Psychology
Correlation
Correlation in psychology refers to the statistical relationship between two or more variables. It measures the extent to which changes in one variable are associated with changes in another. A positive correlation indicates that as one variable increases, the other also increases, while a negative correlation suggests that as one variable increases, the other decreases.
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12 Key excerpts on "Correlation"
eBook - PDFPsychology of Personality
Viewpoints, Research, and Applications
- Bernardo J. Carducci(Author)
- 2015(Publication Date)
- Wiley(Publisher)
By contrast, the major purpose of corre- lational research is to investigate the extent to which Research Methods in Personality Psychology 21 any two variables are associated with one another. For example, a researcher might be interested in studying the relationship between shyness and loneliness or the need for achievement and worker productivity. The Scatter Plot: The Illustrating of Relationships A scatter plot is a graph summarizing the scores obtained by many individuals on two different vari- ables. Figure 1.2a is a scatter plot showing the relation- ship between scores on a measure of shyness and a mea- sure of loneliness. Each point on the scatter plot rep- resents an individual’s score for the two different vari- ables. For example, the point on the scatter plot corre- sponding to Mike’s scores indicates a score of 12 on the measure of loneliness and 20 on the measure of shyness. Interpreting Correlational relationships involves iden- tifying the direction and strength of the relationship between the two variables. Correlational Relationships: Identifying Associations The direction of a Correlational relationship reveals how the two variables are related. The two basic patterns indicating direction are the positive and negative corre- lational relationships. The general pattern of association of a positive Correlational relationship reveals that as the scores on one variable increase, the correspond- ing scores on the other variable also tend to increase. Figure 1.2a shows that as the loneliness scores increase, the corresponding shyness scores also tend to increase. The general pattern of association of a negative corre- lational relationship reveals that as the scores on one variable increase, the corresponding scores on the other variable tend to decrease. Figure 1.2b shows that as the shyness scores increase, the corresponding self-esteem scores tend to decrease.
- Martin Lee Abbott(Author)
- 2016(Publication Date)
- Wiley(Publisher)
11 Correlation Correlation has an intuitive appeal. Most everyone understands that Correlation is concerned with whether changes in one thing are linked to changes in something else. Thus, for example, you may observe that wealthier people seem to have better overall health than those with lower wealth levels. Or, stated differently, as wealth increases, health increases as well. Correlation is a way of understanding the association between two variables. What does association mean? It refers to “relatedness” or the extent to which two events “vary with one another.” To use this language with the wealth–health example just cited, you might say that the increase in wealth (however it is measured) is accom- panied by increases in health (according to its measures). In a general sense, you can say that the values of the one variable (health) change positively as the values of the other variable (wealth) increase. Thus, the values of both variables increase together, or “covary.” Not every Correlation is what it seems, however. There may be additional vari- ables not taken into account in the analysis that give the original two variables the “appearance of covarying.” This possibility of spuriousness (see Chapter 2) hints at the complexity of a seemingly obvious relationship. Is it really wealth that results in health, or is it something (or things) else? In this and the following chapters on regression, I intend to explore this question further. Using Statistics in the Social and Health Sciences with SPSS ® and Excel ® , First Edition. Martin Lee Abbott. © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. 330 Correlation THE NATURE OF Correlation I will examine Correlation in some depth in this chapter. It is a useful procedure for many reasons, and several methods of calculating Correlations exist that are adapted to the different natures of possible research questions.
eBook - PDFExperimental Design and Statistics for Psychology
A First Course
- Fabio Sani, John Todman(Authors)
- 2008(Publication Date)
- Wiley-Blackwell(Publisher)
For instance, you might want to explore the pos-sibility that self-esteem and salary are correlated with one another, and that they are both correlated with ‘years of education’. Also, you might want to measure which one among several variables is the best predictor of a given criterion variable. In this case you need to measure all the variables you want to inves-tigate, and apply some advanced procedures (e.g., partial Correlation, or multiple regression) that are beyond the scope of this book. (See the books by Howell and Allison in the ‘brief list of recommended books’.) SUMMARY OF CHAPTER • Sometimes researchers hypothesize that two variables are related (i.e., change together), without making claims about which variable influences which. These types of hypotheses are tested by means of ‘Correlational studies’. • A relationship between two variables can be explored by means of either Correlational analysis or regression analysis. • Correlational analysis is used to (i) describe the relationship between two variables in a visual and numerical fashion, and to (ii) test the statistical significance of the relationship. • To give a visual description of a relationship, researchers use the ‘scattergram’, which helps to form an idea of (i) the direction (whether it is positive or negative), (ii) the strength (magnitude) and (iii) the form (whether it is linear or non-linear), of the relationship under investigation. • The strength of a relationship can be expressed numerically by calculating a descriptive statistic called the ‘coefficient of Correlation’ (or r ), whose value ranges from − 1 to + 1. This can be calculated in several ways. Normally, the ‘Pearson’s product–moment Correlation coefficient’ (or r ) is used when para-metric assumptions are met (usually when there is an interval scale), while the ‘Spearman rank order Correlation’ ( r s or rho ) is used when parametric assumptions are not met (typically, when there is an ordinal scale).
