2 Reflexivity and Positionality
Stephanie D'Costa
Learning Objectives
By the end of this chapter, you will be able to
- Identify inclusive language to use in their positionality statements.
- Articulate positionalities when writing & presenting their research findings.
- List actionable steps in their research presentations to address social issues.
Thinking through your motivations for research is an act of reflection. Reflection on one’s motivations and positionality is an essential part of every stage of research.
Reflexivity
The ability to be reflexive is vital to the process of picking a research question, conducting research, and analyzing data. To be reflexive is to be able to examine and react to your own emotions, motives, and situation[1]. In psychology research, this requires the ability to critically recognize your influencers and your influence on others. Holland (1999)[2] expounds that reflexivity is the ability to take account of one’s self and the effects of personality or presence of the researcher on the investigation (p. 464). Reflexivity means being sensitive to “how relations of power operate in the research process” (Kirby et al., 2017 p. 50) and affect your relationship with, and perspective of, the subject.
As the subject of psychological research is complex, dynamic, and sometimes conducted upon populations for which you are removed or have privilege over, taking stock of your own position (with its institutional supports, privileges and limitations) is essential for both ethical (the application of moral principles and professional code of conduct to research) and epistemic (the philosophy concerning the nature of knowledge) reasons. Recognition of ethics ensures that there is not exploitation taking place in your research, and epistemology ensures that your own biases are accounted for.
Positionality
A related concept to reflexivity is positionality. Positionality describes one’s worldview and the position one adopts about research and its social and political content (Holmes, 2020, p.1). This involves taking stock of
‘where the researcher is coming from’, [and] concerns ontological assumptions (an individual’s beliefs about the nature of social reality and what is knowable about the world), epistemological assumptions (an individual’s beliefs about the nature of knowledge) and assumptions about human nature and agency (individual’s assumptions about the way we interact with our environment and relate to it) (Holmes, 2020, p.1-2)
Because psychological research is by nature, rarely value-free, researchers must account for their motivations. Beliefs, values, and interests are shaped by our personal identities (e.g. experiences, gender, race, ethnicity, sexuality, (dis)ability statuses, political allegiances, social class, geographic location, history, etc.) and the systems that privilege or marginalize these identities. These positionalities influence our research interests and topics, the perspectives we adopt in carrying out research, our motivations, how we conduct the research, and the outcomes. Positionality also determines the subject we investigate, the participants we choose and the methods we use to conduct research [3]. Hence, if you are uncertain about a research topic or you know the topic but are uncertain about how to narrow it down, it might be worthwhile to think about your positionality. Think about your identity, what you believe about social processes (such as inequality), what you have learned, what your experiences are, and see if that could help you to narrow down your research topic.
Positionality Statements
Intentionally reflecting on your positionality is an important part of the research process. Hence, researchers frequently invest time in developing positionality statements and including them in their papers. Reflecting on your positionality is not only important in helping you to decide on a topic, it can also help shape your methodology and interpret your findings. Positionality statements are also important because our identities and lived realities create biases in how we interpret and view the world. An awareness of our own biases, as researchers, enhances our understanding of how our lived experiences, shaped by systems of power and privilege, inform the way that we conduct research. Below are two examples of positionality statements.
Examples of Positionality Statements
- I position myself as a bricoleur, layering feminist standpoint theory and postcolonial theory, and propose the collaborative data collection and analysis techniques, with particular attention to ethical and cultural sensitivity, using a social constructivist approach to grounded theory…In light of postcolonial critiques of Western researchers and international development, I have often wondered: Am I doing more harm than good? The privilege that accompanies my social location as a White, upper class, Canadian, academic woman means that, despite good intentions, my efforts to support education in postcolonial contexts risk being patronizing, insulting, threatening, imperialist, and recolonizing[4] (p. 1-2)
- Canada is not my birthplace and English is not my first language. I was born in Nigeria in the 90s and came to Canada as a very young child who spoke no English at all, but rather who conversed fluently in my native Igbo. As far as citizenship, I hold a Nigerian and Canadian passport. If identity is to be so simply ascribed, one would say that I am a Black, Igbo, Nigerian-Canadian woman…The simplicity of identities is also what hides the complexity of bellowing and the illusion of agency in determining the totality of who it is that we are [5] (p.43)
In both examples, the researchers are forthright about what influenced their research and their interpretations of social reality that are influenced by their positionality. There are several advantages to this openness. Being candid about our positionality increases the credibility of our research and provides contexts for users of our research. Reflexivity and positionality also improve the authority and validity of our knowledge[6]. We encourage you to develop your own positionality statement.
There are also some critiques to the inclusion of positionality statements that should be considered. As people read your positionality they may develop assumptions about you. For example, being candid about your connection to a topic may indicate your limited experience (e.g. being an outsider to the research area and having limited previous experience working with the population). Additionally, some researchers may not believe that positionality statements matter or belong in the research process given the context of their research paradigm (See the section on Positivism in Chapter 4).
