Null and Alternative Hypotheses for the Dependent-Samples t-Test

Conceptualizing the Dependent-Samples t-Test as a One-Sample t-Test

How is a difference score calculated in the initial step of a dependent-samples t-test?

A researcher conducts a study measuring participants' stress levels before and after a mindfulness workshop. When computing a difference score for each participant, the researcher subtracts the pretest score from the posttest score for the first 15 participants but then switches to subtracting the posttest score from the pretest score for the remaining 15 participants. This approach is acceptable because both subtraction directions are valid ways to compute difference scores.

A clinical psychologist is measuring anxiety levels in patients before (Pre-test) and after (Post-test) a 4-week therapy program. To analyze the data using a dependent-samples $t$-test, the researcher calculates a difference score for each patient using the formula: $Post-test - Pre-test$. Match each patient's scores to the correct difference score.

A researcher is evaluating the best methodological workflow to prepare raw data for a dependent-samples $t$-test. Arrange the steps in the correct order to ensure the resulting difference scores are both statistically valid and intuitively representative of the experimental effect.

You are constructing an analytical plan for a study that evaluates the effectiveness of a 'Mindfulness Workshop' in reducing 'Exam Anxiety' (measured on a scale of 0-50) using a pretest-posttest design. You intend to use difference scores to represent the change for each participant. To ensure your results are intuitive—where a positive mean difference score directly signifies a reduction in anxiety—which data-processing protocol should you implement?

Match each statistical term related to the initial steps of a dependent-samples $t$-test with its correct definition based on how data is processed for analysis.

In a study with paired observations, the purpose of calculating a difference score for each participant is to reduce two scores into a single value that can be analyzed using one-sample $t$-test logic.

A researcher studying a treatment for depression calculates difference scores by subtracting Pre-treatment scores from Post-treatment scores (where higher scores indicate more severe symptoms). If the treatment is effective in reducing symptoms, the resulting difference scores for those participants will be a _____ value.

A researcher studies the effectiveness of a tutoring program on exam performance (scored 0–100). Difference scores are computed as Pretest − Posttest for each participant. If the mean difference score across all participants is −12, this indicates that the tutoring program _____ exam performance on average, because posttest scores were systematically higher than pretest scores.

A peer reviewer is evaluating whether a student researcher correctly executed the initial data-preparation steps for a dependent-samples $t$-test. Rank the following verification checks from the most foundational prerequisite to confirm first (1) to the final logical confirmation (5), reflecting the order in which each step's validity depends on all prior steps being satisfied.

State the initial step required to analyze data using a dependent-samples $t$-test. In your description, specify how the raw paired scores are transformed, the condition that must be met during this calculation, and what type of statistical test the dependent-samples $t$-test functions as once this step is completed.

Determine the formula the researcher should use to calculate the difference scores, compute the difference scores for Participant 1 and Participant 2, and explain why the researcher must apply this formula in the exact same direction to all participants in the study.

A research assistant is calculating difference scores for a dependent-samples $t$-test. For the first 10 participants, they subtract Pretest scores from Posttest scores. For the remaining 10 participants, they subtract Posttest scores from Pretest scores because they want all difference scores to be positive. Identify the error in this application and explain how it must be corrected.