What Does Correlated Mean? How to Read Correlation Coefficients in SPSS

What does correlated mean

In SPSS output, you may see correlated in expressions such as Correlations, Pearson Correlation, or Correlated Variables. The term describes a situation in which two variables are related. When one variable changes, the other tends to change in the same direction or in the opposite direction to some extent.

In quantitative research, the statistic you usually read is the Pearson correlation coefficient, written as r. Its general formula is:

r = Cov(X, Y) / (SDX × SDY)

The value of r ranges from -1 to +1. A positive value indicates that the two variables tend to increase together. A negative value indicates that one variable tends to increase when the other decreases. A value close to 0 indicates a weak or unclear linear correlation in the sample. The word correlated by itself does not tell you whether the relationship is strong or statistically significant. You must also read the absolute value of r, the Sig. (2-tailed) column, and the number of observations shown as N.

If variable CL correlates with HL at r = 0.62, you can say that the two variables have a positive linear correlation in the sample being analysed. You cannot write that CL causes HL, because correlation and causation support different conclusions.

If you are working through several related terms at once, you can also review Statistics to compare how related output tables are read.

What correlated means in quantitative research

Correlation helps you answer an initial question about the degree of association between variables. Before running a regression, you can check whether an independent variable and a dependent variable are related in the direction expected by your hypothesis. If the hypothesis predicts a positive effect but r is negative, review the variable coding, any reverse-coded item, the calculation of the mean score, and the theoretical argument.

A correlation table can also reveal independent variables that are highly correlated with one another. When you enter those variables into the same regression model, multicollinearity may occur. Pearson Correlation is only an initial screening step. Your conclusion about multicollinearity should also use Tolerance and VIF in the Coefficients table rather than relying on one correlation coefficient. For handling unusual observations, see the guide to outliers.

Correlation also appears in models with a mediator or moderator. If your study includes a mediator, the initial correlation between two variables does not replace a bootstrapping test of the indirect effect. If your model includes a moderator, the correlation between the moderator and the other variables does not by itself prove a moderation effect.

Correlation does not replace the hypothesis test for your model. It tells you that two variables move together in the sample, while regression allows you to examine an effect coefficient when several variables appear in the model at the same time. For that reason, the Correlations table is usually descriptive and screening evidence, not the entire conclusion of Chapter 4.

How much correlation is acceptable

There is no single number that determines whether a correlation is acceptable for every research topic. Separate two questions: is the correlation statistically significant, and how strong is it. Read the first question using Sig. (2-tailed) and the second using the absolute value of r.

In a two-tailed test, Sig. (2-tailed) < 0.05 is commonly used to reject the null hypothesis that there is no linear correlation in the population. Interpret this within the testing design and the convention of your study. A value of 0.05 is not a measure of the strength of the relationship.

A coefficient of r = 0.15 may have Sig. < 0.05 when the sample size is large. That does not make it a strong relationship in practical terms. Conversely, a relatively large coefficient with a p-value that does not meet the chosen threshold may be related to sample size, measurement error, or the spread of the data.

Before calculating correlations between representative variables, check how the scale was constructed. If you are unsure how an item, latent variable, and representative score differ, see what is a scale.

How to read correlated in the output

In SPSS, the usual path for running a correlation is Analyze > Correlate > Bivariate. Move the variables you want to check into Variables, keep Pearson selected, choose Two-tailed, and optionally select Flag significant correlations. If your hypothesis has a clear direction and your method permits a one-tailed test, explain the One-tailed choice in advance. Do not choose it after seeing the results.

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

At the intersection of CL and HL, Pearson Correlation = .624 indicates a positive correlation. As CL increases, HL tends to increase in the sample. Sig. (2-tailed) = .000 is the value SPSS displays after rounding, so in your thesis you should write p < 0.001, not p = 0.000. N = 185 means that 185 observations were used for this pair of variables.

The ** next to a coefficient is usually a note that SPSS adds when the coefficient is significant at the 0.01 level, depending on the display settings. You still need to read the Sig. (2-tailed) row when reporting the result. If a cell contains r = -.312, the minus sign indicates an inverse relationship, while the strength is assessed using the absolute value, 0.312.

You should also inspect a scatterplot when the coefficient looks unusual. In SPSS, go to Graphs > Chart Builder, select Scatter/Dot, and place one variable on the X axis and the other on the Y axis. Pearson Correlation reflects a linear relationship, so a clear curve may mean that the Pearson coefficient does not fully describe the data.

What to do when correlated is not acceptable

If Sig. (2-tailed) is greater than or equal to 0.05, first record that there is insufficient statistical evidence to reject the null hypothesis of no linear correlation in the sample. Do not automatically write that the two variables are completely unrelated. A nonlinear relationship, measurement error, or an insufficient sample size may be involved.

Check the coding and score calculation

Review reverse-coded items, missing values, and the formula used to calculate the mean score. An item that should be coded from 1 to 5 but was entered in the opposite direction can reduce the correlation or change its sign. Open Analyze > Descriptive Statistics > Frequencies to check for values outside the expected range.