Writing Positionality Statements
A good positionality statement describes one’s epistemological position (i.e. how one views the world in terms of their philosophy, personal beliefs, theoretical influence and perspectives which guide the research) as well other potential influences on research such as personal characteristics and identities in terms of gender, age, social class, ethnicity and political beliefs (see Holmes, 2020, p. 4). It should also address any predetermined position that the researcher takes (e.g., participant, as an insider or outsider to the population being studied, theoretical influences, etc.), the research context, and a reflexive opinion about how these might affect the research process. Hence, taking stock of positionality requires understanding how “one’s position in the social hierarchy vis-a-vis other groups potentially ‘limits or broadens’ one’s understanding of others” [7] (p. 48). This means interrogating what biases you may have of the groups being studied and how your own social location may influence that bias. Consider the following questions: does your disdain for slow customer service perhaps come from your never having to work in the service industry? Or the opposite? Does your idealization of agricultural work perhaps come from your only having done non-physical city labour? By answering questions about why and how you have come to study your topic, you will be clearer about your presuppositions and forthright with your reader about your relationship to the subject matter.
How to Write a Positionality Statement
Writing a positionality statement helps you to intentionally reflect on your identity, life history, experiences, values, and the things/issues that are important to you. This reflection can help you determine what aspect of your identity is of broader sociological interest, which can be useful in narrowing your research interests. Even if you already know what topic you want to research, a positionality statement can help you to focus your research on issues that are important to who you are or to your political/world views. Here are some things to include in your positionality statement:
- Identity characteristics (e.g., age, gender, sexuality, ethnicity, social class, disability status, citizenship, immigration status, religion, marital status etc.), and how these identities are shaped by societal structures and systems to privilege and marginalize various communities.
- Life experiences (previous or current job, volunteering activities, membership in advocacy groups etc.)
- Political, philosophical and theoretical beliefs (lens through which you view and interpret the world)
- Relationship to phenomena of interest (insider and/or outsider status)
- Clearly reflecting on how these characteristics, experiences, and history relate to the phenomena being researched.
Remember, that it is more than just articulating your identities but more importantly about the research at hand, how do your identities relate to “x” topic. For instance, take the first example statement in the Positionality Statements
- The author clearly states their identity characteristics as a “White, upper-class, Canadian, academic woman”
- She demonstrates professional life experiences in this area of study.
- The author orients her position in theory as “layering feminist standpoint theory and postcolonial theory,…with particular attention to ethical and cultural sensitivity, using a social constructivist approach to grounded theory.”
- Throughout the statement, she recognizes herself as holding an outsider position, which is demonstrated in statements such as “The privilege that accompanies my social location…means that, despite good intentions, my efforts to support education in postcolonial contexts risk…”.
- Finally, there is clear reflexivity taking place throughout the statement, with the author stating how her own identities and position of privilege may be perceived by the very communities she seeks to serve: “…risk being patronizing, insulting, threatening, imperialist, and recolonizing.”
Additional tips:
- There is no limit on the length of your positionality statement, and often the length will be based on the intended use of the positionality statement. For instance, a book’s positionality statement that is integrating multiple concepts may be a fair bit longer than an empirical research article. However, a good guideline to follow is to try to keep it within a paragraph.
- Get a friend or close acquaintance–ideally with knowledge relevant to the topic being researched–to read your draft positionality statement and inform you of any personal details that you might have overlooked that you may have that need more reflexive engagement.
Equity Activity: Developing a Positionality Statement
License & Attribution
“Reflexivity & Positionality” by Stephanie D’Costa is adapted from “A Note on Reflexivity and Positionality” by Oral Robinson and Alexander Wilson is licensed CC BY-NC 4.0.
“Reflexivity & Positionality” is licensed under CC BY-NC-SA 4.0.
- Cambridge Dictionary (2021). Reflexivity. Cambridge Dictionary. https://dictionary.cambridge.org/dictionary/english/reflexivity ↵
- Holland, R. (1999). Reflexivity. Human relations, 52(4), 463-484. ↵
- Holmes, A. G. D. (2020). Researcher Positionality--A Consideration of Its Influence and Place in Qualitative Research--A New Researcher Guide. Shanlax International Journal of Education, 8(4), 1-10. ↵
- Vanner, C. (2015). Positionality at the center: Constructing an epistemological and methodological approach for a western feminist doctoral candidate conducting research in the postcolonial. International Journal of Qualitative Methods, 14(4), 1-12. ↵
- Odozor, E, T. (2020). Making peace with movement: dislocation and the Black Diaspora. In G. S. Dei, E. Odozor and A. V. Jimenez (eds.,), Cartographies of Blackness & Black Indigeneities (pp.41-50). Myers Education Press. ↵
- Smith, L. T. (1999). Decolonising Methodologies: Research and Indigenous Peoples. University of Otago Press. ↵
- Kirby, S. L., Greaves, L., & Reid, C. (2017). Experience research social change: Methods beyond the mainstream. University of Toronto Press. ↵
Learning Objectives
By the end of this chapter, you will be able to
- Define correlational research and give several examples.
- Explain why a researcher might choose to conduct correlational research rather than experimental research or another type of non-experimental research.
- Interpret the strength and direction of different correlation coefficients.
- Explain why correlation does not imply causation.
What Is Correlational Research?
Correlational research is a type of non-experimental research in which the researcher measures two variables (binary or continuous) and assesses the statistical relationship (i.e., the correlation) between them with little or no effort to control extraneous variables. There are many reasons that researchers interested in statistical relationships between variables would choose to conduct a correlational study rather than an experiment. The first is that they do not believe that the statistical relationship is a causal one or are not interested in causal relationships. Recall two goals of science are to describe and to predict, and the correlational research strategy allows researchers to achieve both of these goals. Specifically, this strategy can be used to describe the strength and direction of the relationship between two variables and if there is a relationship between the variables then the researchers can use scores on one variable to predict scores on the other.
