOIR variables.

2.1 NOIR

Nominal, ordinal, interval, and ratio (NOIR) are four levels of measurement that describe the nature of the values that a variable can take. These levels of measurement are hierarchical, with each level including all the characteristics of the levels below it. For example, a ratio variables carries all the characteristic of nominal, ordinal, and interval (and then some!). Here’s a brief explanation of each:

2.1.1 Nominal Level

Nominal variables involve categories without any inherent order or ranking. Examples include gender, where categories are mutually exclusive, yet there is no inherent order or ranking among them. In nominal measurement, the focus is on classifying items into discrete categories. Typically nominal variables are analysed using frequencies. We can determine how many individuals identify within a certain mutually exclusive category. However, they also used in more complex analyses.

As an example, consider the following: individuals may be randomly assigned to one of two groups. One group receives a drug and the other a placebo. Researchers may then determine the impact of the drug versus the placebo on the severity of psychopathological symptoms [not a nominal variable].

As another example, perhaps we measure Grenfell students’ favorite musician. We collect data from a sample of 75 students. We can calculate frequencies of this nominal variable.

2.1.2 Ordinal Level

Ordinal variables possess a meaningful order or ranking or categories, but the intervals between categories are not consistent or meaningful. That is, while relative ranking is meaningful (e.g., category x comes before category y, which comes before category z), the differences between these categories are not uniform (the difference between category x and y is not necessarily the same as the category between category y and z).

For example, consider a typical Likert-style scale. The difference between strongly agree and agree is not necessarily the same difference between agree and neither agree not disagree, regardless of the numbers you may assign to them. Or, as another example, consider educational levels of employees at Grenfell (e.g., high school diploma, bachelor’s degree, master’s degree, PhD). While you might be able to rank them, the differences between the categories is not equal for each level.

The figure below shows both nominal and ordinal data. There is no inherent order for artists. You could impose some sort of order, such as alphabetical, but it is likely not related to the research question of interest. However, education degree has a typical progress (i.e., order): first comes bachelor’s, second masters, third PhD.

2.1.3 Interval Level

Interval variables maintain a meaningful order, and there are consistent intervals between values. However, these variables lack a true zero point, where zero does not represent the absence of the measured quantity. Examples include temperature measured in Celsius or Fahrenheit; when it’s zero degrees out, it does not mean there is no temperature. Also, 20 degrees Celcius isn’t twice as much temperature as 10 degrees. Another example would be IQ scores; An IQ score of zero does not exist.

In interval measurement, researchers focus on both the order and the equal intervals between values. The difference between \(n\) values is equal for each ordered pair. Consider four ordered value:

\(a, b, c, d\)

Interval values have the property such that the difference between \(a\) and \(b\) is the same as the difference between \(b\) and \(c\), which is the same as the difference between \(c\) and \(d\):

\(a-b=b-c=c-d\)

2.1.4 Ratio Level

Ratio variables exhibit a meaningful order, consistent intervals between values, and a true zero point. In this level of measurement, a score of zero represents the absence of the measured quantity. Examples include height, weight, income, and age. Someone 120cm tall is twice as tall as someone who is 60cm tall. Someone who is 50 is twice as old as someone who is 25. Ratio measurement allows for meaningful ratios and absolute distinctions between values.

The following table may be helpful, adapted from Nunnally and Bernstein (1994), who adapted it from Stevens (1951):

Adapted from Nunnally and Bernstein
Scale Operations Transformations Statistics Examples
Nominal \(=\) versus \(\ne\) So many Frequency; mode Gender; political party; employment status
Ordinal \(>\) versus \(<\) Monotonically increasing Median; percentiles SES (low, middle, high); Likert-style items
Interval Equality of intervals General linear Arithmetic mean; variance Temperature
Ratio Equality of ratios Multiplicative Geometric mean Height; weight

2.2 Experimental Variables

There are two main types of variables in experimental psychological research that we will focus on:

2.2.1 Independent Variable (IV)

Independent variables are variables that are manipulated or controlled by the researcher. It is the variable that is hypothesized to cause a change in the dependent variable. For example, in an experiment investigating the effects of a new teaching method on student performance, a researcher may design two teaching methods, and randomly assign participants to one of the two conditions. The teaching method would be the independent variable.

