ANCOVA in SPSS: How to Run, Read, and Report the Results

What ANCOVA tests

ANCOVA, short for Analysis of Covariance, compares the mean of a dependent variable across two or more groups after controlling for the effect of one or more covariates. In SPSS, you usually use ANCOVA when the dependent variable is quantitative, the group variable is categorical, and the covariate is a quantitative variable that may affect the outcome.

For example, you may want to compare academic performance scores between students who learned with method A and those who learned with method B. The two groups may differ in their baseline scores, however. The baseline score is then the covariate. ANCOVA compares the post-intervention scores after adjusting for the baseline score, rather than comparing only the two raw means.

ANCOVA fits a question such as: after controlling for X, do the groups differ in Y? If you have only two groups and no covariate, independent samples t test in SPSS is usually more appropriate. If you have several groups but do not need to control for a covariate, you can also review Repeated Measures ANOVA in SPSS when the data were measured repeatedly over time.

H0 and H1 hypotheses

For ANCOVA, write the hypotheses around your specific research question. H0 usually states that, after controlling for the covariate, the adjusted means of the dependent variable do not differ significantly across the groups.

H1 states that, after controlling for the covariate, the adjusted means of the dependent variable differ significantly for at least two groups. ANCOVA tells you whether there is an overall difference between groups. If the group variable has three or more levels and the test is significant, you need pairwise comparisons or estimated marginal means to determine which groups differ.

With the usual significance level of 5%, the decision rule is as follows: if Sig. or the p-value is below 0.05, reject H0; if the p-value is 0.05 or higher, there is not enough evidence to reject H0. Do not write that H0 has been proved true when the p-value is above 0.05. The result only shows that the data do not provide enough evidence of a difference.

ANCOVA can also test the interaction between the group variable and the covariate. A significant interaction indicates that the relationship between the covariate and the dependent variable changes across groups. Interpreting one overall group effect can then be misleading, so you need to consider simple effects or analyses at suitable levels.

Conditions for using ANCOVA

Check the assumptions before interpreting the output tables. ANCOVA is not just a matter of placing variables in Fixed Factor and Covariate and reading the p-value. If the groups have very different variances, the relationship between the covariate and dependent variable is not linear, or the regression slopes are not equal, the conclusion may not be reliable.

For distribution checks, use Explore to inspect the histogram, Q-Q plot, and descriptive statistics. ANCOVA is reasonably robust to mild departures when the sample size and group sizes are adequate, but you still need to record the shape of the data. If the covariate contains missing values, SPSS usually removes that observation from the model, so the actual sample size may be smaller than the original number of rows.

How to run ANCOVA in SPSS

Prepare and code the data

Each row should represent one person or one unit of observation. Create at least three variables: the dependent variable, the group variable, and the covariate. For example, post_score is the post-intervention score, group is coded 1 and 2, and pre_score is the pre-intervention score.

In Variable View, set the variable labels and value labels for the group variable. If the group variable was entered as text, you can use a coded numeric variable to reduce errors when assigning the Fixed Factor. Check missing values, out-of-range values, and duplicate rows before running the analysis. Do not standardize variables just because you think ANCOVA requires z-scores.

Check the covariate first

Go to Analyze > Descriptive Statistics > Explore. Move the dependent variable and covariate to Dependent List, and move the group variable to Factor List if you need results by group. Select Plots to enable Boxplot and Normality plots with tests, then inspect extreme values and the number of valid observations.

You can also go to Graphs > Legacy Dialogs > Scatter/Dot to create a scatterplot between the covariate and dependent variable. Create separate plots by group if you are checking the regression slopes. If one point is very different from the others, return to the questionnaire or original file and verify it before deciding how to handle it.

Open the Univariate dialog box

Go to Analyze > General Linear Model > Univariate. Move the dependent variable to Dependent Variable. Move the group variable to Fixed Factor(s), then move the quantitative variable you want to control to Covariate(s). This is the easiest place to make a mistake: the group variable belongs in Fixed Factor(s), while the quantitative control variable belongs in Covariate(s).

