Population:

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Correlational Research

IndroductionCorelation refers us relationship between two variables. For example, we could look at the relationship between age and health and ask whether health improves or declines with age. We could also look at the relationship between age and cognitive decline and see if these two variables are related. Below is another example that shows a relationship between two variables:

This example shows that there is a relationship between watching violence on TV and aggressive behavior. However, when we look at correlations we must be aware of three issues:

Correlations does not equal causation

We cannot infer a causal relationship. We cannot say that watching violent TV programs causes people to be more aggressive. All we can say is that there is a relationship between these two variables.

Correlations are bi-directional

The reason we cannot infer causation is that correlations are bi-directional (as represented by the two arrow heads between TV violence and aggression). It is not clear whether watching TV causes aggression or whether aggressive people simply like to watch violent programs.

Third-variable or Alternative Explanations As can be seen in the above diagram, a relationship between two variables does not rule out the possibility that other variables may be important in determining TV watching and aggression. Other variables such as family background, parenting styles, socio-economic-status, the person's personality, or peers may be affecting this relationship.

Correlational studies are used to show the relationship between two variables. Unlike experimental studies, however, correlational studies can only show that two variables are relatedthey cannot determine causation (which variable causes a change in the other). A correlational study serves only to describe or predict behavior, not to explain it. In psychological research, it is important to remember that correlation does not imply causation; the fact that two variables are related does not necessarily imply that one causes the other, and further research would need to be done to prove any kind of causal relationship.

Background and Purpose of Correlation Research

The importance of corre ation research has been emphasised by authors such as Woodworth who published a book entitled Experimental Psychology in 1938 (Woodworth 1938) and Lee Cronbach who published an article entitled The Two Disciplines of Scientific Psychology (Cronbach 1957) woodworth established two major distinctions in quantitative research methods; the distinction between (a) independent and dependent variables and (b) experimental and correlational methods. According to Woodworth, experimental designs/methods are characterised by manipulation of variables while a correlational design/method measures two or more characteristics from the same person and then calculates the correlation between the characteristics. In Woodworths view these two research approaches had equal value correlational research must be distinguished from the experimental method, but standing on apar with it in value, rather than above or below..... (Woodworth 1938:3). Cronbach was also concerned about the fact that correlational research had second-rate status in scientific 3psychology. He believed that asynthesis should take place with advocates of each design valuing them equally, and utilising both strategies. As Cronbach puts it It is not enough for each discipline to borrow from the other.

Correlational psychology studies only variance among organisms; experimental psychology studies only variance among treatments. A united discipline will study both of these, but it will also be concerned with the otherwise neglected interactions between organismic and treatment variables. (Cronbach 1957:681). Whether this synthesis happened remains debatable but issue/topic is certainly worthy of further discussion elsewhere. Interestingly many text books including nursing books provide little discussion on correlational research, with several providing one to three pages in chapters entitled.Data Collection in Correlational Research

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. However, because some approaches to data collection are strongly associated with correlational research, it makes sense to discuss them here. The two we will focus on are naturalistic observation and archival data. A third, survey research, is discussed in its own chapter.

Naturalistic Observation

Naturalistic observation is an approach to data collection that involves observing peoples behavior in the environment in which it typically occurs. Thus naturalistic observation is a type of field research (as opposed to a type of laboratory research). It could involve observing shoppers in a grocery store, children on a school playground, or psychiatric inpatients in their wards. Researchers engaged in naturalistic observation usually make their observations as unobtrusively as possible so that participants are often not aware that they are being studied. Ethically, this is considered to be acceptable if the participants remain anonymous and the behavior occurs in a public setting where people would not normally have an expectation of privacy. Grocery shoppers putting items into their shopping carts, for example, are engaged in public behavior that is easily observable by store employees and other shoppers. For this reason, most researchers would consider it ethically acceptable to observe them for a study. On the other hand, one of the arguments against the ethicality of the naturalistic observation of bathroom behavior discussed earlier in the book is that people have a reasonable expectation of privacy even in a public restroom and that this expectation was violated.

