Baka, L., & Basinska, B.A. (2016). Psychometryczne właściwości polskiej wersji Oldenburskiego Kwestionariusza Wypalenia Zawodowego (OLBI) [Psychometric properties of the polish version of the Oldenburg Burnout Inventory]. Medycyna Pracy, 67(1), 29-41. doi:CrossrefGoogle Scholar
Bakker, A.B., Demerouti, E., & Sanz-Vergel, A.I. (2014). Burnout and work engagement: The JD-R approach. Annual Review of Organizational Psychology and Organizational Behavior, 1(1), 389-411.Google Scholar
Bakker, A.B., & Oerlemans, W. (2011). Subjective well-being in organizations. In K. Cameron, & G. Spreitzer (Eds.), The Oxford handbook of positive organizational scholarship (pp. 178-189). Oxford: Oxford University Press.Google Scholar
Balducci, C., Cecchin, M., Fraccaroli, F., & Schaufeli, W.B. (2012). Exploring the relationship between workaholism and workplace aggressive behaviour: The role of job-related emotion. Personality and Individual Differences, 53(5), 629-634.CrossrefGoogle Scholar
Basinska, B., Gruszczynska, E., & Schaufeli, W. (2014). Psychometric properties of the polish version of the Job-related Affective Wellbeing Scale. International Journal of Occupational Medicine and Environmental Health, 27(6), 993-1004.CrossrefGoogle Scholar
Basińska, B.A. (2016). Emocje w pracy: rozszerzenie teorii Wymagania - Zasoby w Pracy. Gdańsk: Wydawnictwo Politechniki Gdańskiej.Google Scholar
Basińska, B.A. (2013). Emocje w miejscu pracy w zawodach podwyższonego ryzyka psychospołecznego. Polskie Forum Psychologiczne, 18(1), 81-92.Google Scholar
Basinska, B.A., & Wiciak, I. (2015). Kobiety w wydziałach logistyki Policji. Zeszyty Naukowe Uniwersytetu Szczecińskiego. Problemy Zarządzania, Finansów i Marketingu, 41(1), 223-236.Google Scholar
Basinska, B.A., & Wiciak, I. (2012). Fatigue and professional burnout in police offi cers and fi refi ghters. Internal Security, 4(2), 267-275.Google Scholar
Basinska, B.A., Wiciak, I., & Maria Dåderman, A. (2014). Fatigue and burnout in police offi cers: the mediating role of emotions. Policing: An International Journal of Police Strategies & Management, 37(3), 665-680.CrossrefGoogle Scholar
Baumeister, R.F., Bratslavsky, E., Finkenauer, C., & Vohs, K.D. (2001). Bad is stronger than good. Review of General Psychology, 5(4), 323-370. doi:CrossrefGoogle Scholar
Bianchi, R., Schonfeld, I.S., & Laurent, E. (2015). Burnout-depression overlap: A review. Clinical Psychology Review, 36, 28-41. doi:CrossrefGoogle Scholar
Brown, N.J.L., Sokal, A.D., & Friedman, H.L. (2014). The persistence of wishful thinking. American Psychologist, 69(6), 629-632. doi:CrossrefGoogle Scholar
Brown, N.J., Sokal, A.D., & Friedman, H.L. (2013). The complex dynamics of wishful thinking: The critical positivity ratio. American Psychologist, 68(9), 801-813.CrossrefGoogle Scholar
Burns, A.B., Brown, J.S., Sachs-Ericsson, N., Plant, E.A., Curtis, J.T., Fredrickson, B.L., & Joiner, T.E. (2008). Upward spirals of positive emotion and coping: Replication, extension, and initial exploration of neurochemical substrates. Personality and Individual Differences, 44(2), 360-370. doi:CrossrefGoogle Scholar
Cacioppo, J.T., Gardner, W.L., & Berntson, G.G. (1999). The affect system has parallel and integrative processing components: Form follows function. Journal of Personality and Social Psychology, 76(5), 839-855.CrossrefGoogle Scholar
Cardozo, B.L., Crawford, C.G., Eriksson, C., Zhu, J., Sabin, M., Ager, A., & Simon, W. (2012). Psychological distress, depression, anxiety, and burnout among international humanitarian aid workers: A longitudinal study. PLoS one, 7(9), e44948.Google Scholar
