What Is Correlation? How to Read Correlation Coefficients in SPSS

What Is Correlation

Correlation measures the strength and direction of the relationship between two variables. In quantitative research, correlation usually refers to the Pearson correlation coefficient, written as r. This coefficient shows whether two variables tend to change together, but it does not by itself prove that one variable causes the other.

The value of r ranges from -1 to 1. A positive r means that the two variables tend to increase or decrease in the same direction. A negative r means that when one variable increases, the other tends to decrease. The closer r is to 0, the weaker the linear relationship. The Pearson formula is:

r = Cov(X,Y) / (SD(X) × SD(Y))

Here, Cov(X,Y) is the covariance between X and Y, while SD(X) and SD(Y) are the standard deviations of the two variables. You usually do not need to calculate this formula by hand. SPSS calculates r from the numerical data columns you provide, such as the mean scores for the CL, HL, and YD scales.

Correlation is appropriate when you want to examine whether two quantitative variables have a linear relationship. If the data contain strong outliers, a curved relationship, or variables measured at an ordinal level, Pearson correlation may not represent the situation accurately. Check the data before interpreting the result, just as you would when handling outliers in quantitative data.

The Meaning of Correlation in Quantitative Research

Correlation is often used during exploratory data analysis and as preparation for regression analysis. For example, you may hypothesize that service quality is related to satisfaction. The r coefficient helps you see whether the two variables vary together in your survey sample.

In a research model, correlation can answer three practical questions. First, is the direction of the relationship positive or negative. Second, is the relationship weak or strong. Third, does the p-value provide sufficiently clear statistical evidence of the relationship.

You need to separate the magnitude of correlation from statistical significance. A small r can have a p-value below 0.05 when the sample size is large. Conversely, a relatively large r may not reach statistical significance when the sample is small or the data are highly dispersed. Do not look only at r and conclude that a correlation exists. Read Pearson Correlation, Sig. (2-tailed), and N together in the output table.

Correlation can also provide an initial check of whether independent variables may be too similar before you run regression. Do not use one correlation threshold alone to conclude that multicollinearity exists. After running the regression, also check VIF and tolerance in the Coefficients table.

If your topic includes a mediator or moderator, correlation is only initial information. It does not replace mediation or moderation analysis. You can also review the explanations of mediator, moderator, and moderating so that you do not treat these concepts as one single type of relationship.

What Correlation Value Is Acceptable

There is no single r value that applies to every topic. Whether a result is acceptable depends on the research question, the direction of the hypothesis, the sample size, and the theoretical context. You can use the levels below as descriptive conventions, but do not turn them into fixed rules if your department's methods guidance requires something different.

Some sources describe the absolute size of r using weak, moderate, and strong ranges. Those ranges depend on the field and the purpose of the research. For example, a small correlation in consumer behavior may still deserve attention if the variable has theoretical importance and the result is stable.

For the p-value, distinguish statistical significance from practical significance. If Sig. (2-tailed) < 0.05, you can reject H0 that the correlation equals 0 at the 5% significance level, provided the test conditions are appropriate. This result does not show that the effect is large, does not show a causal relationship, and does not confirm the hypothesis if the sign of r is opposite to the predicted direction.

How to Read Correlation in the Output

In SPSS, open Analyze > Correlate > Bivariate. Move the variables you want to check into the Variables box, keep Pearson selected, choose Two-tailed, and click OK. If your hypothesis has a clear direction, a one-tailed test should be specified in advance in the research design, rather than selected after you see the result.

The table below is illustrative output, not the result of a real study. The column names follow the SPSS Correlations table.

Suppose HL represents satisfaction and CL represents service quality. The Pearson Correlation = 0.462 indicates a positive linear relationship of moderate size under the usual descriptive interpretation. In practical terms, respondents with higher service-quality scores in the sample also tend to have higher satisfaction scores.

In SPSS, Sig. (2-tailed) = .000 should not be written as an absolute p-value of zero. If the table displays .000, you can write that p is less than 0.001. With N = 218, the correlation in this example is statistically significant at the 5% threshold. The ** symbol marks a correlation that is significant at the 0.01 level in SPSS, but you should still read the Sig. (2-tailed) row instead of relying only on the asterisk.

Check the symmetric matrix. The correlation between HL and CL must be the same as the correlation between CL and HL. The diagonal cells equal 1 because a variable is being correlated with itself. Dots often appear in the diagonal Sig. cells because SPSS does not test the significance of a variable correlated with itself.

How to write this in your thesis

You can adapt the wording as follows: “The Pearson correlation analysis shows that CL has a positive correlation with HL, with r = [r value], p [< or >] [significance level], N = [sample size]. This result [partially supports/does not support] the expected direction of the relationship between the two variables.” Replace every bracketed section with the actual values from your file.

What to Do When the Correlation Is Not Acceptable

First, identify what “not acceptable” means in your case. The p-value may be larger than the significance level, r may have the opposite sign from the hypothesis, r may be too small in practical terms, or the data may not meet the conditions for Pearson correlation. Each situation calls for a different response.