Importantly, experimental variables are mutually exclusive from which type of NOIR variable it is. An independent variable could, technically, be nominal, ordinal, interval, or ratio.

2.2.2 Dependent Variable (DV)

Dependent variables are variables that are measured or observed without some form of manipulation. Typically, in the context of experimental research, the dependent variables is believed to differ based on the independent variable. It depends on the independent variable. In the example above, perhaps the researchers want to know if the differing teaching methods lead to different student outcomes (e..g, better grades). The research would also need to measure the student outcomes, which would be be the dependent variable.

Importantly, and again, this is mutually exclusive from our NOIR variables. A dependent variable could, technically, be nominal, ordinal, interval, or ratio.

So, why care about all of these variables types? The type of statistical analyses you should use are derived from your hypotheses and the variable types. If you hypothesize that a teaching method (\(x\)) will lead to different student outcomes (\(y\)) you could conduct a t-test, but would not conduct a Pearson’s correlation.

Important

Your research question and hypothesis determine the research method and analyses you use, not the other way around.

2.3 Other Considerations

Researchers also consider and control for extraneous variables, which are variables that are not the focus of the study but could potentially influence the results. Controlling for these variables helps ensure that any observed effects or associations can be attributed to the manipulation of the independent variable.

2.3.1 Extraneous Variables

Extraneous variables are any variables other than the independent and dependent variables that may influence the results of an experiment. These variables are unwanted or unplanned factors that can introduce variability into the study, making it difficult to determine the true effect of the independent variable on the dependent variable.

For example, if a researcher is investigating the effect of a new teaching method on student performance, extraneous variables could include the students’ prior knowledge, motivation, or even the time of day the experiment is conducted.

2.3.2 Confounding Variables

Confounding variables are a specific type of extraneous variable that systematically varies with the independent variable and has a causal relationship with the dependent variable. In other words, confounding variables can lead to a false interpretation of the relationship between the independent and dependent variables.

Confounding variables can obscure the true effects of the independent variable, making it challenging to attribute changes in the dependent variable solely to the manipulated independent variable.

For example, consider a study that examines the impact of a new drug (IV) on memory (DV). However, the researchers fail to consider the participants’ age; it could be a confounding variable. This is because age may independently impact memory performance and could lead to the incorrect conclusion that the drug is influencing memory when age is the actual culprit.

2.4 Concluding Remarks

Variables in psychological research are key elements that researchers manipulate, measure, and analyze to gain a better understanding of psychological phenomena and behavior. How you operationalize and measure your variables will impact how you analyse the data and the conclusions you can draw.

Practice

Identify the type of the following variables (NOIR):

  1. The order of finishing for the participants in a race.

  2. The numerical value representing the income level of individuals in a particular household.

  3. Temperature difference between two consecutive days.

  4. The preferred mode of transportation chosen by respondents.

  5. Number of hours a student spends studying for the exam.

  6. Participant gender,

  7. Customer satisfaction levels on a scale from 1 to 5.

  8. What are the IV and DV in the following experiment?:

A study investigates the impact of sleep duration on memory retention in college students. Participants are randomly assigned to either a group with regular sleep patterns (7-8 hours per night) or a group with restricted sleep (4-5 hours per night). Memory performance is assessed through a standardized memory test administered the following day.

  1. Identify some confounding variables for the previous study.

  1. Ordinal

  2. Ratio

  3. Interval

  4. Nominal

  5. Ratio

  6. Nominal

  7. Ordinal

  8. IV = sleep; DV = standardized memory test