Clore, G.C. (2002). Dlaczego przezywamy emocje. In P. Ekman, J.R. Davidson (Eds.). Natura emocji. Podstawowe zagadnienia (pp. 94-102). Gdańsk: GWP.Google Scholar
Cohen, J., Cohen, P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah NJ: Lawrence Erlbaum Associates Inc.Google Scholar
Cortina, J.M. (1993). Interaction, nonlinearity, and multicollinearity: Implications for multiple regression. Journal of Management, 19(4), 915-922.CrossrefGoogle Scholar
Demerouti, E., Bakker, A.B., Nachreiner, F., & Schaufeli, W.B. (2001). The job demands-resources model of burnout. Journal of Applied Psychology, 86(3), 499-512.CrossrefGoogle Scholar
Demerouti, E., Mostert, K., & Bakker, A.B. (2010). Burnout and work engagement: a thorough investigation of the independency of both constructs. Journal of Occupational Health Psychology, 15(3), 209-222.CrossrefGoogle Scholar
Diener, E. (2000). Subjective well-being: The science of happiness and a proposal for a national index. American Psychologist, 55(1), 34-43. doi:CrossrefGoogle Scholar
Diener, E., Colvin, C.R., Pavot, W.G., & Allman, A. (1991). The psychic costs of intense positive affect. Journal of personality and social psychology, 61(3), 492-503. doi:CrossrefGoogle Scholar
Diener, E., Colvin, C.R., Pavot, W.G., & Allman, A. (1991). The psychic costs of intense positive affect. Journal of Personality and Social Psychology, 61(3), 492-503.CrossrefGoogle Scholar
Diener, E., Oishi, S., & Lucas, R.E. (2003). Personality, culture, and subjective well-being: Emotional and cognitive evaluations of life. Annual Review of Psychology, 54(1), 403-425.CrossrefGoogle Scholar
Diener, E., Wirtz, D., Biswas-Diener, R., Tov, W., Kim-Prieto, C., Choi, D.W., & Oishi, S. (2009). New measures of well-being. In E. Diner (Ed.), Assessing well-being (pp. 247-266). Springer Netherlands.Google Scholar
Fredrickson, B.L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. American Psychologist, 56(3), 218-226.CrossrefGoogle Scholar
Fredrickson, B.L., & Branigan, C. (2005). Positive emotions broaden the scope of attention and thought-action repertoires. Cognition and Emotion, 19(3), 313-332. doi:CrossrefGoogle Scholar
Fredrickson, B.L., & Losada, M.F. (2005). Positive affect and the complex dynamics of human fl ourishing. American Psychologist, 60(7), 678-686.CrossrefGoogle Scholar
Graham, J.W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549-576.CrossrefGoogle Scholar
GraphPad Software Inc. (2016). Scientifi c Software. QuickCalcs. Available at https://graphpad.com/quickcalcs/grubbs1/ [5th December 2016].Google Scholar
Gravetter, F.J., & Wallnau, L.B. (2014). Essentials of Statistics for the Behavioral Sciences (8th ed.). Wadsworth: Cengage Learning.Google Scholar
Grubbs, F.E. (1969). Procedures for detecting outlying observations in samples. Technometrics, 11, 1-21.CrossrefGoogle Scholar
Guastello, S.J. (2014). Nonlinear dynamical models in psychology are widespread and testable. American Psychologist, 69(6), 628-629.CrossrefGoogle Scholar
Hobfoll, S.E. (2002). Social and psychological resources and adaptation. Review of General Psychology, 6(4), 307-324.CrossrefGoogle Scholar
Hobfoll, S.E. (1989). Conservation of resources: A new attempt at conceptualizing stress. American Psychologist, 44(3), 513-524.CrossrefGoogle Scholar
Kim, K.A., & Mueller, D.J. (2001). To balance or not to balance: Confirmatory factor analysis of the affect-balance scale. Journal of Happiness Studies, 2(3), 289-306. doi:CrossrefGoogle Scholar
Lam, C.F., Spreitzer, G., & Fritz, C. (2014). Too much of a good thing: Curvilinear effect of positive affect on proactive behaviors. Journal of Organizational Behavior, 35(4), 530-546.CrossrefGoogle Scholar
