What Is Statistical Significance? How to Read p-values in SPSS

What Is Statistical Significance?

You open the Coefficients table, the ANOVA table, or the result of a test in SPSS and see a Sig. column with values such as 0,032, 0,148, or 0,000. You usually compare that number with the significance level, written as α, to decide whether there is enough evidence to reject the null hypothesis H0.

The significance level is the maximum probability of rejecting H0 that you are willing to accept when H0 is actually true. In quantitative research, you will often choose α = 0,05, which is equivalent to 5%. The basic rule is:

• If the p-value or Sig. < 0,05, reject H0.
• If the p-value or Sig. ≥ 0,05, there is not enough evidence to reject H0.

You need to distinguish these two numbers from the beginning. You choose the significance level α before running the test, while the p-value is calculated from your sample data and the model you run. In other words, α is the decision threshold, while the p-value indicates how compatible your data are with H0 when H0 is assumed to be true.

This interpretation connects directly to the Statistics topic and related concepts such as what degrees of freedom are. Do not read a single Sig. value without checking the test being used, the direction of the hypothesis, and the variable being analysed.

Why the Significance Level Matters in Quantitative Research

The significance level helps you turn a calculation into a statistical decision. Suppose your H1 states that service quality has a positive effect on satisfaction. After you run the regression, SPSS gives you Sig. = 0,021. With α = 0,05, this result is below the threshold, so you have a basis for rejecting H0 and supporting H1 if the regression coefficient has the direction predicted by your hypothesis.

The significance level does not tell you whether an effect is large or small. A very low p-value only indicates stronger statistical evidence against H0. It does not automatically prove that the effect has practical importance. To assess the size of the effect, you also need to read the regression coefficient, the path coefficient, the confidence interval, R², or an effect-size measure, depending on the method.

The significance level is not the probability that H0 is true either. If p-value = 0,03, you must not write that H0 has only a 3% chance of being true. An appropriate interpretation is this: assuming H0 is true, the observed data have a degree of extremeness corresponding to p-value 0,03, and this result is sufficient to reject H0 at α = 0,05.

In your thesis, state the significance level in the methods section before presenting the results. If your study uses several tests, specify which group of tests the selected α applies to. Changing 0,05 to 0,01 after seeing the results makes the decision inconsistent and can create a difficult question during the defence.

What Significance Level Is Acceptable?

The question “what significance level is best” puts the focus in the wrong place. α = 0,05 is not a score where a smaller value is automatically better. It is a threshold that you choose according to your research objective and how cautious you need to be when rejecting H0. A smaller α makes the rejection criterion stricter, but it also increases the chance of failing to detect a real effect.

The levels you will see most often are 0,10, 0,05, and 0,01. The methodological source or requirements of your field may guide the choice, but you need to use one level consistently throughout the relevant hypothesis tests. The table below summarises the practical interpretation.

The sources in the table guide testing practice. They do not turn one threshold into a rule that fits every study. If your supervisor requires α = 0,05, use that level and state it clearly in the methods chapter. If you use α = 0,10 for exploratory research, explain the reason instead of choosing it simply because your results are more likely to meet the threshold.

With one-tailed and two-tailed tests, the p-value may be calculated differently. You need to compare the result with the research hypothesis. The hypothesis “X affects Y” is usually tested two-tailed when no specific direction has been stated. The hypothesis “X has a positive effect on Y” may involve a directional test, but you should use that approach only when the methodological design and software support it.

How to Read Significance in SPSS Output

In SPSS, statistical significance usually appears in the Sig. column, but the table name and the meaning of the column depend on the analysis. In linear regression, you read Sig. in the Coefficients table to assess each independent variable, while the ANOVA table reports the significance of the regression model as a whole. In a t test or ANOVA, the Sig. column may answer a different question.

The table below is illustrative output, not the result of a real study. The column names follow the form commonly shown in SPSS output.

SPSS often displays Sig. = 0,000 when the p-value is smaller than the display limit, not when the p-value is exactly 0. In your thesis, you may write p < 0,001 when the output shows 0,000 and your department's reporting rules allow it. Do not write “Sig. = 0”, because a probability of exactly 0 is not the accurate interpretation here.

If Sig. is smaller than 0,05 but B is negative while your hypothesis predicts a positive effect, you cannot conclude that H1 is supported simply because the p-value meets the threshold. The effect is statistically significant but runs in the opposite direction to the hypothesis. Report the sign, magnitude, and hypothesis decision according to the model you proposed.

The confidence interval provides another way to check the result. For a two-tailed test at α = 0,05, a 95% confidence interval for the coefficient that does not contain 0 usually corresponds to the decision to reject H0. You can also read what a confidence interval is and what 95 confidence means to avoid confusing the significance level with the confidence level.

What to Do When the Significance Level Is Not Met

If the p-value is greater than or equal to α, first record that there is not enough evidence to reject H0. Do not automatically remove the variable, change the scale, or lower α just to make the result meet the threshold. Work through the following checks in order.

