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Null and Alternative Hypotheses for the Dependent-Samples t-Test
The null hypothesis for a dependent-samples -test states that the means at the two times or under the two conditions are identical in the population. When evaluated using difference scores, this hypothesis assumes that the mean difference score in the population is (). Conversely, the alternative hypothesis asserts that the means are not the same, meaning the population mean difference score is not (). Researchers may also use a one-tailed test if they theoretically expect the difference to occur in a specific direction.
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Research Methods in Psychology - 4th American Edition @ KPU
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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 -test, the researcher calculates a difference score for each patient using the formula: . 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 -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 -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 -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 -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 -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 -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 -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.
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When evaluating a dependent-samples t-test using difference scores, what does the null hypothesis state about the population mean difference score?
If a researcher theoretically expects a treatment to change scores in a specific direction, their alternative hypothesis for a dependent-samples t-test should still simply assert that the population mean difference score is not equal to zero.
A clinical psychologist investigates whether a new mindfulness app reduces stress. She measures the stress levels of 25 participants both before and after they use the app for one month. Match each component of her dependent-samples -test to its corresponding description or mathematical notation for this specific study.
A researcher is evaluating the impact of a stress-reduction seminar by measuring the same group's cortisol levels before and after the session. Arrange the steps in the correct logical sequence to establish the statistical framework and formulate the hypotheses for a dependent-samples -test.
In a two-tailed dependent-samples -test, what does the alternative hypothesis () assert about the means of the two conditions in the population?
Match each type of hypothesis for a dependent-samples -test with the conceptual claim it makes about the population being studied.
A psychologist investigates whether a relaxation technique reduces systolic blood pressure. They measure participants before and after the technique, calculating difference scores as . Because the researcher theoretically expects blood pressure to decrease, they conduct a one-tailed dependent-samples -test. The alternative hypothesis () must state that the population mean difference score () is _____.
A clinical psychologist measures the anxiety levels of patients before and after they undergo a mindfulness intervention. To determine if the intervention had an effect, she runs a dependent-samples -test on the difference scores. Under the null hypothesis for this study, the psychologist assumes that the population mean difference score () is equal to .
A sports psychologist measures athletes' reaction times before and after a new visual training program. If the psychologist has a strong theoretical justification to expect that the program will specifically decrease reaction times, they can choose to perform a(n) _____ test rather than a two-tailed test.
A researcher is planning a dependent-samples -test to evaluate the effectiveness of a memory-training exercise by comparing participants' recall scores before and after training. Order the following steps to construct the logical framework of the hypotheses, moving from the baseline null assumption to its mathematical representation, and then to the alternative assumption and its mathematical representation.
Define the null and alternative hypotheses for a dependent-samples -test. In your definition, include both the conceptual explanation of what each hypothesis states about the population means and the corresponding mathematical notation for the mean difference score ().
Based on this scenario, decide whether the researcher should use a one-tailed or two-tailed alternative hypothesis for their dependent-samples -test. Justify your decision using the principles of hypothesis testing for difference scores.
An educational psychologist is testing whether a new study technique improves test scores. They calculate difference scores for each student by subtracting the pre-test score from the post-test score. State the null hypothesis for this dependent-samples -test using the appropriate mathematical notation for the population mean difference score.