Check the Coding and Variable Calculation

Open Variable View and check reverse-coded variables. If an item is worded negatively but has not been reverse-coded, the scale mean may be pulled in the wrong direction. Then check missing values, codes such as 99 or 999, and whether you included nonresponse codes when calculating the mean.

If you ran the correlation on individual items instead of the composite score or mean score of a scale, the result may fluctuate substantially. Before making changes, record how you created the variable and compare it with the method specified in your proposal.

Check Outliers and the Shape of the Relationship

Create a scatterplot for the two variables. A few points far from the rest can increase or decrease r substantially. Do not delete a point simply because it makes the p-value look better. Check whether it is a data-entry error, an invalid respondent, or a genuine observation from the target population.

If the relationship is curved, Pearson correlation may be low even though the variables are related. Describe the limitation of Pearson accurately and consider a test appropriate for the type of data, rather than forcing the result into a linear relationship.

Reconsider the Hypothesis and Sample Size

A correlation that is not statistically significant does not prove that the theory is certainly wrong. The population effect may be small, the sample may contain insufficient information, the scale may not be suitable, or the research context may differ from earlier studies. Report the nonsignificant result and explain it using the limits of the data and research design.

Do not collect additional data solely to push the correlation below a p-value of 0.05. Adding cases requires a clear methodological reason, consistent sampling criteria, and approval from your supervisor. If the sample was collected according to the plan, retaining the nonsignificant result is usually more defensible than changing the data after viewing the output.

Distinguishing Correlation from Regression

Correlation measures the degree of association between two variables, while regression builds an equation to estimate a dependent variable from one or more independent variables. In correlation, X and Y have symmetric roles. Reversing the order of the variables gives the same r. In regression, changing which variable is independent and which is dependent changes the model, coefficients, and interpretation.

For example, CL and HL have r = 0.462. You can state that the two variables have a positive correlation in the sample. You cannot write that service quality increases satisfaction based only on r. If you run a regression with HL as the dependent variable and CL as the independent variable, you will also read R Square, ANOVA, Coefficients, the B or Beta coefficient, and the p-value of the regression coefficient.

Correlation also does not show the influence of other variables. If the relationship between CL and HL is affected by age, income, or service-use frequency, multiple regression allows you to include those variables in the same model. Even then, regression still requires a research design and theoretical reasoning for interpretation. An observed statistical result should not be turned into causal evidence automatically.

You also need to distinguish correlation from covariance. Covariance depends on the measurement units, so it is difficult to compare across pairs of variables. Pearson correlation standardizes covariance to a range from -1 to 1, which makes it easier to report in a thesis.

Common Errors

The first error is writing, “The correlation is 0.462, so CL affects HL.” This confuses correlation with causation. Use verbs such as “has a positive correlation,” “has a linear association,” or “varies in the same direction in the sample,” unless the research design supports a stronger conclusion.

The second error is reporting only r and omitting the p-value and N. A correlation coefficient without its sample size and significance level makes it difficult for the reader to assess the result. At a minimum, report r, the p-value, and the sample size in the results table.

The third error is treating a small p-value as evidence of a strong relationship. The p-value reflects evidence against the hypothesis that r equals 0 in the sample, while the size of r reflects the strength of the association. These two figures answer different questions.

The fourth error is running dozens of correlation pairs and reporting only the pairs with small p-values. When you conduct many tests, the risk of obtaining a significant result by chance increases. Define the variables to be tested from the model and hypotheses before opening SPSS.

The fifth error is using correlation as a substitute for testing scale reliability and validity. If you are building a latent variable from multiple items, check Cronbach's Alpha, corrected item-total correlation, and the appropriate EFA or PLS-SEM procedures. You can read what is a scale to distinguish a scale from a single variable.

Frequently asked questions

What is a correlation coefficient

A correlation coefficient measures the direction and strength of the relationship between two variables. For Pearson correlation, r ranges from -1 to 1. The sign of r shows the direction of the relationship, while the absolute size of r indicates how close or distant the linear relationship is.

What correlation value is acceptable

There is no single r threshold for every topic. Check whether the direction of r matches the hypothesis, whether the p-value meets the selected significance level, and whether the size of r has practical meaning in your field.

Is correlation the same as regression

The concepts are related but different. Correlation describes a symmetric association between two variables, while regression assigns independent and dependent variables to estimate and test a specific model.

What does Sig. 0.000 mean in the Correlations table

The .000 value is how SPSS displays a p-value that has been rounded in the table. Write that p is less than 0.001 rather than writing p equals 0. The result provides strong statistical evidence under the significance level you selected, but it does not by itself show that the correlation is strong or causal.

Is a negative correlation a bad result

A negative correlation only means that the two variables tend to vary in opposite directions. It may fit the hypothesis completely if an inverse relationship was predicted, such as pressure increasing while satisfaction decreases. Check the variable coding and the theoretical interpretation before calling it a bad result.

Open your data file, check the coding again, create the variables required for the analysis, and run Analyze > Correlate > Bivariate. If you need a reference for the analysis steps, use the Statistics topic, or upload your .sav or .csv file to M4 analysis in DoThesis to run and read the results using your own data.