Another reason that researchers would choose to use a correlational study rather than an experiment is that the statistical relationship of interest is thought to be causal, but the researcher cannot manipulate the independent variable because it is impossible, impractical, or unethical. For example, while a researcher might be interested in the relationship between the frequency people use cannabis and their memory abilities, they cannot ethically manipulate the frequency at which people use cannabis. As such, they must rely on the correlational research strategy; they must simply measure the frequency that people use cannabis and measure their memory abilities using a standardized test of memory, and then determine whether the frequency people use cannabis is statistically related to memory test performance.
Correlation is also used to establish the reliability and validity of measurements. For example, a researcher might evaluate the validity of a brief extraversion test by administering it to a large group of participants along with a longer extraversion test that has already been shown to be valid. This researcher might then check to see whether participants’ scores on the brief test are strongly correlated with their scores on the longer one. Neither test score is thought to cause the other, so there is no independent variable to manipulate. In fact, the terms independent variable and dependent variable do not apply to this kind of research.
Another strength of correlational research is that it is often higher in external validity than experimental research. Recall that there is typically a trade-off between internal validity and external validity. As greater controls are added to experiments, internal validity is increased but often at the expense of external validity, as artificial conditions are introduced that do not exist in reality. In contrast, correlational studies typically have low internal validity because nothing is manipulated or controlled, but they often have high external validity. Since nothing is manipulated or controlled by the experimenter, the results are more likely to reflect relationships that exist in the real world.
Finally, extending upon this trade-off between internal and external validity, correlational research can help to provide converging evidence for a theory. If a theory is supported by a true experiment that is high in internal validity as well as by a correlational study that is high in external validity, then the researchers can have more confidence in the validity of their theory. As a concrete example, correlational studies establishing that there is a relationship between watching violent television and aggressive behavior have been complemented by experimental studies confirming that the relationship is a causal one (Bushman & Huesmann, 2001)[1].
Does Correlational Research Always Involve Quantitative Variables?
A common misconception among beginning researchers is that correlational research must involve two quantitative variables, such as scores on two extraversion tests or the number of daily hassles and number of symptoms people have experienced. However, the defining feature of correlational research is that the two variables are measured—neither one is manipulated—and this is true regardless of whether the variables are quantitative or categorical (See the chapter on Variables for a more detailed description). Imagine, for example, that a researcher administers the Rosenberg Self-Esteem Scale to 50 American college students and 50 Japanese college students. Although this “feels” like a between-subjects experiment, it is a correlational study because the researcher did not manipulate the students’ nationalities. The same is true of the study by Cacioppo and Petty comparing college faculty and factory workers in terms of their need for cognition. It is a correlational study because the researchers did not manipulate the participants’ occupations.
Figure 20.1 shows data from a hypothetical study on the relationship between whether people make a daily list of things to do (a “to-do list”) and stress. Notice that it is unclear whether this is an experiment or a correlational study because it is unclear whether the independent variable was manipulated. If the researcher randomly assigned some participants to make daily to-do lists and others not to, then it is an experiment. If the researcher simply asked participants whether they made daily to-do lists, then it is a correlational study. The distinction is important because if the study were an experiment, then it could be concluded that making the daily to-do lists reduced participants’ stress. But if it were a correlational study, it could only be concluded that these variables are statistically related. Perhaps being stressed has a negative effect on people’s ability to plan ahead (the directionality problem). Or perhaps people who are more conscientious are more likely to make to-do lists and less likely to be stressed (the third-variable problem). The crucial point is that what defines a study as experimental or correlational is not the variables being studied, nor whether the variables are quantitative or categorical, nor the type of graph or statistics used to analyze the data. What defines a study is how the study is conducted.
Data Collection in Correlational Research
Again, the defining feature of correlational research is that neither variable is manipulated. It does not matter how or where the variables are measured. A researcher could have participants come to a laboratory to complete a computerized backward digit span task and a computerized risky decision-making task, and then assess the relationship between participants’ scores on the two tasks. Or a researcher could go to a shopping mall to ask people about their attitudes toward the environment and their shopping habits, and then assess the relationship between these two variables. Both of these studies would be correlational because no independent variable is manipulated.
Correlations Between Quantitative Variables
Correlations between quantitative variables are often presented using scatterplots. Figure 20.2 shows some hypothetical data on the relationship between the amount of stress people are under and the number of physical symptoms they have. Each point in the scatterplot represents one person’s score on both variables. For example, the circled point in Figure 20.2 represents a person whose stress score was 10 and who had three physical symptoms. Taking all the points into account, one can see that people under more stress tend to have more physical symptoms. This is a good example of a positive relationship, in which higher scores on one variable tend to be associated with higher scores on the other. In other words, they move in the same direction, either both up or both down. A negative relationship is one in which higher scores on one variable tend to be associated with lower scores on the other. In other words, they move in opposite directions. There is a negative relationship between stress and immune system functioning, for example, because higher stress is associated with lower immune system functioning.