Larsen, J.T., Hemenover, S.H., Norris, C.J., & Cacioppo, J.T. (2003). Turning adversity to advantage: On the virtues of the coactivation of positive and negative emotions. In L.G. Aspinwall, & U.M. Staudinger (Eds.), A psychology of human strengths: Fundamental questions and future directions for a positive psychology (pp. 211-225). Washington, DC: American Psychological Association.Google Scholar
Leone, S.S., Huibers, M.J.H., Knottnerus, J.A., & Kant, I.J. (2008). A comparison of the course of burnout and prolonged fatigue: A 4-year prospective cohort study. Journal of Psychosomatic Research, 65(1), 31-38. doi:CrossrefGoogle Scholar
Lewicka, M., Czapinski, J., & Peeters, G. (1992). Positive-negative asymmetry or “When the heart needs a reason”. European Journal of Social Psychology, 22(5), 425-434. doi:CrossrefGoogle Scholar
Lomas, T., & Ivtzan, I. (2015). Second wave positive psychology: exploring the positive-negative dialectics of wellbeing. Journal of Happiness Studies, 1-16. doi:CrossrefGoogle Scholar
Machin, M.A., & Hoare, P.N. (2008). The role of workload and driver coping styles in predicting bus drivers’ need for recovery, positive and negative affect, and physical symptoms. Anxiety, Stress & Coping: An International Journal, 21(4), 359-375. doi:CrossrefGoogle Scholar
Mäkikangas, A., Rantanen, J., Bakker, A.B., Kinnunen, M.L., Pulkkinen, L., & Kokko, K. (2015). The Circumplex Model of Occupational Well-being: Its Relation with Personality. Journal for Person- Oriented Research, 1(3), 115-129. doi:CrossrefGoogle Scholar
Maslach, C., Schaufeli, W.B., & Leiter, M.P. (2001). Job burnout. Annual Review of Psychology, 52(1), 397-422.CrossrefGoogle Scholar
Ogińska-Bulik, N., & Juczyński, Z. (2016). Ruminacje jako wyznaczniki negatywnych i pozytywnych konsekwencji doświadczonych zdarzeń traumatycznych u ratowników medycznych. Medycyna Pracy, 67(2), 201-211.Google Scholar
Ouweneel, E., Le Blanc, P.M., Schaufeli, W.B., & van Wijhe, C.I. (2012). Good morning, good day: A diary study on positive emotions, hope, and work engagement. Human Relations, 65(9), 1129-1154.CrossrefGoogle Scholar
Parke, M.R., Seo, M., & Sherf, E.N. (2015). Regulating and facilitating: The role of emotional intelligence in maintaining and using positive affect for creativity. Journal of Applied Psychology, 100(3), 917-934.CrossrefGoogle Scholar
Peterson, U., Demerouti, E., Bergström, G., Samuelsson, M., Åsberg, M., & Nygren, Å. (2008). Burnout and physical and mental health among Swedish healthcare workers. Journal of Advanced Nursing, 62(1), 84-95. doi:CrossrefGoogle Scholar
Porath, C., Spreitzer, G., Gibson, C., & Garnett, F.G. (2012). Thriving at work: Toward its measurement, construct validation, and theoretical refi nement. Journal of Organizational Behavior, 33(2), 250-275.CrossrefGoogle Scholar
Rego, A., Sousa, F., Marques, C., & Cunha, M.P.E. (2012). Optimism predicting employees’ creativity: The mediating role of positive affect and the positivity ratio. European Journal of Work and Organizational Psychology, 21(2), 244-270.CrossrefGoogle Scholar
Russell, J.A. (2003). Core affect and the psychological construction of emotion. Psychological Review, 110(1), 145-172.CrossrefGoogle Scholar
Shrira, A., Palgi, Y., Wolf, J.J., Haber, Y., Goldray, O., Shacham-Shmueli, E., & Ben-Ezra, M. (2011). The positivity ratio and functioning under stress. Stress and Health, 27(4), 265-271.CrossrefGoogle Scholar
Tabachnick, B.G., & Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). New Jersey: Pearson Education Inc.Google Scholar
