Introduction

The dependent t-test, also known as the paired-samples t-test, is one of the most important methods of statistical analysis when the goal is to compare the means of two related groups on the same continuous dependent variable. This method is widely used in scientific fields such as social sciences, psychology, medicine, and education, where researchers aim to understand whether observed changes are due to an intervention or a time effect. A typical example is the investigation of cigarette consumption by smokers before and after a six-week hypnotherapy program. In this case, the dependent variable is the daily cigarette consumption, while the two groups correspond to the measurements “before” and “after” the intervention. It is important to note that if the dependent variable is dichotomous, meaning it takes only two categories, then the McNemar’s test is considered more appropriate rather than the dependent t-test.

The Importance of the Dependent t-test

The usefulness of the dependent t-test lies in the fact that it allows the examination of intra-individual differences, since the same participants are evaluated twice. In this way, random variation that might occur when comparing different samples is reduced, and the statistical power of the test is increased. Essentially, this method provides a clearer picture of the effect of an intervention or a change, enabling the researcher to draw safer conclusions.

Assumptions of Application

Before applying the dependent t-test, it is necessary to check certain assumptions that ensure the validity of the results. The first assumption is that the dependent variable must be measured on a continuous scale, that is, at interval or ratio level, such as weight, time, or test scores. The second assumption is that the independent variable must consist of two related groups, meaning the same individuals are measured at two different time points or conditions. A typical example is the evaluation of students before and after the implementation of a new teaching method.

The third assumption concerns the absence of significant outliers in the differences between the two measurements. Outliers, meaning the individual observations that deviate strongly from the general pattern, can negatively influence the validity of the results and distort statistical significance. Finally, the fourth assumption relates to the normality of the distribution of the differences. It is not required that each group separately follows a normal distribution, but the differences between the two measurements should be normally distributed. This can be tested using the Shapiro–Wilk test for normality in SPSS.

Handling Assumption Violations

In practice, researchers often encounter data that do not fully meet all the assumptions mentioned above. This does not necessarily mean that the analysis is impossible or invalid. For instance, if outliers are identified, data processing techniques can be applied, or alternative statistical methods may be selected, such as the non-parametric Wilcoxon signed-rank test. Similarly, in cases of severe violation of normality, the researcher may resort to other appropriate techniques. Thus, even when ideal conditions are not fully satisfied, there are available solutions to ensure reliable results.

Procedure in SPSS Statistics

Running the dependent t-test in SPSS is a relatively simple and user-friendly process. Through the Analyze menu, under the Compare Means option, the researcher selects Paired-Samples T Test and inputs the two related variables to be compared. The software automatically produces the necessary statistical results, presenting the means, standard deviations, as well as the t-value, the degrees of freedom, and the level of significance. The interpretation is straightforward: if the p-value is smaller than the predetermined significance level, usually 0.05, then the null hypothesis is rejected, and the conclusion is that there is a statistically significant difference between the two measurements.

Conclusions

The dependent t-test is a fundamental tool for analyzing data derived from related groups. It offers the opportunity to accurately estimate the effect of an intervention or a time change while reducing the influence of random factors that could obscure the results. However, the validity of the conclusions depends greatly on the adherence to the assumptions and the researcher’s ability to deal with possible violations. SPSS Statistics makes the application of the dependent t-test particularly accessible and effective, contributing to the extraction of valid and reliable conclusions for scientific research.