How to Interpret SPSS Output for a Statistics Assignment (2026 Guide)

This guide walks through descriptive statistics, independent-samples t-tests, one-way ANOVA, linear regression, Pearson correlation, and chi-square tests of independence. Each section shows which values to read and how to turn them into a results paragraph.

Before you interpret a table

1. State the question. Are you comparing means, measuring an association, or predicting an outcome? Check whether observations are independent, paired, or repeated.
2. Check the cases and variables. Confirm the analyzed N, missing values, group codes, measurement units, and any active filters or weights. Different analyses can use different numbers of cases.
3. Review assumptions and diagnostics. Read the relevant plots, warnings, and table footnotes. A small p-value does not show that the analysis was appropriate.
4. Read the size and uncertainty of the result. Report estimates, confidence intervals, and relevant effect sizes alongside the test statistic, degrees of freedom, and p-value.

SPSS menus and labels vary by version. The table names below help you find the relevant results even when your interface looks different.

What does “Sig.” mean in SPSS?

In common hypothesis-test tables, Sig. is a p-value. Under the null hypothesis and the test’s assumptions, it measures how probable a result at least as extreme as the observed result would be. It is not the probability that your hypothesis is true, and it does not measure how important an effect is.

Read the column heading: a two-sided p-value and a one-sided p-value answer different questions. Compare it with the significance level chosen for your analysis, such as α = .05. Do not choose the test direction or threshold after looking at the result.

Interpreting descriptive statistics

Start with the sample size and the distribution of the variable. The mean gives its average; the standard deviation describes spread in the original measurement units. For strongly skewed data, the median and interquartile range may be more informative.

For a complete raw-data walkthrough, follow this SPSS descriptive statistics worked example, including data entry, SPSS syntax, output, and a results paragraph.

The 120 participants had a mean exam score of 67.45 (SD = 12.83), with scores ranging from 31 to 95.

These values describe this sample. They do not establish whether a group difference is statistically significant. Avoid labeling variability “high” or “low” without a meaningful comparison.

Interpreting an independent-samples t-test

An independent-samples t-test compares the means of two independent groups. If the same people were measured twice, a paired-samples analysis may be appropriate instead.

Read Group Statistics for N, means, and SDs. In Independent Samples Test, SPSS provides a pooled-variance row (“Equal variances assumed”) and a separate-variance row (“Equal variances not assumed,” commonly called Welch’s test). Use the row appropriate to your analysis plan.

Levene’s test assesses evidence against equal population variances. Some courses use its p-value to choose the row; follow an explicit course rule when required, but a nonsignificant Levene result does not prove equal variances. Welch’s test does not require equal population variances and can be selected in advance.

The difference is Group 1 minus Group 2: 8.30 points. The confidence interval describes uncertainty in the estimated population mean difference. Check group ordering before interpreting its sign. Here, Cohen’s d using the pooled SD is approximately 0.67; this standardization is separate from the choice of Welch’s test.

Group 1 (M = 74.60, SD = 11.20) scored higher on average than Group 2 (M = 66.30, SD = 13.40), Welch’s t(114.40) = 3.68, p < .001. The mean difference was 8.30 points, 95% CI [3.83, 12.77], with Cohen’s d = 0.67.

Check independence, within-group distributions, and influential outliers. Statistical significance alone does not establish that group membership caused the difference.

Interpreting one-way ANOVA

A one-way ANOVA evaluates whether population means are equal across groups defined by one factor. It is often used for three or more groups. The overall test does not identify which groups differ.

The F ratio is the between-groups mean square divided by the within-groups mean square. Here, p ≈ .003 provides evidence against all three population means being equal. Eta squared is 1284.50 / 10226.60 ≈ .126.

A one-way ANOVA found evidence of differences in mean scores across the three groups, F(2, 87) = 6.25, p = .003, η² = .126.

To name specific group differences, read the relevant planned contrasts or multiple-comparison results. For example, Tukey comparisons assume equal variances, while Games–Howell comparisons do not. When variances differ, consider Welch ANOVA as appropriate to the study and course requirements. Do not invent pairwise results from the overall F test.

Interpreting linear regression output

For linear regression with an intercept, read Model Summary, ANOVA, and Coefficients, then examine the diagnostics. If you need help running the model first, use our SPSS linear regression setup guide.

Model Summary and ANOVA

• R Square = .450: the fitted model accounts for 45.0% of the sample variation in the outcome around its mean. This is not “45% prediction accuracy.”
• Adjusted R Square = .441: adjusts for sample size and the number of predictors. It can decrease when adding a predictor.
• R = .671: is the nonnegative square root of R Square here. Use coefficient signs to determine each predictor’s direction.
• The overall F test: tests whether both population slope coefficients are zero. A significant overall result does not mean that every predictor is significant.