Toker, S., Shirom, A., Shapira, I., Berliner, S., & Melamed, S. (2005). The association between burnout, depression, anxiety, and infl ammation biomarkers: C-reactive protein and fi brinogen in men and women. Journal of Occupational Health Psychology, 10(4), 344-362. doi:CrossrefGoogle Scholar
Tugade, M.M., & Fredrickson, B.L. (2007). Regulation of positive emotions: Emotion regulation strategies that promote resilience. Journal of Happiness Studies, 8(3), 311-333. doi:CrossrefGoogle Scholar
Van Katwyk, P.T., Fox, S., Spector, P.E., & Kelloway, E.K. (2000). Using the Job-Related Affective Well-Being Scale (JAWS) to investigate affective responses to work stressors. Journal of Occupational Health Psychology, 5(2), 219-230.CrossrefGoogle Scholar
Warr, P., Bindl, U.K., Parker, S.K., & Inceoglu, I. (2014). Four-quadrant investigation of job-related affects and behaviours. European Journal of Work and Organizational Psychology, 23(3), 342-363.CrossrefGoogle Scholar
Weiss, H.M., & Cropanzano, R. (1996). Affective events theory: A theoretical discussion of the structure, causes and consequences of affective experiences at work. In B.M. Staw, & L.L. Cummings (Eds.). Research in organizational behavior: An annual series of analytical essays and critical reviews, Vol. 18 (pp. 1-74). US: Elsevier Science/JAI Press.Google Scholar
After becoming familiar with your data using descriptive statistics, you are probably itching to find out if and how certain variables are related to one another. So now we foray into bivariate statistics, meaning we are now dealing with analyzing how two variables are related to one another. Correlation, sometimes known as Pearson’s correlation, is a bivariate statistic that measures how two variables are related to or associated with each other. As this is AP Statistics, you know by now you’re going to need to know more than that to be well prepared for the exam. So what is correlation exactly and how do we interpret it?
In statistics, we are not only interested in describing observations, but how observations are related to each other. Correlation describes the strength and direction of a linear relationship for bivariate quantitative data. It is typically given as a correlation coefficient, usually known as Pearson’s r. This r value reflects the strength and direction of a linear relationship between two variables, or bivariate data. Specific to correlation, we are interested in describing the quality of a linear relationship. It is important to keep in mind that correlation is only appropriate when there is a linear relationship between two variables of interest.
The correlation coefficient r ranges from -1 to +1. An r coefficient of -1 is a very strong linear negative relationship, while at the other end a +1 is a very strong linear positive relationship. A positive correlation is one in which both variables increase. On the other hand, in a negative correlation, one variable increases while the other decreases. A scatter plot will show a positive correlation as an uphill slope, while a negative correlation is a downhill slope.
It is also possible to get a score of 0, which reflects the absence of a linear relationship. The absence of a linear relationship, an r of 0, could mean that there may be some other kind of relationship between two variables. Again, to emphasize, an r of 0 does not mean that there isn’t a relationship; rather it means that a linear relationship does not exist. Instead, it is possible that while r is 0, there may be a curvilinear relationship between the two variables. The further the r coefficient is from -1 and +1, or closer to 0, the weaker the linear relationship between the two variables.
