Questions For Chapter 9's Food For Thought

Here Are The Questions For Chapter 9s Food For Thoughtwhat Is A Betw

Here are the questions for Chapter 9's food for thought: What is a between-subjects design? How does this differ from within-subjects? Define a two-independent sample t-test. What are the assumptions associated with a two-independent sample t-test? A researcher measures the time it takes 13 men and 15 women to complete multiple tasks in a study. She compares the mean difference between men and women using the two-independent-sample t test. What is the critical value for this test if she conducts a two-tailed test at a .05 level of significance? What is the denominator for computing an estimated Cohen's d for a two-independent-sample t test? If the difference between two means is 4, then what will the estimated Cohen's d value be with a pooled sample standard deviation of each of the following: (a) 4 (b) 8 (c) 16 (d) 40. How do you calculate the degrees of freedom for a two-independent sample t-test? What is the pooled sample variance? Pooled sample standard deviation? When an independent sample is selected, are the same or different participants observed in each group? Name three measures used to estimate effect size for the two-independent-sample t test. What are the three steps to compute an estimation formula? In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test. (a) A study measuring differences in attitudes about morality among men and women. (b) A study testing whether night-shift workers sleep the recommended 8 hours per day. (c) An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule. Will each of the following increase, decrease, or have no effect on the value of the test statistic for a two-independent-sample t test? (a) The total sample size is increased. (b) The level of significance is reduced from .05 to .01. (c) The pooled sample variance is doubled. When is the t-test for independent means appropriate to use? How should the t value be interpreted? How do we know what it means? For example, when t(28) = -0.16, p. n.s. - what does this mean?

Paper For Above instruction

Introduction

Understanding the nuances of statistical testing in research designs is essential for accurately interpreting experimental results. Two of the most common methods are the within-subjects and between-subjects designs. These approaches have distinct characteristics and applications, especially when paired with specific statistical tests such as the independent samples t-test. This paper explores these concepts, focusing particularly on the two-independent sample t-test, including its assumptions, calculation methods, effect size estimations, and appropriate applications.

Between-Subjects and Within-Subjects Designs

A between-subjects design involves comparing different groups of participants, where each participant is exposed to only one condition or treatment. For example, in a study comparing the performance of men and women, one group comprises men, and another comprises women. The primary advantage of this design is that it controls for potential contamination from multiple conditions within the same individual, reducing carry-over effects. However, it requires a larger number of participants to achieve adequate statistical power.

In contrast, a within-subjects design involves the same participants undergoing all conditions or treatments. This approach reduces variability caused by individual differences, increasing statistical power with fewer participants. However, it raises concerns about fatigue, learning effects, or order effects that could confound results. The choice between these designs hinges upon research goals, resource availability, and the nature of the variables involved.

The Two-Independent Sample t-Test

The two-independent sample t-test compares the means of two independent groups to determine whether there is a statistically significant difference between them. Its primary assumptions include independence of observations, normally distributed populations, and homogeneity of variances across groups.

To perform the test, the researcher calculates a t-value based on the difference between group means, divided by an estimated standard error derived from the pooled variance—an average of the variances within each group, weighted by their degrees of freedom. The critical value for the t-test depends on the degrees of freedom, which is computed based on sample sizes and variances.

Calculations and Effect Size Estimation

Given a scenario where a researcher compares the time taken by 13 men and 15 women, with a significance level of .05 for a two-tailed test, the critical value can be found from t-distribution tables or statistical software, typically around ±2.00 for this degree of freedom.

The denominator for Cohen's d — a standardized measure of effect size — is the pooled standard deviation, which accounts for variability within both groups. If the mean difference is 4, Cohen's d can be computed by dividing this difference by the pooled standard deviation.

For different pooled standard deviations, the estimated Cohen's d values are as follows:

• (a) 4: d = 4/4 = 1.0
• (b) 8: d = 4/8 = 0.5
• (c) 16: d = 4/16 = 0.25
• (d) 40: d = 4/40 = 0.1

Degrees of Freedom and Variance

The degrees of freedom for a two-independent sample t-test are typically calculated as the sum of the degrees of freedom from both groups: (n1 - 1) + (n2 - 1). Alternatively, when variances are unequal, the Welch correction adjusts the degrees of freedom accordingly.

The pooled sample variance is a weighted average of the variances from both groups, allowing for a single estimate of variability used in the t-test calculation. The pooled standard deviation is simply the square root of the pooled variance.

Participant Selection and Effect Size Measures

When selecting an independent sample, different participants are observed in each group, ensuring independence of observations, which is a critical assumption for the t-test.

Effect size measures for the two-independent sample t-test include Cohen's d, Hedges' g, and eta-squared (η2), which quantify the magnitude of differences irrespective of sample size. Calculating these involves the mean difference and pooled standard deviation or variance.

Application of T-Tests in Studies

Depending on the research question, either a one-sample or a two-independent sample t-test is appropriate. For example:

• Comparing attitudes about morality among men and women: Two-independent t-test.
• Testing whether night-shift workers sleep 8 hours: One-sample t-test.
• Differences in brain activity among rats on different reward schedules: Two-independent t-test.

Factors Influencing Test Statistic Values

Increasing the total sample size generally increases the test statistic value, enhancing the likelihood of detecting a true effect. Conversely, decreasing significance levels reduces the critical value needed for significance, potentially decreasing the test statistic’s significance. Doubling pooled variance increases standard error, which usually decreases the t-value, making it harder to find significant results.

Appropriateness of the Independent Means t-Test

The t-test for independent means is appropriate when the experimental design involves two independent groups, and the assumptions of independence, normality, and equal variances are met. The t value is interpreted by comparing it to critical values from the t-distribution; a larger absolute value indicates a greater likelihood of a significant difference.

For example, when t(28) = -0.16, p > 0.05 (not significant), it means the observed difference is very small relative to variability, and the null hypothesis of no difference cannot be rejected.

Conclusion

Choosing the correct statistical test and understanding how to interpret its results are vital components of rigorous research. The two-independent sample t-test is a versatile tool for comparing means between two groups, relying on assumptions that must be verified. Effect size measures provide additional context about the practical significance of findings. Proper application and interpretation ensure valid conclusions and contribute meaningfully to scientific knowledge.

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