Types

There are three types of correlations that are identified:

1. Positive correlation: Positive correlation between two variables is when an increase in one variable leads to an increase in the other and a decrease in one leads to a decrease in the other. For example, the amount of money that a person possesses might correlate positively with the number of cars he owns.

2. Negative correlation: Negative correlation is when an increase in one variable leads to a decrease in another and vice versa. For example, the level of education might correlate negatively with crime. This means if by some way the education level is improved in a country, it can lead to lower crime. Note that this doesn't mean that a lack of education causes crime. It could be, for example, that both lack of education and crime have a common reason: poverty.

3. No correlation: Two variables are uncorrelated when a change in one doesn't lead to a change in the other and vice versa. For example, among millionaires, happiness is found to be uncorrelated to money. This means an increase in money doesn't lead to happiness.A correlation coefficient is usually used during a correlational study. It varies between +1 and -1. A value close to +1 indicates a strong positive correlation while a value close to -1 indicates ROLE OF CORRELATIONAL RESEARCH

Correlational research has played an important role in the history of educational and psychological research. Early on, the bivariate correlation was used in heredity research and then eventually expanded into all areas of educational and psychological inquiry. Subsequently more sophisticated multivariate extensions enabled researchers to examine multiple variables simultaneously. Correlational research has had and will continue to have an important role in quantitative research in terms of exploring the nature of the relations among a collection of variables. In part, unrelated variables can be eliminated from further consideration, thereby allowing the researcher to give more serious consideration to related variables.

Correlational research can also play an important role in the development and testing of theoretical models. Once the nature of bivariate relations has been determined, this information can then be used to develop theoretical models. The idea here is to attempt to explain the nature of the bivariate correlations rather than to simply report them. At this point, methods such as factor analysis, path analysis and structural equation modeling can come into play.Statistical SignificanceA statistically significant relationship is one that is large enough to be unlikely to have occurred in the sample if there's no relationship in the population. The issue of whether a result is unlikely to happen by chance is an important one in establishing cause-and-effect relationships from experimental data. If an experiment is well planned, randomization makes the various treatment groups similar to each other at the beginning of the experiment except for the luck of the draw that determines who gets into which group. Then, if subjects are treated the same during the experiment (e.g. via double blinding), there can be two possible explanations for differences seen: 1) the treatment(s) had an effect or 2) differences are due to the luck of the draw. Thus, showing that random chance is a poor explanation for a relationship seen in the sample provides important evidence that the treatment had an effect.

The issue of statistical significance is also applied to observational studies - but in that case there are many possible explanations for seeing an observed relationship, so a finding of significance cannot help in establishing a cause-and-effect relationship. For example, an explanatory variable may be associated with the response because:

Changes in the explanatory variable causes changes in the response;

Changes in the response variable causes changes in the explanatory variable;

Changes in the explanatory variable contribute, along with other variables, to changes in the response;

A confounding variable or a common cause affects both the explanatory and response variables;

Both variables have changed together over time or space; or

The association may be the result of coincidence (the only issue on this list that is addressed by statistical significance).

Pearson's Correlation Coefficient

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another. In positively correlated variables, the value increases or decreases in tandem. In negatively correlated variables, the value of one increases as the value of the other decreases.

Correlation coefficients are expressed as values between +1 and -1. A coefficient of +1 indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable. A coefficient of -1 indicates a perfect negative correlation: A change in the value of one variable predicts a change in the opposite direction in the second variable. Lesser degrees of correlation are expressed as non-zero decimals. A coefficient of zero indicates there is no discernable relationship between fluctuations of the variables.

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables.