Click Model. For a basic model, choose Custom to specify the effects to include. Add the group variable and covariate. To check the equal regression slopes assumption, add the interaction between the group and covariate, usually written as group*pre_score. After checking the interaction, you can run the main model without the interaction if it is nonsignificant and your theoretical model permits that specification.

Choose Options and Estimated Marginal Means

Click Options. Move the group variable to Display Means for. Select Descriptive statistics, Estimates of effect size, and Homogeneity tests. You can select Compare main effects if you want to compare the levels of the group variable, then choose an adjustment such as Bonferroni when the group has three or more levels.

Select Estimate of effect size so that SPSS displays Partial Eta Squared. Select Observed power only if your department or supervisor requires it, because observed power does not replace sample-size planning before the study.

Click Plots if you want to create an estimated marginal means chart. Move the group variable to Horizontal Axis and click Add. If you need to display the covariate, choose a few representative values or use the estimated marginal means table produced by SPSS. Then click Continue and OK to run the analysis.

Save the syntax and check the model again

Immediately before or after running the analysis, save the syntax by clicking Paste instead of only clicking OK. The syntax records which variables entered the model, especially when you need to remove an item or rerun the analysis with a different analysis sample.

Check the number of observations analyzed in the Descriptive Statistics table and the missing-data warning at the beginning of the output. If the sample size drops unexpectedly, look for the cause in the covariate or dependent variable. A model that runs successfully does not necessarily mean that the data meet every condition.

Read the output tables and draw the conclusion

ANCOVA output usually includes Descriptive Statistics, Levene's Test of Equality of Error Variances, Tests of Between-Subjects Effects, Estimated Marginal Means, and Pairwise Comparisons if you requested pairwise tests. Tests of Between-Subjects Effects is the central table for interpreting the effects of the covariate and group variable.

The following is illustrative output, not the result of an actual study. The column names follow the format SPSS commonly uses in the Tests of Between-Subjects Effects table.

In this example, the pre_score row has a Sig. value below 0.001, indicating that the covariate is significantly related to post_score after the other model components are included. The group row has a Sig. value of 0.016, which is below 0.05. After controlling for pre_score, there is therefore evidence of a difference between the two groups in post_score.

If Levene's Test has a Sig. value of 0.05 or above, the equal-variances assumption is not considered violated under the rule you selected. If Levene's Test has a Sig. value below 0.05, do not simply move to the group p-value and report a conclusion. Consider the degree of group imbalance, outliers, model specification, and whether another analysis is more suitable.

Partial Eta Squared describes the effect size in the model. Report it together with F, the degrees of freedom, and the p-value, but do not label it small, medium, or large unless you have a convention accepted by your supervisor. Estimated Marginal Means are the means adjusted for the covariate, so they are more appropriate for describing the groups after ANCOVA.

If the group variable has three or more levels, inspect Pairwise Comparisons. Read Mean Difference, Std. Error, Sig., and the confidence interval. When you perform multiple comparisons, state the adjustment method clearly. For data that do not meet distribution or variance conditions, Kruskal Wallis in SPSS may be an alternative when the question only concerns several independent groups, but it does not directly replace ANCOVA with a covariate.

How to write this in your thesis

How to write this in your thesis: “The ANCOVA results show that, after controlling for the effect of [covariate name], the difference in [dependent variable name] between [group 1] and [group 2] is statistically significant, F([df1], [df2]) = [F value], p = [p-value], Partial Eta Squared = [value]. The adjusted mean for [group 1] is [M1], whereas the adjusted mean for [group 2] is [M2]. Therefore, hypothesis H[ ] is [accepted according to the wording required by the department or H0 is rejected].”

Replace every bracketed section with the actual values from your output. If the p-value is 0.05 or higher, write that the result does not show a statistically significant difference after controlling for the covariate. Do not write that the two groups are exactly the same, because the test does not prove absolute equality.