Check That You Are Reading the Correct Sig. Column

Check the table name, dependent variable, independent variable, and test type. In the Coefficients table, the Sig. value on each row is different from the model Sig. value in the ANOVA table. Selecting the wrong column can make every conclusion incorrect.

Check the Data and Variable Coding

Review missing values, reverse-coded items, group codes, and data types. An item that has not been reverse-coded can distort the scale score and change the coefficient and p-value. If you find a data-entry error, correct it in the original data file, record the change, and run the analysis again.

Check the Assumptions and Model Structure

Regression needs to be assessed together with multicollinearity, residuals, and the form of the relationship. If the independent variables are highly correlated, the individual coefficient for each variable may be unstable even when the overall model is significant. Do not use one p-value to judge the entire model.

Report a Non-Significant Result Honestly

If the result still does not meet the threshold after reasonable checks, keep the result and write that the hypothesis was not supported. Running the analysis repeatedly until you find a table with a p-value below 0,05 increases the risk of bias and can raise questions when your data file, syntax, or item-deletion steps are checked.

Distinguishing Significance, p-values, and Confidence Levels

The significance level α is set in advance. The p-value is calculated from the data. For example, you choose α = 0,05 and obtain p-value = 0,021. You make the decision by comparing the two numbers, not by saying that the p-value is the significance level.

The confidence level is often written as 1 - α. When α = 0,05, the corresponding confidence level is 95% when presenting a confidence interval. The two concepts still answer different questions. The significance level supports the decision in a hypothesis test, while the confidence level describes an interval estimate produced by the selected method.

The significance level is also different from what df means and df in SPSS. df is the degrees of freedom used in the distribution of the test statistic. It contributes to the calculation of the p-value, but df is not a probability and is not a pass or fail threshold.

You also need to distinguish statistical significance from practical significance. A large sample can produce a small p-value for a very small effect. When writing the results chapter, report at least the coefficient, p-value, direction of the effect, and a suitable fit or magnitude measure such as R² or the mean difference instead of writing only “there is an effect”.

Common Errors When Using Significance Levels

The first error is writing, “Sig. is smaller than 0,05, so H1 is absolutely true.” Statistical testing provides evidence based on the sample and model. It does not turn a hypothesis into an unchangeable fact.

The second error is using Sig. < 0,05 and Sig. ≤ 0,05 inconsistently. An exact match with the threshold rarely appears because of decimal reporting, but you still need to state the rule clearly. Keep enough decimal places for the reader to check your decision.

The third error is looking only at the p-value and ignoring sample size. The same coefficient can produce different p-values at different sample sizes. Your interpretation should therefore place the p-value next to the coefficient and confidence interval rather than separating the result from its data context.

The fourth error is changing α after viewing the output. If the result is 0,061, do not switch from 0,05 to 0,10 and then write that the hypothesis is supported. If there is a clear methodological reason to use α = 0,10, specify it in advance and explain it in the methods chapter.

The final error is confusing decimal commas in SPSS with decimal points in guidance materials. SPSS may display 0,032 under Vietnamese language settings, while many materials write 0.032. Both forms represent the same value, but you should use one format consistently throughout your thesis.

Frequently asked questions

Is a significance level of 0,05 always the best choice?

No. α = 0,05 is common, but it is not the only option and is not always appropriate. Choose the significance level based on your research design, field requirements, and supervisor's guidance, then apply it consistently throughout the analysis.

If you use α = 0,10 or 0,01, state it clearly in the methods section and explain why. Do not choose a threshold simply because it makes a particular hypothesis meet or miss the criterion.

What significance level should I use in SPSS?

SPSS does not have its own significance level. You usually set α = 0,05 in the methods section and compare it with the Sig. column or p-value in the output. The further the Sig. value falls below α, the stronger the evidence against H0 under the testing rule.

A smaller number does not mean a larger effect. To determine how large the effect is, you need to examine the coefficient and the appropriate effect-size measure.

What does Sig. = 0,000 mean in SPSS?

Sig. = 0,000 usually means that the p-value is smaller than the display limit used by SPSS. You should report it as p < 0,001 when that is consistent with your thesis requirements instead of writing that the p-value equals 0.

The conclusion still depends on the test type, the sign of the coefficient, and the hypothesis being assessed. Do not look only at the 0,000 row and conclude that every hypothesis is supported.

If Sig. is greater than 0,05, does that mean H0 is true?

No. This result only means that you do not have enough evidence to reject H0 at α = 0,05. H0 may be true, or the current data and sample size may not be sufficient to detect the effect.

In your thesis, “there is not enough evidence to reject H0” is more accurate than “H0 is certainly true”.

Can I change the significance level after running SPSS?

You should not change α simply to make the result meet the threshold. Doing so increases the risk of drawing a conclusion based on the observed data and may make readers question your analysis process.

If your proposal or supervisor requires a different level, update the methods section, state the rule clearly, and apply it consistently to the related tests.

Open the .sav or .csv file you are actually using, record the selected α in the methods section, and compare each Sig. column with the hypothesis and the sign of the coefficient instead of marking only the small p-values. If you need to run and interpret the analysis on your real data, DoThesis M4 analysis supports this step in SPSS and SmartPLS.