The strength of a correlation between quantitative variables is typically measured using a statistic called Pearson’s Correlation Coefficient (or Pearson's r). As Figure 20.3 shows, Pearson’s r ranges from −1.00 (the strongest possible negative relationship) to +1.00 (the strongest possible positive relationship). A value of 0 means there is no relationship between the two variables. When Pearson’s r is 0, the points on a scatterplot form a shapeless “cloud.” As its value moves toward −1.00 or +1.00, the points come closer and closer to falling on a single straight line. Correlation coefficients near ±.10 are considered small, values near ±.30 are considered medium, and values near ±.50 are considered large. Notice that the sign of Pearson’s r is unrelated to its strength. Pearson’s r values of +.30 and −.30, for example, are equally strong; it is just that one represents a moderate positive relationship and the other a moderate negative relationship. With the exception of reliability coefficients, most correlations that we find in Psychology are small or moderate in size. Kristoffer Magnusson's website on interpreting correlations provides an excellent interactive visualization of correlations that permits you to adjust the strength and direction of a correlation while witnessing the corresponding changes to the scatterplot.
There are two common situations in which the value of Pearson’s r can be misleading. Pearson’s r is a good measure only for linear relationships, in which the points are best approximated by a straight line. It is not a good measure for nonlinear relationships, in which the points are better approximated by a curved line. Figure 20.4, for example, shows a hypothetical relationship between the amount of sleep people get per night and their level of depression. In this example, the line that best approximates the points is a curve—a kind of upside-down “U”—because people who get about eight hours of sleep tend to be the least depressed. Those who get too little sleep and those who get too much sleep tend to be more depressed. Even though Figure 20.4 shows a fairly strong relationship between depression and sleep, Pearson’s r would be close to zero because the points in the scatterplot are not well fit by a single straight line. This means that it is important to make a scatterplot and confirm that a relationship is approximately linear before using Pearson’s r. Nonlinear relationships are fairly common in psychology, but measuring their strength is beyond the scope of this book.
The other common situations in which the value of Pearson’s r can be misleading are when one or both of the variables have a limited range in the sample relative to the population. This problem is referred to as restriction of range. Assume, for example, that there is a strong negative correlation between people’s age and their enjoyment of hip hop music as shown by the scatterplot in Figure 20.5. Pearson’s r here is −.77. However, if we were to collect data only from 18- to 24-year-olds—represented by the shaded area of Figure 20.5—then the relationship would seem to be quite weak. In fact, Pearson’s r for this restricted range of ages is 0. It is a good idea, therefore, to design studies to avoid restriction of range. For example, if age is one of your primary variables, then you can plan to collect data from people of a wide range of ages. Because restriction of range is not always anticipated or easily avoidable, however, it is good practice to examine your data for possible restriction of range and to interpret Pearson’s r in light of it. (There are also statistical methods to correct Pearson’s r for restriction of range, but they are beyond the scope of this book).
Correlation Does Not Imply Causation
You have probably heard repeatedly that “Correlation does not imply causation.” An amusing example of this comes from a 2012 study that showed a positive correlation (Pearson’s r = 0.79) between the per capita chocolate consumption of a nation and the number of Nobel prizes awarded to citizens of that nation[2]. It seems clear, however, that this does not mean that eating chocolate causes people to win Nobel prizes, and it would not make sense to try to increase the number of Nobel prizes won by recommending that parents feed their children more chocolate.
There are two reasons that correlation does not imply causation. The first is called the directionality problem. Two variables, X and Y, can be statistically related because X causes Y or because Y causes X. Consider, for example, a study showing that whether or not people exercise is statistically related to how happy they are—such that people who exercise are happier on average than people who do not. This statistical relationship is consistent with the idea that exercising causes happiness, but it is also consistent with the idea that happiness causes exercise. Perhaps being happy gives people more energy or leads them to seek opportunities to socialize with others by going to the gym. The second reason that correlation does not imply causation is called the third-variable problem. Two variables, X and Y, can be statistically related not because X causes Y, or because Y causes X, but because some third variable, Z, causes both X and Y. For example, the fact that nations that have won more Nobel prizes tend to have higher chocolate consumption probably reflects geography in that European countries tend to have higher rates of per capita chocolate consumption and invest more in education and technology (once again, per capita) than many other countries in the world. Similarly, the statistical relationship between exercise and happiness could mean that some third variable, such as physical health, causes both of the others. Being physically healthy could cause people to exercise and cause them to be happier. Correlations that are a result of a third variable are often referred to as spurious correlations.
Tyler Vigen's website [New Tab] has some excellent and amusing examples of spurious correlations. (Figure 20.6 provides one such example).
Equity Activity: Implications for correlation being seen as causation
Dr. Mueller's Correlation or Causation? website keeps track of news articles that make large claims based on correlational research. Many of the headlines suggest that a causal relationship has been demonstrated when a careful reading of the articles shows that it has not, because of the directionality and third-variable problems.
License & Attribution
“Correlational Research” by Stephanie D’Costa is adapted from “Correlational Research” by Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton is licensed CC BY-NC-SA 3.0.
“Correlational Research” is licensed under CC BY-NC-SA 4.0.