Check outliers and the scatterplot

Open the scatterplot to see whether the relationship is linear. Check outliers separately before deciding whether to remove an observation. Do not delete a data row simply because it makes the result look better. If you remove one, you need a reason based on the data-cleaning procedure and must record the number of rows removed.

Review scale quality

If several items are combined to represent one construct but the scale has low reliability, the representative score may be unstable. You can review Cronbach's Alpha, Corrected Item-Total Correlation, and the EFA or PLS measurement model results according to your research design. Item removal must be based on theory and the criteria stated in advance, not only on a desire to increase the correlation.

Choose a coefficient that fits the data

Pearson is suitable when you are examining a linear relationship between numerical variables and the data conditions are reasonably appropriate. For ordinal data or when linearity is unsuitable, Spearman may be an option to consider. State the reason for choosing an alternative coefficient in your research methods.

Review the hypothesis and model

If the correlation is not significant, the direction proposed in the hypothesis may not be supported by the data. Reporting a statistically nonsignificant result is valid. Do not run repeated versions of the data simply to find a table with a small p-value.

Distinguishing correlated from easily confused statistics

Correlated is often confused with having an effect. Pearson Correlation describes the association between two variables, while the regression coefficient in Coefficients reflects the expected change in the dependent variable when an independent variable changes, with the other variables in the model held into account. A pair of correlated variables does not mean that the first variable causes the second.

Correlation also differs from R Square. In simple regression, the square of Pearson r may be related to the proportion of variance explained. In multiple regression, R Square is produced by the full set of variables in the model. Do not take each r and call it the model's R Square.

Correlation differs from Covariance in scale. Covariance depends on the measurement units of the variables, while Pearson Correlation is standardized to a range from -1 to +1 and is therefore easier to compare. Sig. is different from r as well. r shows the size and direction of the correlation, while Sig. provides statistical evidence for evaluating the hypothesis about the correlation.

If your study includes a moderator, moderating concerns a variable that changes the strength or direction of the relationship between two other variables. The correlation between the moderator and the other variables does not by itself prove a moderation effect.

Common errors

The first error is looking only at the ** and ignoring the coefficient and Sig.. The asterisks show the significance level according to SPSS's marking system, but they do not show whether the relationship is strong or weak. Read Pearson Correlation, Sig. (2-tailed), and N together.

The second error is writing Sig. = 0.000. The appropriate format is p < 0.001 when the table displays .000 because of rounding. Also check the sample size for each pair of variables, because missing data can make N different across cells.

The third error is using the phrase acceptable correlation as if one threshold applied to every study. Present both the statistical significance criterion and your interpretation of the coefficient's size. If your department or supervisor uses a specific convention, state that convention in the methods chapter.

The fourth error is drawing a causal conclusion from the Correlations table. The statement “CL affects HL” needs to be tested with an appropriate model, such as regression or a structural model. Based on the correlation table, the safer statement is “CL has a positive correlation with HL in the survey sample.”

How to write this in your thesis

You can adapt the following sentence to your actual variables: “The Pearson correlation analysis shows that [variable X] has a [positive/negative] correlation with [variable Y], with r = [value] and Sig. (2-tailed) = [value]. Because [p-value < or ≥ 0.05], this correlation [is or is not] statistically significant at the 5% level.” This sentence describes the correlation result only. It does not establish a causal relationship.

Frequently asked questions

What does correlated mean in SPSS?

Correlated in SPSS means that variables have a relationship with one another. When reading the Correlations table, focus on Pearson Correlation, Sig. (2-tailed), and N to identify the direction, size, statistical significance, and number of observations used.

What Pearson Correlation is considered acceptable?

There is no single r value that is acceptable for every study. Check whether Sig. (2-tailed) meets the significance level you selected, then interpret the absolute value of r in the context of your topic. A small coefficient may be statistically significant while still having limited practical importance.

What does Sig. 0.000 mean in a Correlations table?

Sig. = .000 is the value SPSS displays after rounding. In your thesis, write p < 0.001, then conclude that the correlation is statistically significant at the 5% or 1% level according to the testing rule you selected.

Does a nonsignificant correlation mean that I should remove the variable?

Not necessarily. Check the coding, reverse-coded items, missing values, outliers, scale quality, and the form of the relationship first. If those steps are appropriate, you can keep the variable and report the nonsignificant result rather than removing it simply to make the model look better.

Does Correlation prove a causal effect?

No. Correlation shows that two variables change together in the sample. To assess an effect, you need an appropriate model such as regression, mediation, moderation, or SEM, together with a clear statement of the limits of the research design.

Now open the Correlations table in your SPSS file and record r, Sig. (2-tailed), and N for each pair of variables. Compare those results with your hypotheses before writing the interpretation. If you need to run the analysis on your own .sav or .csv file, DoThesis M4 analysis supports this step.