As a general rule r values between -.3 and +.3 are considered weak correlations. Moderate correlations are between -.3 and -.7, and between .3 and .7. Strong correlations are greater than .7 or less than -.7.
When it comes to correlation, keep in mind that it is a measure of linear relationship. In other words, a correlation is only appropriate when there is a straight line that depicts the relationship between two variables. If the relationship is curvilinear, you will get a correlation coefficient that is close to 0. Thus, in order to calculate correlation it is important to do some exploratory data analysis using a visual display. In particular, you will want to explore the relationship between two variables using a scatterplot to ensure that there is a straight line relationship. Again, an r score is only meaningful if there is a linear relationship. When a scatterplot shows a curve, you are likely to get an r of 0. An r of 0 doesn’t mean a relationship is nonexistent, but that it isn’t linear.
It is also important to keep in mind that the correlation coefficient is influenced by extreme values. Extreme values can influence a positive and strong relationship, so it is important as well to be mindful of outliers when interpreting correlation. When you have a scatterplot, it can be easy to spot observations that are far removed from the rest of scatter pattern. These outliers can drag the shape of the correlation line to be positive or negative, to be weak or to be strong.
You might see scatterplots associated with an r coefficient. Usually, statistical analysis programs will calculate r alongside a scatterplot. However, you will never be asked to calculate an r coefficient from looking at a scatterplot alone. It’s difficult for a person to do this, so you’ll be given other information if you need to find an r coefficient.
How to Interpret Correlation?
When you come across an r statistic, you want to interpret what it reflects about the strength and direction of the linear relationship between the two variables.
Let’s go through some examples to practice interpreting correlation.
In the first example, let’s examine the correlation between murder rate and poverty rate. The Pearson correlation is .63.
We would interpret this r to reflect a moderately strong, positive, linear relationship between two variables. This means that as poverty rate increases, so does the murder rate. Note that this doesn’t mean that murder causes poverty, or that poverty causes murder. Rather, it could be that both poverty and murder are influenced by some other factor, like geographical location or amount of time spent away from the home. We can’t make positive statements about what causes something without further information.
In this example, we examine the relationship between crime and ice cream sales. The Pearson r is .4.
We would interpret this r to reflect a moderately strong correlation with a positive, linear slope relationship between ice cream sales and crime. As ice cream sales increase, so does crime.
This is also a good example of how two seemingly unrelated variables can be correlated. This correlation is probably not by chance. Rather, ice cream sales might be a proxy, or a reflection, of weather. Hotter temperatures might be positively related to more crime being committed, as there is more opportunity to commit crime when people are out and about. Again, we’d have to do more research to figure out the exact reason for the correlation.
For a final example, we have a correlation coefficient for age and income. The Pearson r is .10.
This r coefficient is considered to be fairly weak, as it is near 0. Does it mean that there is no relationship between age and income? This is certainly possibly. However, we could also reason that the relationship between age and income is not linear in character. That is, income does not necessarily increase as age increases. In fact, income may decrease after a certain age. Retirees, for example, may see a great drop in their income after they stop working. Thus, it is possible that the relationship between age and income is actually a curve, in which after a certain age, say after 55 years, income takes a downward turn. There’s a correlation here, but it’s not linear, so a scatterplot isn’t helpful in analyzing it.
Correlation is an important first step in data analysis when we want to know how two variables are related to one another. Typically, statisticians will calculate correlation after already having done a lot of descriptive statistics and identifying outliers. Statisticians will typically explore the relationship between two variables graphically using a scatterplot to ensure that a correlation is appropriate to calculate.
The value of Pearson’s r will always be between -1 and +1. Keep in mind that the correlation coefficient is about the direction and the strength of a linear relationship. However, not all bivariate data will be related in a linear pattern, so correlation is specific to linear relationships. Furthermore, correlated variables are important for multivariate analyses where strong correlations can lead to biased estimates.
Now that we have reviewed correlation, you should feel confident when you encounter correlation questions on the AP Statistics exam. Be sure to check out other Statistics resources, such as Albert.io, and good luck on your exam!
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