# Correlation & Analysis

Correlations

1. What is the definition of a correlation and why would a researcher be interested in using this type of analysis?
2. What is another name for a Positive relationship and a Negative relationship?
3. Describe the association between two variables when the relationship is Negative.
4. Is a correlation a good way to determine cause-and-effect? Why or why not?
5. When a large number of cases are examined and a positive relationship is found, what else should one expect to find?

Conduct a correlational analysis on the following example:

Example: A school psychologist is interested in determining if test anxiety is affecting her students’ performance on their exams. She randomly selected 103 students from her school and conducted a correlational analysis to try and answer her question. She hypothesized that as anxiety increases, test performance decreases.

Based on this example answer the following questions:

1. Why is a correlational analysis the most appropriate technique to test her hypothesis?
2. Use the data set provided and conduct a Bivariate Correlational Analysis using SPSS.

Hint: In the Bivariate Correlations dialogue box in SPSS, select Pearson. Create a Simple Scatterplot with Exam Performance on the Y-axis and Exam Anxiety on the X-axis.

1. Observe and briefly explain the trend seen in the Scatterplot (1-2 sentences).
2. What is the strength and direction of the relationship between Performance and Anxiety?
3. Based on these findings, can she infer that one variable Causes the other (i.e., cause-and-effect)? Why or why not?
4. Discuss the findings using Morgan et al. (2002)

Provide examples of the following using variables and a made up correlation to illustrate your point:

1. Strong positive (direct) correlation

Construct your response like the example given here: A strong positive correlation exists between study time and GPA (r = .74). That is, as study time increases so does GPA.

1. Weak positive correlation
2. Strong negative (inverse) correlation
3. Weak negative correlation

Solution

1. A correlation is simply defined as a relationship between two variables. The whole purpose of using correlation in research is to figure out which variables are connected to each other.
2. When there is positive relationship between two variables, it is often said that there is positive correlation between these two variable and similarly negative relationship is often termed as negative correlation.
3. Negative relationship implies that the high values on one variable are associated with the low values on the other.
4. A correlation between variables does not automatically mean that the change in one variable is the cause of the change in values of the other variable.

Example: smoking causes an increase in the risk of developing lung cancer, or it can correlate with another (e.g. smoking is correlated with alcoholism, but it does not cause alcoholism).

1. When a large number of cases are examined and a positive relationship is found, then one should expect to find a positive slope and a linear relationship.
 Exam Performance (%) Exam Anxiety Exam Performance (%) Pearson Correlation 1 -.441** Sig. (2-tailed) .000 N 103 103 Exam Anxiety Pearson Correlation -.441** 1 Sig. (2-tailed) .000 N 103 103
1. The correlational analysis is the most appropriate techniques because this technique allows us to test whether the correlation is significantly different from 0 or not.
2. Correlations:

**Correlation is significant at 0.01 level (2-tailed)

Graph: 1. From the scatterplot we can observe that most of the student have anxiety score more than 60 and indicating a negative relationship between exam performance and anxiety scores.
2. From the correlation results, we have correlation coefficients -0.441 which indicates a moderate strength of this negative relationship between exam performance and anxiety.
3. The correlation coefficient for exam performance and anxiety score is -0.441 which is moderate negative correlation between them. S on the basis of this analysis we can’t infer that one variable causes another variable because correlation just gives us information about the strength and the direction of the relationship.
1. A strong positive correlation exists between study time and GPA (r = .74). That is, as study time increases so does GPA.
2. A weak positive correlation exist between age and lung cancer for non-smokers (r = .23). As age increases the chance of lung cancer also gets increases for non-smokers.
3. A strong negative correlation between time and speed (r = -0.80). As one drives fast it takes less time to cover the certain distance than those who drive slowly.
4. A weak negative correlation exist between crime and popularity (r = -0.18). As much one gets popular, the less he will be involved in crime.