eBook - PDFEssentials of Psychology
Concepts and Applications
- Jeffrey Nevid(Author)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
naturalistic observation method A method of research based on careful observation of behavior in natural settings. Famed naturalist Jane Goodall spent many years carefully observing the behavior of chimpanzees in their natural environment. AP Images/JEAN-MARC BOUJU Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26 CHAPTER 1 THE SCIENCE OF PSYCHOLOGY The Correlational Method Psychologists use the Correlational method to examine relationships between vari- ables. In Chapter 10, you will read about findings that show a Correlation, or link, between optimism and better psychological adjustment among cancer pa- tients. In Chapter 9, you will see that maternal smoking during pregnancy is correlated, unfortunately, with increased risk of sudden infant death syndrome (SIDS) in babies. A Correlation coefficient is a statistical measure of association between two variables. Correlation coefficients can vary from 21.00 to 11.00. Coefficients with a positive sign represent a positive Correlation in which higher values on one variable are associated with higher values on the other variable (for example, people with higher levels of education tend to earn higher incomes; see ■ Figure 1.8). A negative Correlation, which is denoted by a negative sign, means the reverse: Higher values on one variable are associated with lower values on the other. For example, the longer people are deprived of sleep, the less alert they are likely to be. The size of the Correlation expresses the strength or magnitude of the relationship between the variables.
eBook - PDF- Douglas Bernstein, , , (Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
If the Correlation between two variables is positive — if they both move in the same direction—the Correlation coefficient will have a plus sign in front of it. If there is a minus sign, the Correlation is negative, and the two variables will move in opposite directions. The larger the Correlation coefficient, the stronger the relationship between the two variables. The strongest possible relationship is indicated by either 1 1.00 or 2 1.00. A Correlation of .00 indicates that there is no relationship between variables. Correlation coefficients describe the results of Correlational research to help evaluate hypotheses, but psychological scientists must be extremely careful when interpreting what Correlations mean. The mere fact that two variables are correlated does not guarantee that one causes an effect on the other. And even if one variable actually does cause an effect on the other, a Correlation coefficient can’t tell us which variable is influencing which, or why (see Table 2.1). As an example of this important point, consider the question of how aggression develops. Correlational studies of observational data indicate that children who are in day care for more than thirty hours a week are more aggressive than those who stay at home with a parent. Does separation from parents cause the greater aggressiveness with which it is associated? It might, but psychologists must be careful about jumping to such a conclusion. What may seem an obvious explanation for a Correlational relationship may not always be correct. Perhaps the aggressiveness seen in some children in day care has something to do with the children themselves or with what happens to them in day care, not just with separation from their parents. One way scientists evaluate such alternative hypotheses is to conduct further Correlational studies to look for trends that support or conflict with those hypotheses (Rutter, 2007; West, 2009).