Coefficients: B, Beta, t, and confidence intervals

B is the expected change in the outcome per unit of that predictor, holding the other included predictor fixed. Here, one additional weekly study hour is associated with a 3.60-point higher predicted exam score at the same sleep-hours value.

Beta expresses the coefficient in standard-deviation units. Its magnitude alone does not establish causal importance or how useful a predictor would be in another model. Correlated predictors and measurement choices affect these comparisons.

t and p test a population coefficient against zero. The confidence interval adds information about its precision. These intervals are for slopes, not for a new student’s predicted exam score.

Calculation context: this teaching example assumes predictors with zero sample correlation, each with SD = 2 hours, and an outcome SD = 12 points. The intercept row is omitted because this table illustrates slopes. These conditions make the displayed coefficients, model fit, and standard errors internally consistent.

The two-predictor model accounted for 45.0% of sample variation in exam scores, R² = .450, adjusted R² = .441, F(2, 117) = 47.86, p < .001. Holding sleep hours fixed, each additional weekly study hour was associated with a 3.60-point higher predicted score, 95% CI [2.79, 4.41], p < .001.

Before drawing conclusions, examine residual plots for nonlinear patterns and unequal spread, assess dependence from the study design, and inspect influential cases and collinearity. Approximate normality of errors matters for conventional small-sample tests and intervals. A fitted association alone does not establish causation or performance on new data.

Using Excel as well? See our worked guide to interpreting Excel regression output for the equivalent tables.

Interpreting Pearson correlation

Pearson’s r describes the direction and strength of a linear association. It ranges from −1 to +1: the sign gives direction and the absolute value gives strength. A value near zero can coexist with a strong nonlinear relationship, so inspect a scatterplot.

In a separate fictional example, r = .641 with N = 120 gives p < .001. The corresponding degrees of freedom are N − 2 = 118.

Study hours and exam scores were positively correlated, r(118) = .641, p < .001. Students with more reported study hours tended to have higher scores.

Use context when describing strength; universal “weak/moderate/strong” bands can mislead. Check outliers, missing-data handling, and the assumptions behind the reported p-value. Correlation does not establish causation. IBM’s bivariate-correlations documentation explains the available coefficients and test options.

Interpreting a chi-square test of independence

Use this test to examine association between two categorical variables. Begin with the crosstab so the counts and percentages give meaning to the test statistic.

The Pearson chi-square statistic is 12.22, with df = (2 − 1)(3 − 1) = 2 and p ≈ .002. Expected counts under independence are 30, 22.5, and 22.5 in each row, so none is below 5. Cramér’s V is approximately .285.

Course-format preference was associated with cohort, χ²(2, N = 150) = 12.22, p = .002, Cramér’s V = .285. Online preference was reported by 53.3% of Cohort A and 26.7% of Cohort B.

Those percentages describe the table; the overall test does not separately test every cell. The observations must be independent and categories mutually exclusive. Check the expected-count footnote. A common rule flags the approximation when any expected count is below 1 or more than 20% are below 5. Sparse tables may need an appropriate exact or Monte Carlo procedure. See NIST’s explanation of chi-square independence tests.

A checklist for writing your SPSS results

• Name the test and explain why it matches the question and study design.
• Report the analyzed sample size, relevant descriptive statistics, and meaningful units.
• Include the effect estimate, appropriate confidence interval, test statistic, degrees of freedom, and p-value.
• Explain direction and magnitude in ordinary language; discuss practical meaning in context.
• Report relevant diagnostics and limitations, including missing data or multiple comparisons.
• Describe a nonsignificant finding as insufficient evidence against the null, rather than proof of no effect.

The examples here illustrate common reporting conventions, not a universal assignment template. Follow your required style and precision. The APA numbers and statistics guide can help with formatting. Build your interpretation from your own output rather than copying an example paragraph.

Frequently asked questions

Which p-value should I report?

Use the p-value for the test and row you actually selected. Do not substitute Levene’s p-value for the t-test p-value, or the overall regression F-test p-value for an individual coefficient’s p-value.

What if my p-value is displayed as .050?

Inspect more decimal places if a decision depends on the threshold; .050 may be rounded from either side of .05. Apply your preselected decision rule and report the estimate and uncertainty, rather than treating the threshold as the whole result.

Why is my sample size smaller than expected?

Missing values, filters, case selection, and different exclusion settings can change the analyzed sample. Check the case-processing information and active settings before interpreting the result.

Software references

• IBM: independent-samples t-test
• IBM: one-way ANOVA post hoc tests
• IBM: linear regression statistics