Image Descriptions
Figure 20.1. A vertical bar chart titled by its axes compares stress levels by whether someone keeps a Daily To-Do List. The y-axis is Stress (scale 0–30). Two bars are shown: Yes (purple) reaches about 18, and No (orange) reaches about 25. The difference suggests lower stress among people who use a daily to-do list. [Return to Figure 20.1]
Figure 20.2. Rectangular scatterplot with tan background. The x-axis is Stress (0–25) and the y-axis is Physical Symptoms (0–10). About twenty blue dots form an upward pattern—higher stress is associated with more symptoms. One dot around Stress ≈ 10, Symptoms ≈ 3 is highlighted with a circle. A long, dotted arrow extends left from this circled point along the same y-level, and a short, dotted arrow points down beneath it, indicating example movements (e.g., lowering stress and/or symptoms) relative to that observation. [Return to Figure 20.2]
Figure 20.3. A row of five colored panels illustrates correlation strength and direction: (1) yellow—points form a tight downward line (strong negative); (2) orange—looser downward trend (moderate negative); (3) red—cloud of points (near zero correlation); (4) purple—loose upward trend (moderate positive); (5) blue—tight upward line (strong positive). Below, a labeled axis reads –1.00, –0.50, 0, +0.50, +1.00, matching the visual progression. [Return to Figure 20.3]
Figure 20.4. A tan-background scatterplot with Hours of Sleep per Night on the x-axis (0–14) and Depression on the y-axis (0–12). About twenty blue points form a curved pattern: higher depression scores near 4 hours and near 12 hours, with the lowest cluster around 7–8 hours. A dashed curve overlays the points, tracing the U-shape to highlight the curvilinear association between sleep duration and depression. [Return to Figure 20.4]
Figure 20.5. Tan scatterplot with Age on the x-axis (0–100) and Enjoyment of Hip-Hop on the y-axis (0–10). Points cluster at high enjoyment (6–8) for ages roughly 15–25, emphasized by a light blue rectangle. From about age 30 onward, points trend downward toward mid and lower enjoyment levels, with scattered values through ages 30–80. The pattern suggests a negative relationship between age and enjoyment of hip-hop. [Return to Figure 20.5]
Figure 20.6. A dual-axis line graph titled “Number of people who drowned by falling into a pool correlates with Films Nicolas Cage appeared in.” Years 1999–2009 run along the x-axis. The left y-axis (red) is Swimming pool drownings from 80 to 140 drownings; the right y-axis (black) is Nicolas Cage from 0 to 6 films. Two lines track together: a red line for drownings and a black line for Cage films. Both dip around 2003, rise to peaks in 2007 (≈125 drownings, ≈4–5 films), drop sharply in 2008, and rise again in 2009. The legend labels Nicholas Cage (black) and Swimming pool drownings (red). The chart satirically illustrates a spurious correlation by visual similarity, not causation. [Return to Figure 20.6]
The way that one’s position in the social hierarchy potentially shapes his/her/their identity and mediates access to power, opportunities and understandings of others.
Learning Objectives
By the end of this chapter, you will be able to
- Students will articulate the difference between descriptive and inferential statistics.
- Students will identify some specific types of descriptive statistics.
What Are Statistics?
Statistics include numerical facts and figures. For instance:
- The largest earthquake measured 9.2 on the Richter scale.
- Men are at least 10 times more likely than women to commit murder.
- One in every eight South Africans is HIV positive.
- By the year 2050, there will be 12 people aged 65 and over for every new baby born.
The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the statistics are interpreted. For example, consider the following three scenarios and the interpretations based on the presented statistics. You will find that the numbers may be right, but the interpretation may be wrong. Try to identify a major flaw with each interpretation before we describe it.
- A new advertisement for Ben & Jerry’s ice cream introduced in late May of last year resulted in a 30% increase in ice cream sales for the following three months. Thus, the advertisement was effective.
Major flaw: Ice cream consumption generally increases in the months of June, July, and August, regardless of advertisements. This effect is called a history effect and leads people to interpret outcomes as the result of one variable when another variable (in this case, one having to do with the passage of time) is actually responsible. - The more churches in a city, the more crime there is. Thus, churches lead to crime.
Major flaw: Both increased churches and increased crime rates can be explained by larger populations. In bigger cities, there are both more churches and more crime. This problem, which we will discuss in more detail in the chapter on sampling, refers to the third-variable problem. Namely, a third variable can cause both situations; however, people erroneously believe that there is a causal relationship between the two primary variables rather than recognizing that a third variable can cause both. - Seventy-five percent more interracial marriages are occurring this year than 25 years ago. Thus, our society accepts interracial marriages.
Major flaw: We don’t have the information we need. What is the rate at which marriages are occurring? Suppose only 1% of marriages 25 years ago were interracial, and so now 1.75% of marriages are interracial (1.75 is 75% higher than 1). But this latter number is hardly evidence suggesting the acceptability of interracial marriages. In addition, the statistic provided does not rule out the possibility that the number of interracial marriages has seen dramatic fluctuations over the years, and this year is not the highest. Again, there is simply not enough information to understand fully the impact of the statistics.
As a whole, these examples show that statistics are not only facts and figures; they are something more than that. In the broadest sense, “statistics” refers to a range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data.
Statistics is the language of science and data. The ability to understand and communicate using statistics enables researchers from different labs, different languages, and different fields to articulate to one another exactly what they have found in their work. It is an objective, precise, and powerful tool in science and in everyday life.
What a Statistics Course Is Not
Many psychology students dread the idea of taking a statistics course, and more than a few have changed majors upon learning that it is a requirement. That is because many students view statistics as a math class, which is actually not true. While many of you will not believe this or agree with it, statistics isn’t math.