In the results chapter, present the material in this order: sample description, assumption checks, the ANCOVA table, estimated marginal means, and the hypothesis conclusion. You can shorten the thesis table, but keep the output file and syntax so you can explain the analysis when asked. If you need other SPSS analyses, review SPSS topics or compare your reporting with Levene's test in SPSS so that the assumptions are reported consistently.

What to use when an assumption is violated

If the relationship between the covariate and dependent variable is not linear, consider transforming a variable, adding a nonlinear term when theory supports it, or choosing a more suitable regression model. Do not force ANCOVA simply because the proposal names that test.

If the regression slopes differ across groups, keep the Group*Covariate interaction in the model and interpret the interaction. When the interaction is significant, a conclusion about one average group effect may hide differences at different covariate levels.

If variances are unequal or the groups are seriously unbalanced, check outliers and data-entry errors first. When the question only concerns two independent groups, Mann Whitney in SPSS may be more suitable if the dependent variable is ordinal or strongly skewed. Mann Whitney, however, does not control for the covariate in the way ANCOVA does.

If you have pre- and post-measures from the same people, identify the design before choosing the test. ANCOVA with the pre-score as the covariate is a common approach, while data collected at several time points may require another model. State why you selected the method, and do not change the test only to obtain a smaller p-value.

Common errors

The first error is placing the covariate in Fixed Factor(s). SPSS then treats it as a categorical variable, so the model and degrees of freedom no longer match the research question. Check the variable name and its position in the Univariate dialog box.

The second error is ignoring the interaction between the group and covariate. If the study requires the equal regression slopes assumption, check Group*Covariate before interpreting the main effect of group. A favorable p-value in the final table does not compensate for an unchecked model.

The third error is reading Descriptive Statistics and drawing a conclusion instead of using Estimated Marginal Means. ANCOVA adjusts the means for the covariate, so the raw mean difference may differ from the adjusted difference.

The fourth error is deleting outliers until the result becomes significant. Every removed observation needs a reason based on the data or design, recorded in the syntax and reported transparently. If the result changes after handling the observation, present the primary analysis and a robustness check when appropriate.

The final error is writing “Sig. = 0.000”. SPSS displays .000 because of rounding, which does not mean that the p-value is exactly 0. Write p < 0.001. Also report F, the degrees of freedom, Partial Eta Squared, and the adjusted means instead of recording only whether the result passed or failed.

Frequently asked questions

How is ANCOVA in SPSS different from ANOVA?

ANOVA compares group means without adjusting for a quantitative variable outside the model. ANCOVA adds a covariate to control for its effect before comparing the groups. Use ANCOVA only when the covariate has a theoretical basis and was measured appropriately.

Can ANCOVA be used with only two groups?

Yes. ANCOVA can compare two groups after controlling for a covariate. Without a covariate, an independent samples t test is usually more concise. With two groups, still read the ANCOVA group effect together with Levene's Test, the regression-slope check, and the estimated marginal means.

What should I do if Levene's Sig. is below 0.05?

First check outliers, data-entry errors, and the imbalance between groups. Then consider the robustness of the result, report the violation clearly, and ask your supervisor about an alternative model. Do not automatically delete a group or change the test without recording the reason.

Do I need to check Shapiro-Wilk before running ANCOVA?

You should inspect the distribution and outliers with Explore, a histogram, and a Q-Q plot. Shapiro-Wilk is supporting information, especially because its p-value is sensitive to sample size. The final decision should consider the design, plots, group sizes, and degree of skewness.

Can ANCOVA be used when the covariate is a Likert variable?

This depends on how you constructed the variable and your methodological argument. A single Likert item is ordinal, whereas the total or mean score from several items is often treated as quantitative in quantitative research. Describe how you created the variable and support the choice with appropriate methodological literature.

Open the .sav file, check the positions of group, covariate, and the dependent variable, then run the model with the syntax saved before writing the conclusion. If you want to run the analysis on your own .sav or .csv file and retain the output tables, M4 analysis by DoThesis supports this step.