eBook - PDFStatistics for the Social Sciences
A General Linear Model Approach
- Russell T. Warne(Author)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
However, one variable that my students collected (video game scores) was ratio-level, and the second variable (intelligence test scores) was interval-level. Therefore, they needed a different analysis method to analyze their data. That statistical method is called Correlation, and it is the topic of this chapter. Learning Goals After studying this chapter you should be able to: • Explain the purpose of a Correlation and when it is appropriate to use it. • Calculate Pearson’ s r to measure the strength of the relationship between two variables. • Interpret the effect size (r 2 ) for a Correlation. Purpose of the Correlation Coefficient My students’ example of video game scores and intelligence test scores is typical of the types of data that social scientists calculate Correlations for. Because both variables are interval- or ratio-level data, it is usually not feasible to use any previous NHST procedures because interval-level data does not create discrete groups (e.g., two sets of scores created by a nominal variable). Rather, what is needed is a statistic that describes the relationship between two variables without using any nominal groups. That statistic is the Correlation coefficient. Definition of a Correlation A Correlation coefficient is a statistic that measures the strength of the relationship between two variables. If two variables have a relationship between them, we say that they are correlated. In fact, the word “related” is in the word correlated; the “cor-” prefix means “together, ” indicating that Correlation occurs when two things (in this case, variables) are related to one another. When there is a strong Correlation between two variables, there is a consistent pattern in the way that scores from each variable occur together. When there is a weak Correlation between two variables, the pattern of how scores occur together is inconsistent.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Correlation and Dependence In statistics, Correlation and dependence are any of a broad class of statistical relationships between two or more random variables or observed data values. Familiar examples of dependent phenomena include the Correlation between the physical statures of parents and their offspring, and the Correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the Correlation between electricity demand and weather. Correlations can also suggest possible causal, or mechanistic relationships; however, statistical dependence is not sufficient to demonstrate the presence of such a relationship. Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. In general statistical usage, Correlation or co-relation can refer to any departure of two or more random variables from independence, but most commonly refers to a more specialized type of relationship between mean values. There are several Correlation coefficients , often denoted ρ or r , measuring the degree of Correlation. The most common of these is the Pearson Correlation coefficient, which is sensitive only to a linear relationship between two variables (which may exist even if one is a nonlinear function of the other). Other Correlation coefficients have been developed to be more robust than the Pearson Correlation, or more sensitive to nonlinear relationships. ________________________ WORLD TECHNOLOGIES ________________________ Several sets of ( x , y ) points, with the Pearson Correlation coefficient of x and y for each set.
- Bruce M. King, Patrick J. Rosopa, Edward W. Minium(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
114 CHAPTER 7. Correlation Any report of r or r S values, therefore, should include a careful description of the measures used and the circumstances under which the Correlation coefficients were obtained. Similarly, values reported by others may or may not hold up under the conditions with which you are concerned. Take the others’ results only as working hypotheses, subject to confirmation under your conditions. 7.13 S U M M A R Y In behavioral science, it is often important to determine the degree to which two variables vary together. The two basic tasks are (1) determining the degree of association between two variables and (2) predicting a person’s standing in one variable when we know the standing in an associated variable. In this chapter, we dis- cussed the problem of association; we consider prediction in the next chapter. The Pearson product-moment Correlation coefficient, r, is the most commonly used measure of association when two quantita- tive variables are characterized by a linear (straight-line) relation- ship. It reflects agreement between relative standing in one variable and relative standing in the other and so is an index of how well bivariate data points hug the straight line of best fit. The sign of the coefficient specifies whether the two variables are positively or negatively (inversely) related. The magnitude of the coefficient varies from zero when no association is present to ±1.00 when the Correlation is perfect. Making a scatter diagram of the data points of a bivariate dis- tribution is an excellent preliminary step to see whether there is any association between two variables. It also provides a rough check on the accuracy of the calculated value of r, and it lets us examine several conditions (such as the linearity of the rela- tionship) that may influence the Correlation coefficient and its interpretation. We can use Spearman’s Correlation coefficient, r S , in place of Pearson’s r if the paired observations are converted to ranks.
eBook - PDF- Catherine A. Sanderson, Saba Safdar(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
Figure 2.2 shows the different types of Correlations. In some cases, we don’t have to worry about the direction of the association between two variables because if one of the variables is fixed (cannot change), we can be certain that it was not caused by the other variable. For example, if we conduct a naturalistic observation study and find that men are more aggressive than women, we can be sure that the aggression did not lead to their gender (a fixed variable). Similarly, if the data regarding the two variables were collected at two different periods of time, we can be certain that the second variable could not have caused the first variable. For example, if we measure students’ attendance for a social psy- chology class in a given semester and then measure their academic performance in the course at the end of the semester, we might find that attendance is a good predictor of academic per- formance in the course, but not the other way around. However, even in cases where it is clear that one of the variables could not have caused the other, we still can’t be certain that the other variable causes the Correlation between the two variables. There is still a possibility that a third variable caused them both, explaining the observed association between the two variables. For example, hair loss and coronary heart disease are positively correlated: people who are bald are more likely to have coronary heart disease. However, it would be inaccurate to say that balding causes coronary heart disease; rather, both balding and coronary heart disease are the result of getting older (the “third variable” in this example). Figure A shows a positive Correlation (as student grades increase, positive professor evaluations increase), Figure B shows a negative cor- relation (as hostility increases, number of friends decreases), and Figure C shows no Correlation (as physical attractiveness increases, number of colds doesn’t change).