Although math is a central component of it, statistics is a broader way of organizing, interpreting, and communicating information in an objective manner. Indeed, great care has been taken to eliminate as much math from this course as possible (students who do not believe this are welcome to ask the professor what matrix algebra is). Statistics is a way of viewing reality as it exists around us in a way that we otherwise could not.
Why Do We Study Statistics?
Virtually every student of the behavioral sciences takes some form of statistics class. This is because statistics is how we communicate in science. It serves as the link between a research idea and usable conclusions. Without statistics, we would be unable to interpret the massive amounts of information contained in data. Even small datasets contain hundreds—if not thousands—of numbers, each representing a specific observation we made. Without a way to organize these numbers into a more interpretable form, we would be lost, having wasted the time and money of our participants, ourselves, and the communities we serve.
Beyond its use in science, however, there is a more personal reason to study statistics. Like most people, you probably feel that it is important to “take control of your life.” But what does this mean? Partly, it means being able to properly evaluate the data and claims that bombard you every day. If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest. Statistics provides tools that you need in order to react intelligently to information you hear or read. In this sense, statistics is one of the most important things that you can study.
To be more specific, here are some claims that we have heard on several occasions. (We are not saying that each one of these claims is true!)
- Four out of five dentists recommend Dentine.
- Almost 85% of lung cancers in men and 45% in women are tobacco-related.
- Condoms are effective 94% of the time.
- People tend to be more persuasive when they look others directly in the eye and speak loudly and quickly.
- Women make 75 cents to every dollar a man makes when they work the same job.
- A surprising new study shows that eating egg whites can increase one’s life span.
- People predict that it is very unlikely there will ever be another baseball player with a batting average over 400.
- There is an 80% chance that in a room full of 30 people at least two people will share the same birthday.
- 79.48% of all statistics are made up on the spot.
All of these claims are statistical in character. We suspect that some of them sound familiar; if not, we bet that you have heard other claims like them. Notice how diverse the examples are. They come from psychology, health, law, sports, business, etc. Indeed, data and data interpretation show up in discourse from virtually every facet of contemporary life.
Statistics are often presented in an effort to add credibility to an argument or advice. You can see this by paying attention to television advertisements. Many of the numbers thrown about in this way do not represent careful statistical analysis. They can be misleading and push you into decisions that you might find cause to regret. For these reasons, learning about statistics is a long step toward taking control of your life. (It is not, of course, the only step needed to do so.) The purpose of this course, beyond preparing you for a career in psychology, is to help you learn statistical essentials. It will make you into an intelligent consumer of statistical claims.
You can take the first step right away. To be an intelligent consumer of statistics, your first reflex must be to question the statistics you encounter. The British Prime Minister Benjamin Disraeli is quoted by Mark Twain as having said, “There are three kinds of lies—lies, damned lies, and statistics.” This quote reminds us why it is so important to understand statistics. So let us invite you to reform your statistical habits from now on. No longer will you blindly accept numbers or findings. Instead, you will begin to think about the numbers, their sources, and most importantly, the procedures used to generate them.
The above section puts an emphasis on defending ourselves against fraudulent claims wrapped up as statistics, but let us look at a more positive note. Just as important as detecting the deceptive use of statistics is the appreciation of the proper use of statistics. You must also learn to recognize statistical evidence that supports a stated conclusion. Statistics are all around you, sometimes used well, sometimes not. We must learn how to distinguish the two cases. In doing so, statistics will likely be the course you use most in your day-to-day life, even if you do not ever run a formal analysis again.
Types of Statistical Analyses
Now that we understand the nature of our data, let’s turn to the types of statistics we can use to interpret them. There are two types of statistics: descriptive and inferential.
Descriptive Statistics
Descriptive statistics are numbers that are used to summarize and describe data. The word “data” refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, data is plural. One piece of information is called a datum.) If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.
Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you’ll be studying in another section. Here we focus on (mere) descriptive statistics.
Some descriptive statistics are shown in Table 24.1. The table shows the average salaries for various occupations in the United States in 1999. Descriptive statistics like these offer insight into American society. It is interesting to note, for example, that we pay the people who educate our children and who protect our citizens a great deal less than we pay people who take care of our feet or our teeth.
|
Occupation |
Salary |
|---|---|
|
Pediatricians |
$112,760 |
|
Dentists |
$106,130 |
|
Podiatrists |
$100,090 |
|
Physicists |
$76,140 |
|
Architects |
$53,410 |
|
School, clinical, and counseling psychologists |
$49,720 |
|
Flight attendants |
$47,910 |
|
Elementary school teachers |
$39,560 |
|
Police officers |
$38,710 |
|
Floral designers |
$18,980 |
For more descriptive statistics, consider Table 24.2. It shows the number of unmarried men per 100 unmarried women in U.S. metro areas in 1990. From this table we see that men outnumber women most in Jacksonville, North Carolina, and women outnumber men most in Sarasota, Florida. You can see that descriptive statistics can be useful if we are looking for an opposite-sex partner! (These data come from the Information Please Almanac.)