The first step in studying the relationship between two continuous variables is to draw a scatter plot of the variables to check for linearity. The correlation coefficient should not be calculated if the relationship is not linear. For correlation only purposes, it does not really matter on which axis the variables are plotted. However, conventionally, the independent (or explanatory) variable is plotted on the x-axis (horizontally) and the dependent (or response) variable is plotted on the y-axis (vertically).

The nearer the scatter of points is to a straight line, the higher the strength of association between the variables. Also, it does not matter what measurement units are used.

Values of Pearson's correlation coefficient

Pearson's correlation coefficient (r) for continuous (interval level) data ranges from -1 to +1:

r=-1data lie on a perfect straight line with a negative slope

r=0no linear relationship between the variables

r=+1data lie on a perfect straight line with a positive slope

Positive correlation indicates that both variables increase or decrease together, whereas negative correlation indicates that as one variable increases, so the other decreases, and vice versa.

RANGE OF THE CORRELATION COEFFICIENT

The graphic shows that the correlation coefficient (little r) can range from a -1 through 0 to a +1. If you get a value outside that range you have made a mistake calculating little r.Notice that values of r less than 0 indicate a negative or inverse relationship between variables.Notice that values of r greater than 0 indicate a positive or direct relationship between variables.Finally, notice that a value of r = 0 indicates no relationship between variables. The farther the r value is from zero, the greater the relationship.Benefits of Correlational Research

An experiment is not always the most appropriate approach to answering a research question. Sometimes it is not possible to carry out a true experiment for practical or ethical reasons because it is impossible to manipulate the independent variable. If a researcher was to look at the psychological effects of long-term ecstasy use, it would not be ethical to randomly assign participants to a condition of long-term ecstasy use. An experiment is also not feasible when examining the effects of personality and individual differences since participants cannot be randomly assigned into these categories. Correlational research allows a researcher to determine if there is a relationship between two variables without having to randomly assign participants to conditions.

The strength of correlational research is its predictive capabilities. With a large sample size, you can use one variable to predict the likelihood of the other when there is a strong correlation between the two. For instance, you could take two measurements from 1,000 familieswhether the father is an alcoholic and whether a son is an alcoholicand calculate the correlation. If there is a strong correlation between the two measurements, it will allow you to predict, within certain limits of probability, what the chances are that the son of an alcoholic father will also have a problem with alcohol.

1. Most of the variables show some kind of relationship. For instance, there is relationship between price and supply, income and expenditure etc. With the help of correlation analysis we can measure in one figure the degree of relationship.

2. Once we know that two variables are closely related, we can estimate the value of one variable given the value of another. This is known with the help of regression.

3. Correlation analysis contributes to the understanding of economic behavior, aids in locating the critically important variables on which others depend.

4. Progressive development in the methods of science and philosophy has been characterized by increase in the knowledge of relationship. In nature also one finds multiplicity of interrelated forces.

5. The effect of correlation is to reduce the range of uncertainty. The prediction based on correlation analysis is likely to be more variable and near to reality.

Limitations of Correlational Research

A correlational study serves only to describe or predict behavior, not to explain it. Always remember that correlation does not imply causation. Since there is no random assignment to conditions, a researcher cannot rule out the possibility that there is a third variable affecting the relationship between the two variables measured. Even if there is no third variable, it is impossible to tell which factor is influencing the other. Only experimental research can determine causation. In the above example, while a research could predict the likelihood of an alcoholic father having an alcoholic son, they could not describe why this was the case.

An excellent example used by Li (1975) to illustrate the "third variable" problem is the positive correlation in Taiwan in the 1970's between the use of contraception and the number of electric appliances in one's house. Of course, using contraception does not induce you to buy electrical appliances or vice versa. Instead, the third variable of education level affects both.

Another popular example is that there is a strong positive correlation between ice cream sales and murder rates in the summer. As ice cream sales rise, so do murder rates. Is this because eating ice cream makes us want to murder people? The actual explanation is that when the weather is hot, more people buy ice cream, but they also go out more, drink more, and socialize more, leading to an increase in murder rates. Extreme temperatures observed in the summer also have been shown to increase aggression. In this case, there are many other variables at play that feed the correlation between murder rates and ice cream sales.

