The paired-samples t-test serves the purpose of assessing whether the mean discrepancy between interconnected observations is statistically significant. These observations may involve the same individuals evaluated at two distinct time points or be subjected to two conditions concerning the same dependent variable. Alternatively, you might have two sets of participants matched based on one or more attributes and then evaluated on a single dependent variable. The paired-samples t-test is also known as the dependent t-test, repeated measures t-test, or referred to as the paired t-test.
For instance, consider a scenario where you want to investigate whether there is a significant mean difference in the daily step count of individuals before and after a four-week fitness training program. In this case, your dependent variable would be “daily step count,” and you would have two linked groups, one representing step counts “before” the program and the other “after” the program. Another example is evaluating whether there is a mean difference in the test scores of students who received two different teaching methods (traditional versus online) for the same course. Here, your dependent variable would be “test scores,” and the related groups would be scores obtained from the “traditional” and “online” teaching methods.
The paired-sample t-test is a valuable statistical tool for examining changes or differences within related data pairs, whether it involves the same individuals over time, different conditions, or matched groups with shared characteristics.
Four assumptions need to be considered to run a paired-samples t-test. The first two relate to your choice of study design and the nature of your data, while the second two relate to the paired-samples t-test itself:
- Assumption #1: You have one continuous dependent variable. Continuous variables can take on infinite values within a given range. For instance, temperature, time, height, weight, distance, age, blood pressure, speed, electricity consumption, and sound level are typical continuous variables. For instance, the temperature in a room can be any value within the limits of the thermometer, such as 22.5°C, 22.51°C, and so on. Similarly, time can be measured to any level of precision, like seconds, milliseconds, or even smaller units. Height and weight can vary infinitely within their possible range, measured in units like meters or feet, and can include fractions (like 1.75 meters). Distance between two points, age measured in years, months, days, and even smaller units, blood pressure measured in millimeters of mercury (mmHg), speed measured in units like kilometers per hour or miles per hour, electricity consumption measured in kilowatt-hours or other units, and sound level measured in decibels are other examples of continuous variables that can take on a range of continuous values.
- Assumption #2: You have one independent variable, including two categorical, related groups or matched pairs (i.e., a dichotomous variable). This situation often arises when the same participants are involved in both groups. For instance, suppose you want to assess the impact of a new dietary supplement on weight loss. You measure the weights of 20 individuals (the dependent variable) both before and after they take the supplement. The first group represents the participants’ weights before taking the supplement, while the second group represents the same individuals’ weights after taking the supplement. The paired-samples t-test can also be applied to compare different participants (e.g., matched pairs), although this is less common.
- Assumption #3: There must be no significant outliers among the differences observed between the two related groups. Outliers refer to values that deviate significantly from the rest of the data, either extremely small or large. For example, if you have a group of students who scored between 65 and 80 out of 100 on a challenging math test, but one student scored 99, that score would be considered an outlier. Outliers can strongly impact your results as they can substantially influence the mean and standard deviation of the difference scores, affecting the outcome of the statistical test. Outliers are especially important when dealing with smaller sample sizes, as their effect becomes more pronounced.
- Assumption #4: The distribution of differences in the dependent variable between the two related groups should approximate a normal distribution. This assumption is necessary when conducting a paired-samples t-test for statistical significance testing. However, the paired-samples t-test is considered “robust” in handling violations of normality to some extent. It can still yield valid results even if the data is not normally distributed. Therefore, this test typically requires only approximately normal data. Additionally, as the sample size increases, the distribution can deviate from normality, and thanks to the Central Limit Theorem, the paired-samples t-test can still provide reliable results. In this context, your focus would be determining whether the difference scores between the two paired observations exhibit a normal distribution.
SPSS Statistics generates two tables that provide all the necessary information for reporting the outcomes of a paired-sample t-test. In this section, we will guide you through the interpretation of these tables, encompassing descriptive statistics, the assessment of differences between measurements, determining statistical significance, examining null and alternative hypotheses, and calculating effect size.
To commence, you can utilize the SPSS Statistics output to present informative, descriptive statistics, which offer insights into your data and will be integral when you present your findings. Additionally, we will delve into the evaluation of differences between the two variables, considering various measures of variability such as standard deviation, standard error of the mean, and 95% confidence intervals.
Subsequently, once you have reported the magnitude of the mean difference and its plausible range, you can ascertain whether a statistically significant disparity in means exists between your two related groups. We will elucidate how to interpret the t-value, degrees of freedom, and p-value in this context. Building upon this result, we will guide you in articulating your report’s null and alternative hypotheses.