|
Cities with Mostly Men |
Men per 100 Women |
Cities with Mostly Women |
Men per 100 Women |
|---|---|---|---|
|
1. Jacksonville, North Carolina |
224 |
1. Sarasota, Florida |
66 |
|
2. Killeen–Temple, Texas |
123 |
2. Bradenton, Florida |
68 |
|
3. Fayetteville, North Carolina |
118 |
3. Altoona, Pennsylvania |
69 |
|
4. Brazoria, Texas |
117 |
4. Springfield, Illinois |
70 |
|
5. Lawton, Oklahoma |
116 |
5. Jacksonville, Tennessee |
70 |
|
6. State College, Pennsylvania |
113 |
6. Gadsden, Alabama |
70 |
|
7. Clarksville–Hopkinsville, Tennessee–Kentucky |
113 |
7. Wheeling, West Virginia–Ohio |
70 |
|
8. Anchorage, Alaska |
112 |
8. Charleston, West Virginia |
71 |
|
9. Salinas–Seaside–Monterey, California |
112 |
9. St. Joseph, Missouri |
71 |
|
10. Bryan–College Station, Texas |
111 |
10. Lynchburg, Virginia |
71 |
These descriptive statistics may make us ponder why the numbers are so disparate in these cities. One potential explanation, for instance, as to why there are more women in Florida than men may involve the fact that elderly individuals tend to move down to the Sarasota region and that women tend to outlive men. Thus, more women might live in Sarasota than men. However, in the absence of proper data, this is only speculation.
You probably know that descriptive statistics are central to the world of sports. Every sporting event produces numerous statistics, such as the shooting percentage of players on a basketball team. For the Olympic marathon (a foot race of 26.2 miles), we possess data that cover more than a century of competition. (The first modern Olympics took place in 1896.) Table 24.3 and Table 24.4 show the winning times for women and men, respectively. (Women have only been allowed to compete since 1984.)
There are many descriptive statistics that we can compute from the data in these tables. To gain insight into the improvement in speed over the years, let us divide the men’s times into two pieces, namely, the first 13 races (up to 1952) and the second 13 (starting from 1956). The mean winning time for the first 13 races is 2 hours, 44 minutes, and 22 seconds (written 2:44:22). The mean winning time for the second 13 races is 2:13:18. This is quite a difference (over half an hour). Does this prove that the fastest men are running faster? Or is the difference just due to chance, no more than what often emerges from chance differences in performance from year to year? We can’t answer this question with descriptive statistics alone. All we can affirm is that the two means are “suggestive.”
Examining Table 24.3 and Table 24.4 leads to many other questions. We note that Takahashi (the lead female runner in 2000) would have beaten the male runner in 1956 and all male runners in the first 12 marathons. This fact leads us to ask whether the gender gap will close or remain constant. When we look at the times within each gender, we also wonder how far they will decrease (if at all) in the next century of the Olympics. Might we one day witness a sub-2-hour marathon? The study of statistics can help you make reasonable guesses about the answers to these questions.
To summarize, there are a variety of ways that statisticians use to describe a data set:
- Exploratory data analysis uses graphs and numerical summaries to describe the variables and their relationship to each other. You will learn how to organize a data set by grouping the data into intervals called classes and forming a frequency distribution.
- Center of the Data uses measures of central tendency to locate the middle or center of a distribution where most of the data tends to be concentrated. The three best-known measures of central tendency used by statisticians are discussed later in this section of the text: the mean, median, and mode.
- Spread of the Data uses measures of variability to describe how far apart data points lie from each other and from the center of the distribution. The section on variability discusses the four most common measures of variability: range, interquartile range, variance, and standard deviation.
- Shape of the Data can be either symmetrical (the normal distribution) or skewed (positive or negative). The section on probability and the normal distribution reveals how the shape of the distribution can easily be discernible through graphs.
- Fractiles or Quantiles of the Data uses measures of position that partition, or divide, an ordered data set into equal parts: first, second, and third quartile; percentiles; and the standard score (z-score). A fractile is a point where a specified proportion of the data lies below that point. Section 2.5 discusses how fractiles are used to specify the position of a data point within a data set.
It is also important to differentiate what we use to describe populations vs. what we use to describe samples. A population is described by a parameter; the parameter is the true value of the descriptive in the population, but one that we can never know for sure. For example, the Bureau of Labor Statistics reports that the average hourly wage of chefs is $23.87. However, even if this number were computed using information from every single chef in the United States (making it a parameter), it would quickly become slightly off as one chef retires and a new chef enters the job market. Additionally, as noted above, there is virtually no way to collect data from every single person in a population. In order to understand a variable, we estimate the population parameter using a sample statistic. Here, the term statistic refers to the specific number we compute from the data (e.g., the average), not the field of statistics. A sample statistic is an estimate of the true population parameter, and if our sample is representative of the population, then the statistic is considered to be a good estimator of the parameter.
Even the best sample will be somewhat off from the full population, earlier referred to as sampling bias, and as a result, there will always be a tiny discrepancy between the parameter and the statistic we use to estimate it. This difference is known as sampling error, and, as we will see throughout the course, understanding sampling error is the key to understanding statistics. Every observation we make about a variable, be it a full research study or observing an individual’s behavior, is incapable of being completely representative of all possibilities for that variable. Knowing where to draw the line between an unusual observation and a true difference is what statistics is all about.
Inferential Statistics
Descriptive statistics are wonderful at telling us what our data look like. However, what we often want to understand is how our data behave. What variables are related to other variables? Under what conditions will the value of a variable change? Are two groups different from each other, and if so, are people within each group different or similar? These are the questions answered by inferential statistics, and inferential statistics are how we generalize from our sample back up to our population.