- Aparna Raghvan(Author)
- 2020(Publication Date)
- Society Publishing(Publisher)
Causal, Comparative, and Correlational Approaches in ... 137 Experimental research is a type of research in which the primary equivalence amongst research participants is done by creating more than one group. After the creation of a group, manipulation of a provided experience for these groups is done and then the measurement of the influence of this manipulation. Each of the three research designs differs according to their pros and cons. More than focusing on the pros and cons, it is very important to understand what the difference in each of the research designs is. 6.2. CorrelationAL RESEARCH: SEEKING RELA-TIONSHIPS AMONG VARIABLES Correlational research is in contrast to the descriptive research. Descriptive research is designed in order to provide primarily the static illustrations or pictures. On the other hand, the Correlational research comprises the measurement of two or more variables which are relevant to the research. Then, an assessment of the association or relationship that exists between these variables is done. For example, the variables of height and weight are methodically related or correlated for the simple reason that the taller people usually weigh more than shorter people. Similarly, the time dedicated to the study and the memory mistakes are also correlated. This is so because the more time a person dedicates to study a topic or a list of words, the fewer errors he or she will make.In the case when there are two variables present in the research design, one of the variables is known as the predictor variable. The other variable is known as the outcome variable. One method of arranging or organizing the data from a Correlational study with two variables is by using a graph. A graph is used to illustrate the values of every measured variable. This illustration can be done with the help of a scatter plot. A scatter plot is a kind of visual or pictorial representation of the relationship that exists between the two variables.
eBook - PDF- Douglas G. Altman(Author)
- 1990(Publication Date)
- Chapman and Hall/CRC(Publisher)
While this way of looking at large numbers of variables can be helpful when one really has no prior hypotheses, significant associations really need to be confirmed in another set of data before credence can be given to them. Another common problem of interpretation occurs when we know that each of two variables is associated with a third variable. For example, if A is positively correlated with B and B is positively correlated with C it is tempting to infer that A must be positively correlated with C. Although this may indeed be true, such an inference is unjustified - we cannot say anything about the Correlation between A and C. The same is true when one has observed no association. For example, in the data of Mazess et al. (1984) the Correlation between age and weight was 0.05 and between weight and %fat it was 0.03 (Figure 11.3). This does not imply that the Correlation between age and %fat was also near zero. In fact this Correlation was 0.79, as we saw earlier (Figure 11.1). These three two-way relations are shown in Figure 11.8. Correlations cannot be inferred from indirect associations. Correlation is often used when it would be better to use regression methods, discussed in section 11.10 onwards. The two methods are compared in section 11.17. Interpretation of Correlation 299 Figure 11.8 Scatter diagrams showing each two way relation between age, %fat, and weight of 18 normal adults (Mazess et al., 1984) . 11.9 P R E S E N T A T I O N OF C O R R E L A T I O N Where possible it is useful to show a scatter diagram of the data. In such a graph it is often helpful to indicate different categories of observations by using different symbols, for example to indicate patients' sex. The value of r should be given to two decimal places, together with the P value if a test of significance is performed.
eBook - PDFStatistics for the Social Sciences
A General Linear Model Approach
- Russell T. Warne(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
This is probably surprising because the Correlation with just 10 individuals was much smaller: +0.221. This discrepancy occurred because Pearson’ s r values are unstable when sample sizes are small – a characteristic that r shares with every other sample statistic. Therefore, to obtain stable Correlations you must have a large sample size. Stronger Correlations stabilize with smaller samples than do weaker Correlations. Larger sample sizes are also required for 348 Correlation Warning: Correlation Is Not Causation A Correlation quantifies the strength of a relationship between an independent and a dependent variable. It is because of this function of a Correlation that we can interpret the Pearson’ s r values in Table 12.8 and understand the strength and direction of a Correlation between two variables. There is a temptation, though, to interpret a relationship between two variables as an indication that changes in the independent variable cause changes in the dependent variable. For example, Table 12.8 indicates that the Correlation between depression and job satisfaction is r = –0.43 (Faragher et al., 2005), meaning that people with higher levels of depression tend to be less satisfied with their jobs. Some readers may believe that this Correlation indicates that higher levels of depression cause individuals to be less satisfied with their jobs. Although this interpretation is seductive, it is not the only possible interpretation of a Correlation. There are three different interpretations (i.e., models) that a Correlation can support. These possible interpretations are shown in Figure 12.6. The first possibility is that the changes in the independent variable (X) cause changes in the dependent variable (Y). The second possibility is that changes in the dependent variable (Y) cause changes in the independent variable (X). The final possibility is that a third, unknown variable (Z) can cause changes in X and Y.
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