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Example of an Independent-Samples t-Test
To illustrate an independent-samples -test, consider a study comparing the calorie estimates of two distinct groups: frequent junk food eaters () and rare junk food eaters (). The researcher calculates the sample means and standard deviations for both groups. For the frequent eaters, the mean () is with a standard deviation () of . For the rare eaters, and . Using the independent-samples -test formula, the computed score is . The degrees of freedom () for this combined sample of participants are (). For a two-tailed test with an alpha level of , the critical value is . Because the computed score () is more extreme than the positive critical value (), the researcher rejects the null hypothesis. This indicates that the corresponding -value () is less than , providing sufficient statistical evidence to conclude that individuals who regularly eat junk food significantly underestimate calories compared to those who rarely eat it.
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Research Methods in Psychology - 4th American Edition @ KPU
Related
Degrees of Freedom (Independent-Samples t-Test)
Multiple Comparisons
Null and Alternative Hypotheses for the Independent-Samples t-Test
Formula for the Independent-Samples t-Test
Example of an Independent-Samples t-Test
What is the primary purpose of conducting an independent-samples t-test?
Arrange the steps in the correct logical sequence for conducting a statistical analysis to compare the average scores of two distinct groups of participants.
A researcher recruits 60 university students and randomly assigns 30 to a mindfulness training group and 30 to a no-training control group. After four weeks, she measures each participant's self-reported stress score (on a 0–100 scale). Because each participant appears in only one group, she plans to use an independent-samples t-test to determine whether the two groups differ in mean stress scores. Is this an appropriate choice of statistical test for this study?
Match each component of a research study to its specific analytical role when determining if there is a significant difference between two groups using an independent-samples -test.
You are designing a research study to evaluate whether a new 'peer-tutoring program' results in higher final exam scores than 'independent study'. Arrange the following steps in the correct logical sequence to construct a valid research protocol that appropriately utilizes an independent-samples -test to compare the two groups.
An independent-samples -test is used to determine if there is a significant difference between the means of three or more distinct groups.
A researcher wants to determine whether there is a statistically significant difference between the average scores of two completely separate groups of participants. Which of the following best explains why an independent-samples -test is the appropriate statistical procedure for this analysis?
A researcher uses an independent-samples -test to evaluate whether there is a significant difference between the means of two separate groups. If it is later discovered that the same individuals were actually measured in both groups, the researcher must judge the results of the analysis as _____ because the assumption of distinct samples was violated.
Match each research design component with the scenario that describes its application for an independent-samples -test.
A clinical psychologist wants to determine if a new therapy reduces depression. They assign one group of participants to receive the therapy and a separate, independent group to a waitlist control. To evaluate whether the difference between the mean depression scores of these two distinct groups is statistically significant, they must conduct an _____ -test.
Define the independent-samples -test, state its primary statistical goal, and identify the two types of research designs in which this analytical method is appropriate according to the provided text.
Explain why an independent-samples -test is appropriate for this scenario. In your response, classify the specific type of research design used here and explain how the groups fit the requirements of this statistical test.
A researcher wants to evaluate whether a new mindfulness training program reduces stress. They randomly assign one group of participants to receive the training and a separate group to a no-training control condition. Identify the specific experimental design used and name the statistical test that should be applied to compare the means of these two groups.
Learn After
In the junk food calorie estimation study, what is the computed score for the independent-samples -test comparing frequent and rare junk food eaters?
In the junk food calorie estimation study, the researcher chose a two-tailed test because prior theory clearly predicted that frequent junk food eaters would underestimate calories relative to rare eaters.
Match each statistical element from the junk food calorie estimation study to its role in the independent-samples -test decision-making process.
In the calorie estimation study, the researcher compares frequent junk food eaters () and rare junk food eaters (). Based on the rejection of the null hypothesis and these sample means, the researcher concludes that individuals who regularly eat junk food significantly _____ calories compared to those who rarely eat it.
Order the steps a researcher takes in this study to evaluate the hypothesis and conclude whether frequent junk food eaters estimate calories differently than rare eaters.
In the junk food calorie estimation study, what was the degrees of freedom () for the combined sample of participants?
Explain the statistical reasoning behind the decision to reject the null hypothesis in the junk food calorie estimation study. In your explanation, detail how the computed score compares to the critical value and how the -value relates to the alpha level.
Based on this scenario, write a brief, professional conclusion interpreting the statistical results. State whether the researcher should reject or fail to reject the null hypothesis, and explain what this means in terms of the calorie estimates of frequent vs. rare junk food eaters.
Explain how the degrees of freedom () were calculated in this independent-samples -test. Your explanation should link the final value to the sample sizes of the two groups.