For example, we will learn how to use a t-statistic to determine whether people change over time when enrolled in an intervention. We will also use an F-statistic to determine if we can predict future values of a variable based on current known values of a variable. There are many types of inferential statistics, each allowing us insight into a different behavior of the data we collect. This course will only touch on a small subset (or a sample) of them, but the principles we learn along the way will make it easier to learn new tests, as most inferential statistics follow the same structure and format.
A Note about Statistical Software
Many pieces of technology support statistical analysis and quantitative data analysis done by psychologists. Commonly used technologies include the proprietary Statistical Package for the Social Sciences (SPSS), the free and open-source tool JASP, and the programming language R. Several of the figures used in this text were generated using JASP, but providing an overview or introduction to these technologies is outside the scope of this work. Instruction manuals can be found on the JASP website.
Mathematical Notation
As noted earlier, statistics is not math. It does, however, use math as a tool. Many statistical formulas involve summing numbers. Fortunately, there is a convenient notation for expressing summation. This section covers the basics of this summation notation.
Let’s say we have a variable X that represents the weights (in grams) of 4 grapes:
|
Grape |
X |
|---|---|
|
Grape 1 |
4.6 |
|
Grape 2 |
5.1 |
|
Grape 3 |
4.9 |
|
Grape 4 |
4.4 |
We label the weight of Grape 1 as X1, of Grape 2 as X2, etc. The following formula means to sum up the weights of the four grapes:
[latex]\displaystyle\sum_{i=1}^{4} X_i[/latex]
The Greek letter [latex]\sum[/latex] indicates summation. The “i = 1” at the bottom indicates that the summation is to start with X1, and the 4 at the top indicates that the summation will end with X4. The Xi indicates that X is the variable to be summed as i goes from 1 to 4. Therefore,
[latex]\displaystyle \sum_{i=1}^{4} X_i = X_1 + X_2 + X_3 + X_4 = 4.6 + 5.1 + 4.9 + 4.4 = 19[/latex]
The symbol
[latex]\displaystyle \sum_{i=1}^{3} X_i[/latex]
indicates that only the first 3 scores are to be summed. The index variable i goes from 1 to 3.
When all the scores of a variable (such as X) are to be summed, it is often convenient to use the following abbreviated notation:
[latex]\displaystyle \sum\nolimits X[/latex]
Thus, when no values of i are shown, it means to sum all the values of X.
Many formulas involve squaring numbers before they are summed. This is indicated as
[latex]\displaystyle \sum X^{2} = 4.6^{2} + 5.1^{2} + 4.9^{2} + 4.4^{2} = 21.16 + 26.01 + 24.01 + 19.36 = 90.54[/latex]
Notice that:
[latex]\displaystyle (\sum x)^{2} \ne \sum x^{2}[/latex]
because the expression on the left means to sum up all the values of X and then square the sum (192 = 361), whereas the expression on the right means to square the numbers and then sum the squares (90.54, as shown).
Some formulas involve the sum of cross products. Below are the data for variables X and Y. The cross products (XY) are shown in the third column. The sum of the cross products is 3 + 4 + 21 = 28.
|
X |
Y |
XY |
|---|---|---|
|
1 |
3 |
3 |
|
2 |
2 |
4 |
|
3 |
7 |
21 |
In summation notation, this is written as:
[latex]\displaystyle \sum XY = 28[/latex]
Equity Activity: Descriptive Statistics and data disaggregation
In addition to using the above statistical procedures, the data disaggregation process can be applied to identify equity gaps. Disaggregation means breaking down data into smaller groupings, such as income, gender, and racial/ethnic groupings. Disaggregating data can reveal deprivations or inequalities that may not be fully reflected in aggregated data.
The National Center for Mental Health Promotion and Youth Violence Prevention provides two examples of the importance of disaggregating data into smaller subpopulations (National Center Brief 2012)[3]. One area where data disaggregation is commonly used is to show disproportionate minority contact, such as the number of times a minority youth is involved with the court system. In fact, the Office of Juvenile Justice and Delinquency Prevention (OJJDP) uses a specific indicator (Relative Rate Index) to show if there are differences in arrest rates or court sentences, for example, between racial/ethnic groups that are not explained by simple differences in population numbers. A similar step was taken by the Department of Health and Human Services (HHS) as part of the Affordable Care Act. Disaggregated data can be used to see if there are meaningful differences by subpopulations in who is accessing mental services and what treatments are successful.
In descriptive statistics, a particular group of interest (or target group) can be disaggregated by certain characteristics, such as race, ethnicity, gender, age, socio-economic status, disability, education level, employment in different sectors (e.g., health care, biotechnology, cybersecurity), salary levels, and other different factors. Disaggregating data is viewed as a critical first step while embarking on the equity-minded journey. According to the Annie E. Casey Foundation (2020), “disaggregating data and presenting it in a meaningful way can help bring attention and commitment to the solving of social and racial equity problems.”[4]
Practice Problems
Short Answer Reflections
Test Your Knowledge
License & Attribution
“Descriptive and Inferential Statistics” by Rebecca Anguiano is adapted from "Introduction" by Linda R. Cote Ph.D.; Rupa G. Gordon Ph.D., Chrislyn E. Randell Ph.D., Judy Schmitt, and Helena Marvin, which is licensed CC BY-NC-SA 4.0 and "Descriptive Statistics" by Lynette H. Bikos, which is licensed by CC BY-NC-SA.
“Descriptive and Inferential Statistics” is licensed under CC BY-NC-SA 4.0.