ISSUES IN CORRELATIONAL RESEARCH

When consuming or conducting correlational research, there are a number of issues to consider, with some issues being positive and others negative in nature. On the positive side, once descriptive research has helped to identify the important variables, correlational research can then be used to examine the relations among those important variables. For example, researchers may be interested in determining which variables are most highly related to a particular outcome, such as student achievement. This can then lead into experimental research in which the causal relations among those key variables can be examined under more tightly controlled conditions. Here one independent variable can be manipulated by the researcher (e.g., method of instruction), with other related variables being controlled in some fashion (e.g., grade, level of school funding). This then leads to a determination of the impact of the independent variable on the outcome variable, allowing a test of strong causal inference.

On the negative side, a limitation of correlational research is that it does not allow tests of strong causal inference. For example, if researchers find a high bivariate correlation between amount of instructional time (X) and student achievement (Y), then they may ask if this correlation necessarily implies that more instructional time causes higher achievement. The answer is not necessarily. Two variables X and Y can be highly correlated for any of the following reasons and others: (a) X causes Y; (b) Y causes X; (c) Z causes both X and Y, but X and Y are not causally related; (d) X and Y both cause Z, but X and Y are not causally related; and (e) many other variables might be involved. In addition, for a causal relationship X must occur before Y. Thus a bivariate correlation coefficient gives information about the nature of the relations between two variables, but not why they are related. Theoretical models of educational and psychological phenomena tend to be rather complex, certainly involving more than simply two variables. More sophisticated correlational methods, such as factor analysis, path analysis, or structural equation modeling, have the ability to examine the underlying relations among many variables and can, therefore, be used as a basis to argue for causal inference.

Another limitation of correlational methods is they commonly suggest that the variables are linearly related to one another. For example, variables X and Y can be shown to have a linear relationship if the data can be nicely fitted by a straight line. When variables are not linearly related, correlational methods will reduce the strength of the relationship (in other words, the linear relation will be closer to zero). Therefore, nonlinear relationships will result in smaller linear correlations, possibly misleading the researcher and the field of inquiry. Outliers, observations that are quite a bit different from the remaining observations, will also reduce the strength of the relationship. It is wise for researchers to examine their data to see if (a) variables are linearly related (e.g., by the use of scatterplots), and (b) there are any influential observations (i.e., outliers).ConculusionFindings from correlational research can be used to determine prevalence, relationships among variables and to forecast events from current data and knowledge. In spite of its many uses however, Prudence is required when using the design and analysing data . To assist researchers in reducing mistakes key issues were sing led out for discussion and several options put forward for analysing data.

A final limitation of correlational research occurs when a researcher seeks to consider the relations among every possible variable. The idea is if researchers examine the relations among enough variables, then certainly some variables will be significantly related. While there is an exploratory consideration here, in terms of seeing which variables are related, there is a statistical consideration as well. That is, if researchers examine enough bivariate correlations, they will find some variables that are significantly related by chance alone. For example, if they examine 100 correlations at the .05 level of significance, then they expect to find five correlations that appear to be significantly different from zero, even though these correlations are not truly different from zero. In this case, the more sophisticated multivariate correlational methods can be useful in that fewer tests of significance tend to be done than in the bivariate case.

Correlational methods of inquiry have been popular in educational and psychological research for quite some time in part because they are foundational in nature in terms of their ability to examine the relations among a number of variables. Also, correlational methods can be used to develop and test theoretical models (e.g., factor analysis, path analysis, structural equation modeling). Despite the limitations of correlational research described here, these methods will continue to be used. Additional information on correlational methods can be found in Grimm and Yarnold (1995, 2000), Lomax (2007), and Schumacker and Lomax (2004).